ELEN E4896 MUSIC SIGNAL PROCESSING Lecture 4: Analog Synthesizers

E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17

Lecture 4:Analog Synthesizers

Dan EllisDept. Electrical Engineering, Columbia University

[email protected] http://www.ee.columbia.edu/~dpwe/e4896/1

1. The Problem Of Electronic Synthesis2. Oscillators3. Envelopes4. Filters

ELEN E4896 MUSIC SIGNAL PROCESSING

mailto:[email protected]

mailto:[email protected]

http://labrosa.ee.columbia.edu

http://labrosa.ee.columbia.edu


1. The Problem of Electronic Synthesis• How can we synthesize notes and music

... and have it sound as good as real instruments?

• Real instrument tones are complex

2

Piano

Plucked Violin

Trumpet

Bowed Violin


The Analog Synthesizer• Minimum “useful” configuration

Pitch + harmonicsAmplitude variation (dynamics)Spectral variation

(1970s technology)

3

Min

imoo

g, 19

72

Oscillator Filter

Envelope

PitchTrigger

Vibrato

t

t

f

+

Cutofffreq

Gain

Sound

++


Digital Simulation of Analog• E.g. Loomer Aspect

http://www.loomer.co.uk/aspect.htm

4






PureData (Pd)• Visual metaphor based on analog synths

“wires” connect modules

• Tutorial: http://en.flossmanuals.net/PureData/

5

http://en.flossmanuals.net/PureData/

http://en.flossmanuals.net/PureData/


2. Oscillators• Pitch = sinusoid?

only a single color

• Real instruments have more harmonicsstatic spectrum determines instrument sound?

• Additive: Combine individual harmonicscalculating sinusoids in real time is expensive...

• Subtractive: Shape harmonics with filtersstart with a spectrally rich signal“shape” harmonics efficiently with LTI filters

6


Basic waveforms• Sinusoid

• Square wave

• Pulse waveform

• Sawtooth

• Triangle

7


Aside: Bandlimiting• It’s easy to sample “ideal” simple waveforms

but the ideal ones are not bandlimited➝ lots of aliased energy

• Solution: Bandlimited waveformse.g. fill a table with precalculated sum of sinusoids up to a fixed frequency

• Variable waveforms can be derivedPWM by integrating bandlimited impulseshttps://ccrma.stanford.edu/~stilti/papers/blit.pdf

8

https://ccrma.stanford.edu/~stilti/papers/blit.pdf

https://ccrma.stanford.edu/~stilti/papers/blit.pdf


Modulation• Stationary spectra sound unnatural

real sources have random “jitter”

• Variations in pitch“Low Frequency Oscillator” frequency modulation

random noise

• Variations in timbrecan be imposed by filters...Pulse-width modulation

9


Aside: PWM Spectrum• What are harmonics of Pulse-Width Modulated

(PWM) waveforms?consider as impulses convolved with a pulse W➝ Fourier transforms multiply

or integral of sum of two opposite impulse trains with relative delay W(good for bandlimiting)

10

0 500 1000-0.50

0.51

1.5

0 500 1000-0.50

0.51

1.5

0 500 1000-0.50

0.51

1.5

0 200 400-40

-20

0

20

40

0 200 400-40

-20

0

20

40

0 200 400-40

-20

0

20

40

time

frequency

=

pw(t) =�

p(t)� p(t�W )dt


3. Envelopes• Notes need to be limited in time

simple gating not enoughamplitude envelope

• Different (real) instruments have clear variations in envelopestruck/plucked vs. bowed/blown

11


ADSR• 4-parameter classic envelope model

Attack - initial rise timeDecay - fall time immediately following initial attackSustain - amplitude of asymptote of decaywhile key is held downRelease - decay from sustain to zero after key released

12

Tobi

as R

. - M

etoc

Key depressed


Pd ADSR Abstraction• Any patch can become a “unit”

13


4. Filtering• Amplitude modulation alone is not enough

real instruments have time-varying spectrae.g. plucked string

• Generally just LPF (+ resonance)high frequencies die away after initial transientresonance can give some BPF effect

14


The Biquad filter• Flexible circuit design to achieve

variable cutoff frequencybut just single pole-pair LPF (or repeats)constant Q (bandwidth/center freq) resonance

• Analog synths provided 12-24 dB/oct rolloff15

-1 0 1-1

-0.50

0.51

s plane

10-1 100 101-50

0

50

gain

/ dB

freq / rad/s

-1 0 1-1

-0.50

0.51

Real

Imag

Real

Imag

z plane

0 0.2 0.4 0.6 0.8 1-50

0

50

norm freq / π

gain

/ dB


5. Examples• Juno-106 preset patches

from http://www.synthmania.com/juno-106.htm

16

Brass Trumpet

Piano Strings

http://www.synthmania.com/juno-106.htm

http://www.synthmania.com/juno-106.htm


Summary• Analog synthesizers provided

musical flexibility with simple units20 years of evolution

• Need instrument-like dynamics to make an interesting soundbut only up to a point...

• Analog synths provide intuitive controlseach “knob” has a distinct effect

17

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ELEN E4896 MUSIC SIGNAL PROCESSING Lecture 4: Analog Synthesizers