TUBE (Transistor Utility for Blonde Emulation)€¦ · determining how to generalize these polynomials to the entire frequency spectrum. The main obstacle we faced was that the harmonics

TUBE

(Transistor Utility for Blonde Emulation) Second Semester Report

Spring Semester 2012

Full Report

By

Dave Anderson

Sean Byers

Prepared to partially fulfill the requirements for ECE402

Department of Electrical and Computer Engineering

Colorado State University

Fort Collins, Colorado 80523

Project Advisors: Dr. Mahmood Azimi-Sadjadi, Dr. Ali Pezeshki

Dave Anderson, Sean Byers Page ii

Abstract

The audio industry has a large and dedicated interest in analog processing rather than digital.

Analog electronics are more expensive and tend to be fragile and large. This is why a recent

trend is emerging towards the modeling of analog electronics digitally. Vacuum tube amplifiers,

in particular, have a very sought-after analog sound. Every vacuum-tube amplifier sounds very

different, based on how the tubes are biased, how many gain stages there are, etc. We chose,

then, an amplifier with a single gain stage and a single gain tube made by Fender starting in the

late 1940s called the Champ to digitally emulate.

We first recorded signals in a recording studio, using both live guitar and pre-recorded signals

pumped through a 1960 Fender Champ. From here we were able to determine the amount of

harmonic distortion occurring at different frequencies and amplitudes. The simplest way of

modeling harmonic distortion, we decided, is using polynomials. Much of the project was spent

determining how to generalize these polynomials to the entire frequency spectrum. The main

obstacle we faced was that the harmonics were out of phase with respect to one another, which a

polynomial cannot replicate.

We determined that phase shifts in harmonics are not audible in a mono signal. What a human

hears in terms of a mono signal is uniquely determined by the magnitude spectrum of the signal.

By eliminating phase, a new waveform was created that sounded identical and that a polynomial

could easily be fit to. The algorithm required filtering to match the frequency response of the

amp, as well as the polynomial, which was programmed in Simulink along with a GUI.

Reactions to the sound produced were generally positive.

Dave Anderson, Sean Byers Page iii

Table of Contents Abstract ........................................................................................................................................... ii

List of Figures ................................................................................................................................ iv

List of Tables .................................................................................................................................. v

Chapter I.......................................................................................................................................... 1

Introduction ................................................................................................................................. 1

Motivation ................................................................................................................................... 2

Chapter II ........................................................................................................................................ 3

Background ................................................................................................................................. 3

Current Technology .................................................................................................................... 3

Chapter III ....................................................................................................................................... 5

Research ...................................................................................................................................... 5

Chapter IV ....................................................................................................................................... 8

Data Collection and Analysis...................................................................................................... 8

Alternate Model Derivation methods based on polynomials .................................................... 18

Graphical User Interface (GUI) for Simulink ........................................................................... 26

Chapter V ...................................................................................................................................... 29

Conclusions and Future Work .................................................................................................. 29

References ..................................................................................................................................... 30

Bibliography ................................................................................................................................. 31

Appendix A: Abbreviations .......................................................................................................... 32

Appendix B: Budget ..................................................................................................................... 33

Appendix C: Letters ...................................................................................................................... 34

Letter 1: Sponsorship proposal to Agilent Technologies .......................................................... 34

Letter 2: Response from Agilent Technologies ........................................................................ 35

Letter 3: Thank you to Agilent Technologies ........................................................................... 36

Appendix D: GUI Code ................................................................................................................ 37

Acknowledgements ....................................................................................................................... 46

Dave Anderson, Sean Byers Page iv

List of Figures Figure 1 - Guitars and Tube Amplifier Tested ................................................................................ 2

Figure 2 - Fender Champ Amplifier Schematic .............................................................................. 4

Figure 4 - Passive One-Port WDF Elements [1] ............................................................................. 5

Figure 3 - Tube vs. Transistor Output Characteristics .................................................................... 5

Figure 5 - Filter Bank Schematic on the left, and on the right are Analog Nobs to Vary

Implemented Filter Banks ............................................................................................................... 6

Figure 6 - Hamming Window with Transform [4] ......................................................................... 7

Figure 7 - base signal waveform produced for recording ............................................................... 8

Figure 8 - Fender Champ response to base signal showing amplitude scaling of different

frequencies ...................................................................................................................................... 8

Figure 9 - Audacity plot of the spectra of F3 frequency from base signal ..................................... 9

Figure 10 - Audacity plots of the spectra of amplifiers' responses to F3 sine wave portion of base

signal ............................................................................................................................................. 10

Figure 11 - Audacity plots of waveforms from various amplifiers at 5 different frequencies

(amplitude vs. time) ...................................................................................................................... 11

Figure 12 - Clipped Sine waveform in Audacity .......................................................................... 12

Figure 13 - Fig. 6 signal spectra in audacity ................................................................................. 12

Figure 14 - Response of Behringer clean to high amplitude sine wave showing clipping and

ripple ............................................................................................................................................. 12

Figure 15- Behringer clean impulse response ............................................................................... 13

Figure 16- Behringer clean response to low amplitude square wave (bottom) and square wave

convoluted with Behringer clean impulse response (top) ............................................................. 13

Figure 17 - base signal spectrogram (DFT size 4096) .................................................................. 14

Figure 18 - Champ base signal response spectrogram (DFT size 4096) ...................................... 14

Figure 19 - Base signal and Champ DFTs at F3 frequency .......................................................... 15

Figure 20- F3 waveform and spectra for Champ and 3rd order "Champ modeling" polynomial 15

Figure 21- Champ (blue) vs. 5th order "Champ modeling" polynomial (red) using polyfit method

....................................................................................................................................................... 16

Figure 22- Champ waveform (blue) vs. 5th order Matlab Fourier series fit (red) ........................ 16

Figure 23- Comparison of waveforms and spectra at F3 frequency for base signal, Champ,

Behringer clean and final "Champ Modeling" simulation using a Fourier series/ polynomial. ... 17

Figure 24-Even(top) and odd(bottom) parts of Champ response to sine waves at F3 frequency. 18

Figure 25-Even(top) and odd(bottom) parts of Champ response to sine waves at C4 frequency. 19

Figure 26-proposed block diagram for real-time processing ........................................................ 19

Figure 27-proposed processing block diagram for frequency sub bands ..................................... 20

Figure 28-polynomial fit for Champ data between 0 and 1kHz ................................................... 20

Figure 29-Polynomial fir for Champ data between 6 and 7kHz ................................................... 21

Figure 30- Waveforms collected from the second Champ at 4 different frequencies .................. 22

Figure 31-spectrogram of Champ response to linear chirp, showing odd harmonics .................. 22

Dave Anderson, Sean Byers Page v

Figure 32-comparison of original signal and spectra with a signal derived from only the

magnitude portion of the spectra................................................................................................... 23

Figure 33- Input-Output relationships for the Champ at 2 different amplitudes, showing the

amplitude dependency of the fits .................................................................................................. 24

Figure 34 - original signal, signal with roll-off, filtered roll-off signal ........................................ 25

Figure 35 - final block diagram for real-time processing ............................................................. 25

Figure 36 - Graphical User Interface for Simulink Model ........................................................... 26

Figure 37 - Simulink Model Identifying key GUI Functions ....................................................... 27

Figure 38 - GUI Identifying key Simulink Functions ................................................................... 28

List of Tables Table 1 - Budget Balance after spring 2012 Semester .................................................................. 33

Table 2 - Anticipated Budget Required for the Full Year ............................................................ 35

Chapter I

Introduction Vacuum tubes contain three terminals which are a cathode, plate, and grid. The vacuum tube

was invented in early 1900s and was used for all of the amplification required in circuits. The

ability to amplify signals enabled electrical guitar players to play for very big crowds for

increased sound projection capabilities. Having analog amplification is an inherent advantage of

vacuum tubes over transistor amplifiers which are digital. One thing that is required for live

performances is relatively no lag time between the musicians playing a chord and everyone at the

venue being able to hear the amplified chord. Replicating the tube sound is difficult because of

its nonlinear and dynamic frequency properties discussed in later in Chapters 3 and 4.

Transistor amplifiers were invented in 1950s, and slowly became more prominent with improved

efficiency of producing silicon wafers and the MOS transistor in 1960. The advantages of

transistor amplifiers having an increased lifespan, reliability, size, and cost just to name a few,

enabled transistors to replace the vacuum tubes’ role by storm. While transistors became the

main amplifying component, they did not have the ability the vacuum tube amplifier had to

distort signals by creating the “classic” rich tone that everyone was familiar with for music.

Replicating the desired sound with transistor amplifiers is the focus of this paper.

There are three different types of amplifiers compared to produce a higher quality and cheaper

device. The Marshall MG15 amplifier represents a transistor amplifier, Behringer TM300

represents a tube modeler, and the Fender Champ amplifier represents the best tube amplifier

base sound. In order to test the amplifiers, the signals produced were recorded at a recording

studio to try to get the purest sound possible. This means ideally blocking out all noises besides

the output signal.

The three amplifiers were tested at Wilson Recording Studio with 24 bit/sample for high

resolution and 96 samples/kHz to avoid antialiasing that occurs with vacuum tube amplifiers.

Musical notes ranging from 174.71Hz to 1318.51Hz were used which correspond to F3, C4, G4,

D5, A5, and E6 on the guitar. Each frequency that was put through the amplifiers had their

amplitude varied from -125dB to 0dB. The amplifiers were also tested with live playing of five

different guitars with the output signals of the amplifiers being captured by a large diaphragm

condenser and Old Shure 545 microphones. The five guitars used consisted of the Epiphone

Dot, 57 Telecaster, 71 Single-Coil SG100, 84 Kubicki, and Zia Guitar.

Dave Anderson, Sean Byers Page 2

Figure 1 - Guitars and Tube Amplifier Tested

In Chapter 2, the background of the project will be discussed giving more details into the

amplifiers available and their effects. Chapter 3 will discuss our research and Chapter 4 will

discuss the team’s decisions.

Motivation Many studio professionals still enjoy the sound of vacuum tube amplifiers over transistor

amplifiers when they need to create the best sounding music. Even though transistors are

cheaper to manufacture, the vacuum tubes’ distortion produces a higher quality sound that is

worth the higher price resulting in continued use by some studio professionals. In order to

produce the same sound quality as a tube amplifier, transistor amplifiers require techniques to

deliberately change the output signal discussed in Chapter 3.

Current silicon transistor technology produces relatively inexpensive amplifiers compared to

tubes; creating a transistor circuit to replicate a tube sound is worth investigating as this paper

shows because of its ability to reduce the cost to produce identical functioning product. The

main question this paper investigates is how to implement this idea practically to produce a high

quality product.


Chapter II

Background Evaluating an output signal that passes through a system knowing the input will give insight of

how the system distorts a signal. The same idea was used on a vacuum tube when it produced a

signal. The signals produced from the tube amplifier are periodic and nonlinear. Since it is not a

linear signal the black box approach to take the input signal and output signal to define a filter

for all frequencies will not work. Nonlinear signals are signals that do not have outputs directly

proportional to their inputs. The main method for analyzing nonlinear signals is by using

waveshaping. Waveshaping can be done by using a lookup-table, filter bank, polynomials, and

Fourier Series. Using a lookup-table is the only method not utilized due to its infinite

possibilities for outputs.

Filter banks are used to implement different conditions to the input signal depending on the

frequency of the signal. The idea behind a filter bank is to account for the changing equations

depending on the input frequency that a vacuum tube inherently implements. With frequencies

between two filters there will be what is called a weighting of the filters depending on the

frequency to have one of the filters have a greater impact on the output signal’s characteristics.

Polynomials are similar to Fourier Series when the a sine input is plugged into the x(t)’s of

Fourier series differs because it says that for every periodic signal the Fourier Series is able to

represent the signal by a combination of sine and cosine inputs at different frequencies.

Current Technology Vacuum tube amplifiers like the Fender Champ amplifier are becoming very expensive as the

vacuum tubes required to replace the existing ones become increasingly difficult to obtain. The

schematic of the Fender Champ amplifier is shown in Figure 2. A transistor amplifier that

emulates a vacuum tube amplifier that is commercially available and is readily available is the

Peavey Vypyr which costs $100 and has terrible quality for its emulation. Transistor amplifiers

that emulate general tube amplifiers would be similar to the Behringer TM300 Tube Amp

Modeler. The problem with this product is that many if not all of its settings give poor quality

and even produces awful quality distortion when the amplification is increased. Specific tube

emulating amplifiers like the Boss FBM-1 costs around $300 which is relatively cheap for

recording studios, but still relatively expensive for your average person. This device emulates

the 59 Fender Bassman in specific.


Software tube emulators are good at producing the tube sound that is desired, but is designed to

work in studios where the device can have time to process the information. Whereas a live

performance would require the device to immediately process the signal to be synchronized with

the rest of the band. This is the main reason why this project is avoiding software emulation.

Figure 2 - Fender Champ Amplifier Schematic


Chapter III

Research

Triode vacuum tubes are similar to transistor amplifiers with their gate characteristics. The

difference that is apparent between them is the tube amplifier doesn’t have clean linear

characteristics with changes in the curves because of secondary emission from the tube itself.

This plays a key role when trying to emulate the tube amplifier because of this characteristic.

Wave Digital Filters (WDF) could be used to emulate tube amplifier sounds. The problem with

WDF is the modeling is meant for linear time invariant (LTI) circuits. There is a way of having

port resistances in the circuit to acquire the nonlinearities. This however takes a lot of

computation and is complicated meaning the processing would be slow and not plausible for our

goal to be able to use the device in live shows.

Figure 4 - Passive One-Port WDF Elements [1]

Figure 3 - Tube vs. Transistor Output Characteristics


Waveshaping is a method of developing and computing nonlinear waveforms. The most

straightforward theoretical method of waveshaping is by using a lookup-table to produce an

output given an input. The problem this method has is that creating a high-resolution lookup-

table would take a lot of memory and if that were not used a low resolution table would have an

audible difference to an actual tube amplifier that it would sound bad. Oversampling of a signal

is many times required due to the nonlinear characteristics of the signal there could be aliasing

that exceeds the Nyquist frequency.

Another way of computing a nonlinear waveform would be to break the desired output into

multiple sections for frequency to break it up into more of a linear system. This would enable

the bands to dominate for certain frequencies and overlap with frequencies in the middle to give

a better blended output signal rather than having an abrupt change at the boundaries of

frequencies. This idea is known as customized waveshaping or using filter banks to create the

different outputs for various frequencies. This means that each frequency band would have some

sort of polynomial approximation to emulate the tube amplifier sound at that frequency and as

the frequency changes the polynomial would have less effect on the circuit when getting closer

to another frequency band until the previous polynomial ideally plays no part in the output

signal.

To analyze the signals that were produced required knowing information regarding waveform

properties that was already discussed, types of windowing methods and spectra analysis. The

type of window can have an effect on what is shown over an interval. The Hamming window

was predominately used in the project because it is a raised cosine shown in Figure 6 helps

represent audio signals giving the system a less than 1% error in the system.

Figure 5 - Filter Bank Schematic on the left, and on the right are Analog Nobs to Vary Implemented Filter Banks


Figure 6 - Hamming Window with Transform [4]

Spectra analysis which is also shown in Figure 6 is important because the representation can give

the frequency domain’s characteristics. The characteristics involve the dominate frequency,

power, distortion, harmonics, bandwidth, and other spectral components that are not easily

detectable in the time domain waveforms. When using a hamming window along with the

frequency domain, the noise and dominate frequencies will be distinguishable with a high

enough amplitude.


Chapter IV

Data Collection and Analysis The actual signal processing and analysis work started as soon as we went to the recording

studio. We went to Wilson studios in Longmont, CO and did nearly 7 hours of recording,

accumulating 18:35 of recordings at 96 kHz and 24-bit resolution, making for 187 MB of data.

The recording studio served several purposes for us. First, it allowed us to get very high quality

digital recordings using high quality equipment, like cables and microphones. Secondly, it

allowed us to spend quite some time talking with Chuck Wilson, our producer, who has spent

many years in professional audio and could lend us some very good advice as to where to take

the project.

We came up with a very thorough recording scheme prior to the session, with Chuck's help. We

knew that we were going to evaluate several amplification methods: the Fender Champ, the

Marshall MG15, the Behringer TM300 on four different settings (bypass, clean, hi-gain, hot),

and every signal recorded directly without any amplification. In order to do the recordings

effectively, there needed to be some kind of a standard signal driven the same way through every

amplifier. Therefore, just having a guitar played through every one of them would not work, as it

would be different every time and there would be no sort of control. We decided to go with a

standard signal made in Matlab that would contain sine waves with a range of amplitudes and

frequencies as well as guitar notes corresponding to the same frequencies as the sine waves. The

periodic sequence of a guitar string vibrating is very different than a sine wave but it also very

predictable, meaning that both portions of the base signal turned out to be very important. The

base signal is shown below in its amplitude vs. time graphical interpretation in Audacity.

Figure 7 - base signal waveform produced for recording

The first half of the signal shows 6 signals increasing in amplitude. The first is a sine wave

corresponding to the musical note F3 at 174.61 Hz. It increases from an amplitude of 0 to an

amplitude of 1 (or 0 dB). The following five sine waves follow the same amplitude increase

pattern but are notes corresponding to C4 (261.63 Hz), G4 (392.00 Hz), D5 (587.33 Hz), A5

(880.00 Hz), and E6 (1318.51 Hz). The second half of the signal has the same 6 frequencies

played on guitar. The picture below shows the signal produced by the Champ in response to the

base signal, which obviously resembles the base.

Figure 8 - Fender Champ response to base signal showing amplitude scaling of different frequencies


We ended up doing several recordings for each amplifier, rather than just the standardized signal.

Since this is an audio application, the signal sounds are more important than whether it is

identical to what is recorded, we recorded with many different types of guitars in order to get a

very well rounded idea of what effect the amplifier was having. In addition to the standard

signal, we recorded with an Epiphone Dot guitar, a 1984 Kubicki guitar that had active pre-

amplified pickups, a 1971 Gibson SG with Single coil pickups, a Zia guitar with humbucking

pickups, and a 1957 Fender Telecaster. The Telecaster was particularly interesting for two

reasons. For one, it was the guitar that the Fender Champ amp was originally designed to

amplify, meaning that the signal distortion we get from the Telecaster would be the one worth

the most attention. Secondly, this particular guitar was used by the Saturday Night Live band for

a few years. When the guitars were played, a standard playing scheme was used that included

chords, single notes, and chopping, which is essentially playing notes and not letting them ring

out. Overall, we really feel that we got quite a wide range of recordings done which accurately

represent the way that all of the amplifiers are distorting the signals.

The first analysis done in finding what made the tube amplifier sound so much better than the

transistor amp and the modeling pedal was to look at the spectra of the signals collected at the

studio. We knew that the spectra of each signal should contain the base frequency, but that it

would certainly contain something different and that this is what probably gave the amplifier its

characteristic sound.

The spectra was first analyzed in Audacity, a free audio analysis program. This was initially used

rather than Matlab due to the ease of use of the program and the fact that it is able to graph the

spectra in a way tailored to audio, so that only the range of human hearing is on the graph and

that peaks actually have their corresponding musical notes written out. The program allows the

user to graphically select a section of data and compute the FFT of it. For the first set of graphs,

we did not necessarily choose any part of the signals, just made sure to get only the parts that had

a constant amplitude change. An example of the spectra plotted from a chosen part of a signal is

shown below as well as the spectra produced by Audacity.

Figure 9 - Audacity plot of the spectra of F3 frequency from base signal


The gray area selected of the signal is the part which Audacity computes the spectra. We can see

that the spectra is what we expect: A single peak at 174 Hz with some side frequencies caused by

the windowing of the function. In this case, it can be seen on the spectra window that a Hann

window was used. This process was repeated for all of the frequencies and all amplifiers. It

would take far too much space to show all of the spectra here, so to save space only the spectra

for the F3 note similar to that above will be shown.

Figure 10 - Audacity plots of the spectra of amplifiers' responses to F3 sine wave portion of base signal

There are obvious differences in the spectra. The lower frequency spike in the two amplifiers is

due to AC power at 60 Hz, and is not present in the Behringer since it was powered by a battery.

However, it is very clear that all the amplifiers produce a large number of harmonics with


varying amplitudes. This was not easy to mathematically analyze in Audacity so in the future we

used Matlab for spectra.

The additional focus was on the waveforms of the various signals. What was very interesting was

that all of the waveforms turned out to be very different. The waveforms are shown below for the

F3 frequency.

Base signal

Fender Champ

Marshall MG15

Behringer – bypass

Behringer – clean

Behringer – hi-gain

Behringer - hot

Figure 11 - Audacity plots of waveforms from various amplifiers at 5 different frequencies (amplitude vs. time)


The signal distortion analysis always had to do with transforming the base waveforms into

whatever was created by the amplifier, and there are many different ways to have this occur. The

first investigations had to do with the Behringer pedal, from which it was obvious that there was

clipping happening. A program was written in Matlab that would clip the base signal. This signal

and its spectra are shown in the graphs below.

It is very reasonable that clipping will create harmonics, which matches the harmonics from the

Behringer pedal, at least for the first four above the base frequency. The waveforms from the

clipping program do not really match the Behringer waveforms, though. From here, it was

assumed that the Behringer had clipping mixed with an impulse response, which is why it shows

a slight ripple before flattening out, as shown in the figure below.

To test this assumption, we tested the response of the Behringer pedal to

impulses and to single amplitude sine waves and single amplitude square

waves. The amplitudes of these waves had to be scaled down until there was

no clipping happening. The impulse response of the Behringer is shown

below.

Figure 12 - Clipped Sine waveform in

Audacity

Figure 13 - Fig. 6 signal spectra in audacity

Figure 14 - Response

of Behringer clean to

high amplitude sine

wave showing

clipping and ripple


The graph above shows the convolution of the Behringer's impulse response with the same

square wave that was driven through the Behringer, as well as the Behringer's response to it.

The two waveforms are so close to each other that we feel as though the Behringer's method has

been successfully determined as a mixture of clipping and an impulse response, to give a mix of

harmonics and waveshaping. However, after quite a bit of waveform and spectral analysis, we

began to think that the Behringer pedal was not really coming close to the actual Champ.

Therefore rather than using the Behringer's distortion methods as a building block for the

Champ, we attempted to show that our methods could come closer to the actual Champ than the

Behringer. The spectrograms of the Champ versus the base signal turned out to be very

informative. The spectrograms of the base signal and the Champ's base signal response are

shown below.

Figure 15- Behringer clean impulse response

Figure 16- Behringer clean response to low amplitude square wave (bottom) and square wave convoluted with Behringer clean

impulse response (top)


Figure 17 - base signal spectrogram (DFT size 4096)

Figure 18 - Champ base signal response spectrogram (DFT size 4096)

Though it was difficult to obtain any real quantitative data from a spectrogram graph, it was very

apparent that the Champ was adding harmonics to the sine wave portion of the signal. These

harmonics were also determined to be integer multiples of the original frequency, which is what

a polynomial would do to a sine wave. When a sine wave is plugged in to a third order

polynomial, we derived that the output signal would be equal to either

A(sin(x))+B(sin2(x))+C(sin

3(x)) or (A + 3C/4)sin(x) + (B/2)sin(2x) + (C/4)sin(3x). By using the

magnitudes of these harmonics in the spectra as the coefficients of the equation with the

multiples of x, we could solve for the coefficients in the polynomial equation. The DFT that was

used to calculate the first polynomial is shown below.


Figure 19 - Base signal and Champ DFTs at F3 frequency

By using the peaks' intensities relative to each other of base = 1, first harmonic = 0.171, second

harmonic = 0.116, we came up with the coefficients for the polynomial of A = 0.826, B = 0.342

and C = 0.232. The F3 sine wave can be plugged into this polynomial to obtain the waveforms

and spectra shown in the graphs below.

Figure 20- F3 waveform and spectra for Champ and 3rd order "Champ modeling"

polynomial


It is very promising that the polynomial was able to so well approximate the first two harmonics

above the base frequency. This meant that a polynomial was certainly a step in the right

direction, since it could be quantitatively adjusted and fit to both the spectra and/or the

waveform. The next experiment was to use the Matlab polyfit function to match the input sine

waves used in the studio to the Champ waveforms using a least squares fit. The waveform match

up of the 5th order polynomial against the actual Champ signal is shown below.

It is clear that the polynomial can match the main waveform of the Champ, but there is a slight

hump before the main peak of the polynomial which cannot be matched, even with a high order

polynomial. Fortunately, Matlab also provides a curve fitting tool that can fit data with a Fourier

series. The 5th order Fourier series fit to the same section of data is shown below.

This 5th order Fourier series fit to the data is better at first glance because it is able to simulate

the hump that occurs before the main peak, and if it is at the same order as the original

Figure 21- Champ (blue) vs. 5th order "Champ modeling" polynomial (red) using polyfit

method

Figure 22- Champ waveform (blue) vs. 5th order Matlab Fourier series fit (red)


polynomial it can have the same spectra. As a preliminary derivation, the difference between the

polynomial fit and the Champ waveform is found. The original sine wave is then filtered using a

digital derivative filter to create a cosine wave. Another Polynomial fit is done to find the best fit

between the remaining signal (the difference between the Champ waveform and the first

polynomial) and the cosine wave. In this way, a Fourier series fit for the original amplitude

varying signal was determined. We were able to obtain results that fit both the waveform and

spectra of the F3 frequency very closely, as shown below.

The actual polynomial derived by our program is an , where

The simulation shows both an improvement over the Behringer waveform and spectra when

compared with the actual Champ amplifier. Our original goal for the semester was to create an

algorithm that would model the champ with better results than the Behringer pedal and we can

say with confidence that we were successful in reaching this objective.

Figure 23- Comparison of waveforms and spectra at F3 frequency for base signal, Champ, Behringer clean and final "Champ

Modeling" simulation using a Fourier series/ polynomial.


Alternate Model Derivation methods based on polynomials

The polynomial above worked fairly well for a post-processing algorithm, meaning that all the

information in the signal was already available. There are several different ways in which to

implement the pair of polynomials in real time. The first is using the original signal for one

polynomial and the derivative of the original signal for the second polynomial. This didn’t seem

to work as the derivative function would need to be optimized for a particular bandwidth to avoid

its amplitude exploding beyond our control, and we had not yet found an appropriate bandwidth.

The more obvious choice was to base one of the polynomials on the original signal and one on a

phase shifted version of the original signal.

There were several ways that these polynomials could be derived. The first was using a constant

90 degree phase shift in between the two input signals. The signals can be separated into even

and odd parts using the formulas below and a polynomial can be fit from a sine wave to the odd

part and a cosine wave to the even part

.

It is apparent, though, that the even and odd portions of the Champ’s waveforms vary

significantly with both amplitude and frequency. The graphs below show the even and odd

portions of the F3 and C4 note Champ outputs.

Figure 24-Even(top) and odd(bottom) parts of Champ response to sine waves at F3 frequency.


Figure 25-Even(top) and odd(bottom) parts of Champ response to sine waves at C4 frequency.

These notes are only ~87 Hz away from each other and already differences in the

waveforms are apparent.

Based on the previous data, we decided to try a subbanding approach, where the signal

would be split up into frequency components with different polynomials. The data that was

obtained from the recording studio was not conducive to this sort of approach, since it stopped at

1318 Hz. Luckily, however, there was a lot of guitar data that had a full audio spectrum

bandwidth and this could be broken down into frequency components.

The next question to address was how coarse to make the subbands. Obviously, the waveforms

would be slightly different at every frequency along the spectrum, so any degree of coarseness

would be an approximation to the real distortion. One idea was that the Champ seemed to cut off

all frequencies above 12 kHz, and above 8 kHz there didn’t seem to be much harmonic

distortion. So breaking the range of 0-8kHz into 1kHz bands would give 8 fairly coarse bands.

The only way we had of fitting something to this data was to fit the guitar input to the guitar

output at these different bands.

It also became apparent that as it became difficult to break “random” signals like guitar into

consistent even and odd parts, more phase shifts would be necessary to better approximate the

waveforms.

The processing now broke into the following structure:

Figure 26-proposed block diagram for real-time processing


Each “processing” block was a simplified version of this structure below.

Figure 27-proposed processing block diagram for frequency sub bands

The processing was now getting fairly complicated, at perhaps 8 subbands and 8 phase shifts,

with 5th

order polynomials. A few of the subband fits are shown in the graphs below.

Figure 28-polynomial fit for Champ data between 0 and 1kHz


Figure 29-Polynomial fir for Champ data between 6 and 7kHz

The band from 0 to 1kHz actually has a fairly decent fit. The 6-7kHz fit is not very good at all.

This was the general trend of the fits: as the frequency increased the fit became less and less

accurate. By increasing the order of the polynomials we were able to get a slightly better fit. The

problem was that the coefficients started to become very large, which produced problems

generalizing to other amplitudes than the ones they were derived for.

At this time we were given access to another Champ amplifier by a friend, Steven Sandler. In

addition to more data collection across a wider frequency range, we wanted to test whether or not

the uneven wave shapes were due to acoustic reflections rather than the amp itself. Rather than

single frequencies for a period of time, chirps were used from 0-5kHz. Rather than recording the

amp with a microphone, a sampler was plugged directly in to the amp’s “line out” jack. Below

are selected waveforms from across the spectrum and a spectrogram showing the linear chirp as

well as its harmonics.


Figure 30- Waveforms collected from the second Champ at 4 different frequencies

Figure 31-spectrogram of Champ response to linear chirp, showing odd harmonics

Interestingly, the answer seems to be that the wave shapes are still uneven, but that there are no

even harmonics present in the new data. The even harmonics are likely caused by acoustic

reflections. Therefore, our polynomial should only have odd powers. However, this did not help

us to match polynomials to the wave shapes, so a new method had to be determined.

We began to look now at the frequency spectrum rather than the waveforms. Doing some

research and experimentation, we decided that the phase information present in the data did not

affect the sound. Humans do hear phase information, but only in stereo signals. This information

is used to determine the location of the source of the sound. Since a guitar amp is a mono signal,

the phase information does not matter to the sound.

A new signal can be created by using the following equation:


This new signal has a different waveform than the original, but an equivalent frequency

magnitude spectrum and, as determined experimentally, an identical sound. The graph below

shows this happen.

Figure 32-comparison of original signal and spectra with a signal derived from only the magnitude portion of the spectra

The new signal is 1-1, which eliminates the need for phase shifts. A single polynomial can be

shown to accurately describe the relationship from input to output. These new waveforms were

also fairly frequency-independent. Not completely, of course, but using a single waveform was a

decent approximation to the entire spectrum.

A new problem arose, however, which was that the waveforms were very amplitude dependent.

There was no single curve fit that could describe the distortion occurring at amplitude 0.5 and

1.0, as shown in the graph below.


Figure 33- Input-Output relationships for the Champ at 2 different amplitudes, showing the amplitude dependency of the

fits

This anomaly occurs because the waveform that matches the sound of the original has a roll off

(saturation) on one side and a sharp peak on the other. Every waveform requiring a sharp peak

will need its own polynomial, which occurs at all amplitudes.

The work now involved coming up with some sort of dynamic range detection to tailor fit the

polynomial to the input amplitude. This was very effective in a post-processing algorithm but

Simulink was not able to process the information in real-time, so another solution had to be

found.

Taking inspiration from amplifier output stages, I purposely clipped the signal to force a

maximum amplitude and low-pass filtered what I got afterwards. The graphs below show this

transformation.


Figure 34 - original signal, signal with roll-off, filtered roll-off signal

In this fashion the number of polynomials needed can be reduced. In fact, one polynomial now

fairly accurately approximates the distortion in the original signals.

The final block diagram for the Champ approximation is shown below.

Figure 35 - final block diagram for real-time processing

A problem we encountered with the processing is that there was a significant delay between what

was played and what came out of our algorithm. This was either due to the time it took to process

the information or due to the way Matlab interacted with the computer to obtain audio data. The

amount of delay between input and output that is audible and will affect instrumentation is

around 100ms [5]. Our FIR filters had a maximum of 1ms delay processing due to the inherent

delay in FIR filtering. We knew that this was not the cause of our delay. The decision was made

at this point to move away from modeling in Matlab and into the Max audio software from

Cycling ’74, a real-time audio algorithm development environment.


Graphical User Interface (GUI) for Simulink A problem that we encountered with creating a software representation of a physical amplifier

was a way to change its settings as if it were built into hardware. A way to do this is to create

what is called a graphical user interface (GUI). With a GUI the user can change explicit settings

to get a desired output. This also gives the user a quick and easy to understand way to

manipulate a complicated program. With this goal in mind, we created a GUI that had main

features that a hardware device would include.

Since we were using Matlab’s Simulink, we had to create a GUI that would interface with it.

The best thing to do was to create a Matlab GUI since it has built in methods to enable the

function of GUIs. In order to create a GUI a basic layout of the interface has to be created which

can be seen below in Figure 36. This shows how a GUI is mapped out for the user to see.

Figure 36 - Graphical User Interface for Simulink Model

With this interface mapped out for the user’s benefit, it is still nothing more than a picture.

While the picture may seem basic, it is intended for exactly that reason. People don’t like it

when the device they are trying to control is hard to understand. That is why things like sliders,

pushbuttons, and checkboxes are distinct. Basic interfaces are a required design when dealing

with the public. While this sounds condescending, it is not because it is meant as a basic

functioning program. Programs that have higher levels of complexity require complex designs,

but with our design, we want the public to be able to take one look at the interface and

understand its functions.


In order to give the picture in Figure 36 usability, we have to create parameters for the user to be

able to interface with it. We need to enable the “picture” to do different actions depending on

what the user manipulates with the keyboard or mouse and in what position they’re located. This

means that the program has to understand different parameters based on the keyboard or mouse

from the user. This does not mean you have to account for the different types of keyboards and

mice used, but instead their location and what is being typed.

The text that is mapped throughout the GUI has no function besides letting the user know what

the function is near its location. The boxes on the right-hand side of the GUI are meant to be

pushbuttons that a user can click to enable. The “Start Simulation” button will change to “Stop

Simulation” after it is clicked to let the user know that it is now running the simulation. Also,

the sliders on the GUI are meant to update the boxes below them labeled with “##” depending on

their value. The value in those boxes also has to change the slider functions to that correct

position depending on the number typed in.

Creating the simulation of the buttons would be a pain to create from scratch, because the person

creating the GUI would have to take into account that when someone clicks a button it should

look like it is being pushed in when clicked. Otherwise, the user wouldn’t know if the

pushbutton was pushed and would likely click it again. This is a problem because if the function

of the pushbutton was complex it could easily be called again and crash the program if it was

required to do a lot. Luckily, Matlab has built in functions for how the sliders, pushbuttons, and

checkboxes function so they do not have to manually be programmed.

Along with the interface being able to change itself depending on what is executed, it has to be

able to manipulate the actual Simulink model that was created. In order to do this, code was

written to change different “Gain” blocks in Simulink to achieve treble, bass, volume, gain, and

bypass/champ configuration. The main idea is shown in Figure 37 and Figure 38, which show

with colored boxes what is occurring in the model and the GUI respectively.

Figure 37 - Simulink Model Identifying key GUI Functions


Figure 38 - GUI Identifying key Simulink Functions

The treble and bass sliders were implemented by taking the signal that was inputted from the

guitar and split into two different sub-bands depending on their frequency. The frequency

overlapping occurred at 1500Hz, because even though the frequencies go up to around 12kHz,

the bass is considered to be lower frequencies than just the half-way point of 6kHz. When the

two signals are split up, if the original sound without any changes is desired, the treble and bass

will both be set to one. If a different output is desired they can be changed with a range of zero

to one.

The gain is the amount the signal is amplified after it is inputted, and the volume is gain of the

signal right before it is outputted to the speakers. This difference is important, because the gain

allows the signal to be amplified very high, and get a high distortion while the volume simply

changes how soft or loud it is played. The volume can change from zero to ten and the gain can

change from zero to one hundred.

The “Champ Configuration” checkbox allows the user to play the sound that is produced from

the guitar and directly output it to the speaker, or have our model manipulate the guitar signal

and be able to change amplification, treble, and bass. This is done by simultaneously changing

two blocks (one from on to off and the other from off to on), this way the signal can only travel

through one path like a switch.

The coding for the GUI is shown in Appendix D.


Chapter V

Conclusions and Future Work We are very satisfied with the results but there is undoubtedly more work that can be done on the

data. There is no simple way to recreate the signals we saw from the Champ amplifier, because it

is a nonlinear system that phase shifts its harmonics in a frequency-varying way. This means that

there are many different generalizations that can be made for the data and various optimization

techniques. What the ultimate goal of a project such as this is, though, is whether or not the

model sounds good.

As soon as the model fully works in real time, it would be fairly interesting to optimize it further,

perhaps using a sub band variation of the final model we derived and conduct a blind study with

a group of listeners and a real Champ amplifier. We are very confident that the sound can be

accurately represented using a variation of our model, but it is not clear which variation will

sound the best to a human ear.

The group learned quite a bit from this project, both analog and digital. We learned signal

analysis methods that enabled us to separate useful information from a sea of static and also how

amplifiers are created and what components create the “analog” sound. This project was a unique

and educational opportunity to combine passions with academics, and it has inspired us to

continue investigations in audio.


References [1] J. Pakarinen and M. Karjalainen, "Enhanced Wave Digital Triode Model for Real-Time Tube

Amplifier Emulation," Dept. of Signal Processing and Acoustics, Helsinki University of

Technology, Helsinki, Finland, Digital Object Identifier 10.1109/TASL.2009.2033306, Apr.

2010.

[2] J. Pakarinen and D. T. Yeh, "A Review of Digital Techniques for Modeling Vacuum-Tube

Guitar Amplifiers," Dept. of Signal Processing and Acoustics, Helsinki University of

Technology, Helsinki, Finland, Center for Computer Research in Music and Acoustics, Stanford

University, Palo Alto, CA, Computer Music Journal, 33:2, pp. 85–100, Summer 2009.

[3] J. Pakarinen and M. Karjalainen, "WAVE DIGITAL SIMULATION OF A VACUUM-

TUBE AMPLIFIER," Dept. of Signal Processing and Acoustics, Helsinki University of

Technology, Helsinki, Finland, Rep. 142440469X, 2006.

[4] J. Smith, “Spectral Audio Signal Processing,” Center for Computer Research in Music and

Acoustics, Stanford University, Dec. 2011

[5] S. Cheshire, “Latency and the Quest for Interactivity,” Dept. of Computer Science, Stanford

University, Nov. 1996.


Bibliography [1] U. Zolzer, Digital Audio Signal Processing, Hamburg, Germany: Wiley, 2008.


Appendix A: Abbreviations DFT: Discrete Fourier Transform

FFT: Fast Fourier Transform

FIR: Finite Impulse Response

WDF: Wave Digital Filter


Appendix B: Budget Event Money Spent/Received Budget Balance Beginning of Semester $300 $300 Donation from Agilent $100 $400 Behringer TM300 pedal ($26) $374 LCD Panel ($4) $370 Studio Time ($200) $170 Roland Duo-Capture ($90) $80 Extension Cable ($15) $65 Surge Protector ($7) $58 Impedance Matching Transformer ($15) $43

Table 1 - Budget Balance after spring 2012 Semester

In total, $357 of $400 was spent on the project.


Appendix C: Letters

Letter 1: Sponsorship proposal to Agilent Technologies DSP for Audio Signals:

A digital modeling system for a wide variety of tube amp sounds.

October 15, 2011

Dan Ferguson

Agilent Corporation

Dear Mr. Ferguson,

I want to thank you in advance for considering sponsorship of student-originated Senior Design

projects at Colorado State University. It takes a lot of work and motivation to design a project

and learn to be your own boss, all the way from concept to implementation. We would like to

introduce our project idea and team members to you before beginning to discuss our proposed

budget.

Our project concept is the creation of a digital modeling system for old tube guitar amps. Ask

any guitar aficionado: tube amps have cleaner sound and warmer tone than solid-state amps.

Unfortunately, many of the original tone machines are either too expensive or too rare to make

them of much use to anyone who wants to play them live. Software and Hardware

implementations of modeling systems like this are common but most of them are very limited in

their use. Every tube amp sounds different, and so every modeling algorithm will produce a

different sound. Our idea is to work with recording studios to record an old tube amp, the Fender

Champ, that has never had a specific model made for it. We will also look at some algorithms

already in place in commercial hardware, in order to find general differences between those and

a real tube amp. Using these comparisons, we will create hardware that will simulate a wide

variety of tube sounds and have use in both an analog (eg. Live blues concert) and digital (eg.

Sampling software) worlds.

Our team includes Dave Anderson, Sean Byers, and professor Mahmood Azimi. Dave is an

electrical engineering student with a strong interest in computer programming, signal processing

and, above all, music. Sean Byers is also an electrical engineering student with an interest in

analog electronics. Professor Azimi works with signal processing at CSU.


Type of expense Hourly Cost # of hours Total Cost

Studio Time $50 12-15 $600-750

Behringer TM300 pedal N/A N/A $26

Hardware Design and

Components

N/A N/A $400

Total Cost $1026-$1176

Money Raised so far $400

Money required $626-776

Table 2 - Anticipated Budget Required for the Full Year

We would like to request a $500 sponsorship from Agilent for the full academic year. We would

love to see our project fully realized, and with primarily student funding this just is not possible.

If you choose to sponsor our team and project, we thank you very much in advance for such an

exciting opportunity.

Letter 2: Response from Agilent Technologies Hi Dave, Thank you for submitting your proposal. After reviewing all the project submissions,

I’ve decided to award $100 to your team from Agilent Technologies. I will work with Olivera to

get those funds transferred to your project team, and we’ll keep you informed of that process. I

would also like to give some feedback to you and your project mates regarding the proposal:·

First of all, I enjoy any project that combines your engineering studies with personal

interests/passions. Your project seems to be a great example of that – modern implementation of

old school guitar amplifiers! Very interesting…· I know the time frame to create your

proposal was short, and I understand that creating a 1-2 page proposal is also tough. Having said

this, though, I have these comments: I’d like to see more about timelines and milestones for

your project. I have a high-level understanding, but would like to have seen a project schedule

that shows how you’ll converge towards your desired final outcome. With all the tools available

these days for creating documents, I’d like to have seen a more “visually attractive” proposal –

one that made use of color, or diagrams, or pictures, etc., to help convey the information. You

did include a table for your budget – that was important. But I’d like to have had more

information about the actual project, conveyed in an engaging format. You introduce your team,

which is important. I’d like to have known more about the specific roles of each member – what

subsystems each was involved with, what each person was accountable for, etc. This could have

been easily incorporated in a project milestone table, for example. In particular, I’d like to have

understood more about the actual “comparative study” you mention – a study to compare the

recorded sounds of the actual Fender Champ to the fabricated sounds of the algorithmic

implementation. That would seem to be very intensive – so many sounds to compare, so many


combinations of sounds, etc. This seems to be a key element in your project, so would like to

have seen a little bit more information about that stage. Again, thanks for submitting your project

for funding. It seems a very interesting project, and I’ll look forward to hearing more about it as

you approach E-Days. Also, note that Agilent will have another funding round offered in the

Spring – it will be a bit more formal, but there will be another chance for you and your team to

apply for additional funding. Stay tuned… Dan Ferguson

Electronics Manufacturing Test

Americas Service & Support Manager

Agilent Technologies

(970) 679-3641

[email protected]

Letter 3: Thank you to Agilent Technologies Hi Dan,

Thank you very much for the award! We really appreciate not only the money but the

recognition of our project and of our hard work.

We would also like to thank you for the feedback on our proposal. We will undoubtedly be

writing more of these as the year goes on and it really helps us.

Thank you again. If you have any questions about the project or us please do not hesitate to let us

know. We will be sure to acknowledge this contribution on our website and in our

documentation.

Dave Anderson and Sean Byers


Appendix D: GUI Code function varargout = ChampGUI(varargin)

% CHAMPGUI MATLAB code for ChampGUI.fig

% CHAMPGUI, by itself, creates a new CHAMPGUI or raises the existing

% singleton*.

%

% H = CHAMPGUI returns the handle to a new CHAMPGUI or the handle to

% the existing singleton*.

%

% CHAMPGUI('CALLBACK',hObject,eventData,handles,...) calls the local

% function named CALLBACK in CHAMPGUI.M with the given input arguments.

%

% CHAMPGUI('Property','Value',...) creates a new CHAMPGUI or raises the

% existing singleton*. Starting from the left, property value pairs are

% applied to the GUI before ChampGUI_OpeningFcn gets called. An

% unrecognized property name or invalid value makes property application

% stop. All inputs are passed to ChampGUI_OpeningFcn via varargin.

%

% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one

% instance to run (singleton)".

%

% See also: GUIDE, GUIDATA, GUIHANDLES

% Edit the above text to modify the response to help ChampGUI

% Last Modified by GUIDE v2.5 09-Apr-2012 21:23:35

% Begin initialization code - DO NOT EDIT

gui_Singleton = 1;

gui_State = struct('gui_Name', mfilename, ...

'gui_Singleton', gui_Singleton, ...

'gui_OpeningFcn', @ChampGUI_OpeningFcn, ...

'gui_OutputFcn', @ChampGUI_OutputFcn, ...

'gui_LayoutFcn', [] , ...

'gui_Callback', []);

if nargin && ischar(varargin{1})

gui_State.gui_Callback = str2func(varargin{1});

end

if nargout

[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});

else

gui_mainfcn(gui_State, varargin{:});

end

% End initialization code - DO NOT EDIT

% --- Executes just before ChampGUI is made visible.

function ChampGUI_OpeningFcn(hObject, eventdata, handles, varargin)

% This function has no output args, see OutputFcn.

% hObject handle to figure

% eventdata reserved - to be defined in a future version of MATLAB

% handles structure with handles and user data (see GUIDATA)

% varargin command line arguments to ChampGUI (see VARARGIN)


% Choose default command line output for ChampGUI

handles.output = hObject;

% Update handles structure

guidata(hObject, handles);

% UIWAIT makes ChampGUI wait for user response (see UIRESUME)

% uiwait(handles.TUBEEditor);

% Get the value of the treble edit box and synch the GUI

value = get_param([bdroot '/Gain1'],'Gain');

set(handles.eTreble,'String',value);

% Set the treble slider and synch the GUI

NewValue = str2double(value);

set(handles.sTreble,'Value',NewValue);

% Get the value of the bass edit box and synch the GUI


set(handles.eBass,'String',value);

% Set the bass slider and synch the GUI


set(handles.sBass,'Value',NewValue);

% Get the value of the volume edit box and synch the GUI


set(handles.eVolume,'String',value);

% Set the volume slider and synch the GUI


set(handles.sVolume,'Value',NewValue);

% Get the value of the gain edit box and synch the GUI

value = get_param([bdroot '/Gain'],'Gain');

set(handles.eGain,'String',value);

% Set the gain slider and synch the GUI


set(handles.sGain,'Value',NewValue);

% Get the value of the gain to determine bypass status with GUI

set(handles.cbChamp,'Value',0);

set_param([bdroot '/Gain6'],'Gain',num2str(0));


% Assign gui, startstop, switch, and gain handles to the base workspace

assignin('base','testbench_handles',handles)

assignin('base','startstopBypass_hObject',handles.pbStart)

assignin('base','editTreble_hObject',handles.eTreble)

assignin('base','editBass_hObject',handles.eBass)

assignin('base','editGain_hObject',handles.eGain)

% --- Outputs from this function are returned to the command line.

function varargout = ChampGUI_OutputFcn(hObject, eventdata, handles)

% varargout cell array for returning output args (see VARARGOUT);

% hObject handle to figure




% Get default command line output from handles structure

varargout{1} = handles.output;

% --- Executes on button press in pbBehringer.

function pbBehringer_Callback(hObject, eventdata, handles)

% hObject handle to pbBehringer (see GCBO)



[y Fs]=wavread('beep.wav');

sound(y, Fs);

% --- Executes on button press in pbMarshall.

function pbMarshall_Callback(hObject, eventdata, handles)

% hObject handle to pbMarshall (see GCBO)




sound(y, Fs);

% --- Executes on button press in pbChamp.

function pbChamp_Callback(hObject, eventdata, handles)

% hObject handle to pbChamp (see GCBO)




sound(y, Fs);

% --- Executes on button press in pbStart.

function pbStart_Callback(hObject, eventdata, handles)

% hObject handle to pbStart (see GCBO)



mystring = get(hObject,'String');

status = get_param(bdroot,'simulationstatus');

if strcmp(mystring,'Start Simulation')

% Check the status of the simulation and start it if it's stopped

if strcmp(status,'stopped')

set_param(bdroot,'simulationcommand','start')

end

% Update the string on the pushbutton

set(handles.pbStart,'String','Stop Simulation')

elseif strcmp(mystring,'Stop Simulation')

% Check the status of the simulation and stop it if it's running

if strcmp(status,'running')

set_param(bdroot, 'SimulationCommand', 'Stop')


end

% Update the string on the pushbutton

set(handles.pbStart,'String','Start Simulation')

else

warning('Unrecognized string for pbByConfig') %#ok<WNTAG>

end

% --- Executes on slider movement.

function sTreble_Callback(hObject, eventdata, handles)

% hObject handle to sTreble (see GCBO)



% Hints: get(hObject,'Value') returns position of slider

% get(hObject,'Min') and get(hObject,'Max') to determine range of slider

% Get the value of the gain slider and determine what the gain value should be

NewValue = get(hObject,'Value');

value = num2str(NewValue);

% Update the model's gain value

set_param([bdroot '/Gain1'],'Gain',value)

% Set the value of the gain edit box

set(handles.eTreble,'String',value);

% Update simulation if the model is running



set_param(bdroot, 'SimulationCommand', 'Update')

end

% --- Executes during object creation, after setting all properties.

function sTreble_CreateFcn(hObject, eventdata, handles)

% hObject handle to sTreble (see GCBO)


% handles empty - handles not created until after all CreateFcns called

% Hint: slider controls usually have a light gray background.

if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))

set(hObject,'BackgroundColor',[.9 .9 .9]);

end


function sBass_Callback(hObject, eventdata, handles)

% hObject handle to sBass (see GCBO)












set(handles.eBass,'String',value);





end


function sBass_CreateFcn(hObject, eventdata, handles)

% hObject handle to sBass (see GCBO)






end


function sGain_Callback(hObject, eventdata, handles)

% hObject handle to sGain (see GCBO)









set_param([bdroot '/Gain'],'Gain',value)


set(handles.eGain,'String',value);





end



function sGain_CreateFcn(hObject, eventdata, handles)

% hObject handle to sGain (see GCBO)






end


function sVolume_Callback(hObject, eventdata, handles)

% hObject handle to sVolume (see GCBO)










set(handles.eVolume,'String',value);





end


function sVolume_CreateFcn(hObject, eventdata, handles)

% hObject handle to sVolume (see GCBO)






end

function eTreble_Callback(hObject, eventdata, handles)

% hObject handle to eTreble (see GCBO)



% Hints: get(hObject,'String') returns contents of eTreble as text

% str2double(get(hObject,'String')) returns contents of eTreble as a double


value = get(hObject,'String');




% Set the value of the gain slider

set(handles.sTreble,'Value',NewValue);





end


function eTreble_CreateFcn(hObject, eventdata, handles)

% hObject handle to eTreble (see GCBO)



% Hint: edit controls usually have a white background on Windows.

% See ISPC and COMPUTER.

if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))

set(hObject,'BackgroundColor','white');

end

function eBass_Callback(hObject, eventdata, handles)

% hObject handle to eBass (see GCBO)



% Hints: get(hObject,'String') returns contents of eBass as text

% str2double(get(hObject,'String')) returns contents of eBass as a double






set(handles.sBass,'Value',NewValue);





end


function eBass_CreateFcn(hObject, eventdata, handles)

% hObject handle to eBass (see GCBO)








end

function eGain_Callback(hObject, eventdata, handles)

% hObject handle to eGain (see GCBO)



% Hints: get(hObject,'String') returns contents of eGain as text

% str2double(get(hObject,'String')) returns contents of eGain as a double




set_param([bdroot '/Gain'],'Gain',value)


set(handles.sGain,'Value',NewValue);





end


function eGain_CreateFcn(hObject, eventdata, handles)

% hObject handle to eGain (see GCBO)







end

function eVolume_Callback(hObject, eventdata, handles)

% hObject handle to eVolume (see GCBO)



% Hints: get(hObject,'String') returns contents of eVolume as text

% str2double(get(hObject,'String')) returns contents of eVolume as a double







set(handles.sVolume,'Value',NewValue);





end


function eVolume_CreateFcn(hObject, eventdata, handles)

% hObject handle to eVolume (see GCBO)







end

% --- Executes on button press in cbChamp.

function cbChamp_Callback(hObject, eventdata, handles)

% hObject handle to cbChamp (see GCBO)



% Hint: get(hObject,'Value') returns toggle state of cbChamp

% Update gain blocks to change from bypass to champ or vice versa

value = get(hObject,'Value');

if value == 1



else



end


function cbChamp_CreateFcn(hObject, eventdata, handles)

% hObject handle to cbChamp (see GCBO)




Acknowledgements We would like to thank:

Dr. Mahmood R. Azimi-Sadjadi for formulating the original idea for this project.

Dr. Ali Pezeshki for advising this project and helping us with mathematical signal processing.

Olivera Notaros for leading the senior design program in the college of Electrical and Computer

Engineering at CSU.

Chuck Wilson for recording us in his studio, lending us his many years of audio expertise and

suggestions, finding a 1960 Fender Champ for us to record and giving us a huge discount on

recording costs.

Agilent Technologies for supporting our project with a $100 donation.

The ECE department for giving us $300 of funding for our project.

Steven Sandler for allowing us to borrow and experiment on his Champ amplifier.

Documents

TUBE (Transistor Utility for Blonde Emulation)€¦ · determining how to generalize these polynomials to the entire frequency spectrum. The main obstacle we faced was that the harmonics