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ECE 6640Digital Communications
Dr. Bradley J. BazuinAssistant Professor
Department of Electrical and Computer EngineeringCollege of Engineering and Applied Sciences
ECE 6640 2
Course/Lecture Overview
• Syllabus• Personal Intro.• Textbook/Materials Used• Additional Reading• ID and Acknowledgment of Policies
• Textbook• Chapter 1
ECE 6640 3
Syllabus
• Everything useful for this class can be found on Dr. Bazuin’s web site!– http://homepages.wmich.edu/~bazuinb/
• The class web site is at– http://homepages.wmich.edu/~bazuinb/ECE6640/ECE6640_Sp14.htm
• The syllabus …– http://homepages.wmich.edu/~bazuinb/ECE6640/Syl_6640.pdf
ECE 6640 4
Who am I?
• Dr. Bradley J. Bazuin– Born and raised in Grand Rapids Michigan– Undergraduate BS in Engineering and Applied Sciences, Extensive
Electrical Engineering from Yale University in 1980– Graduate MS and PhD in Electrical Engineering from Stanford
University in 1982 and 1989, respectively.– Industrial Experience – Digital, ASIC, System Engineering
• Part-time ARGOSystems, Inc. (purchased by Boeing) 1981-1989• Full-time ARGOSystems, Inc. 1989-1991• Full-time Radix Technologies 1991-2000
– Academic Experience – Electrical and Computer Engineering• Term-appointed Faculty, WMU ECE Dept. 2000-2001• Tenure track Assistant Professor, WMU ECE Dept. 2001-2007• Tenured Associate Professor, WMU ECE Dept. 2007- present
Research Activities and Interests
• Sunseeker – Adviser to solar car team– Electrical Systems: Li battery protection system, Controller Area Network (CAN)
based sensors and controllers, Solar Array Energy Collection and Conversion• Center for the Advancement of Printed Electronics (CAPE)
– Printed electronic device design, fabrication and testing– Semiconductor Physics
• Physical Layer Communication Signal Processing– Software Defined Radios (SDR)– Mulitrate Signal Processing (digital channel bank analysis and synthesis, filter-decimation and
interpolation-filter design methods)– Adaptive Filtering and Systems (channel equalization, smart-antenna spatial beamforming)
• Communication-based Digital Signal Processing Algorithm Implementation– Xilinx programmable devices– Parallel processing, hosts including NVIDIA GPUs with CUDA and multithreaded applications
ECE 6640 5
ECE 6640 6
Required Textbook/Materials
• Bernard Sklar, Digital Communications, Fundamentals and Applications, Prentice Hall PTR, Second Edition, 2001. ISBN: 0-13-084788-7.
• SystemView by ELANIX CD with textbook
• MATLAB, Student Edition• MATLAB Signal Processing Toolbox
– The MATH Works,MATLAB and Signal Processing Toolbox http://www.mathworks.com/
ECE 6640 7
Supplemental Books and Materials
• John G. Proakis and Masoud Salehi, “Digital Communications, 5th
ed.,” McGraw Hill, Fifth Edition, 2008. ISBN: 978-0-07-295716-7.• John G. Proakis and Masoud Salehi, “Communication Systems
Engineering, 2nd ed.”, Prentice Hall, 2002. ISBN: 0-13-061793-8.• A. Bruce Carlson, P.B. Crilly, “Communication Systems, 5th ed.”,
McGraw-Hill, 2010. ISBN: 978-0-07-338040-7.• Leon W. Couch II, “Digital and Analog Communication Systems, 7th
ed.”, Prentice Hall, 2007. ISBN: 0-13-142492-0.• Stephen G. Wilson, “Digital Modulation and Coding, ” Prentice-Hall,
1996. ISBN: 0-13-210071-1.• Ezio Biglieri, D. Divsalar, P.J. McLane, M.K. Simon, “Introduction
to Trellis-Coded Modulation with Applications”, Macmillan, 1991. ISBN: 0-02-309965-8.
ECE 6640 8
Identification and Acknowledgement
• Identification for Grade Posting, Course and University Policies, and Acknowledgement
• Please read, provide unique identification, sign and date, and return to Dr. Bazuin.
ECE 6640 9
Course/Text Overview1. Signals and Spectra.
Digital Communication Signal Processing. Classification of Signals. Spectral Density. Autocorrelation. Random Signals. Signal Transmission through Linear Systems. Bandwidth of Digital Data.
2. Formatting and Baseband Modulation.
Baseband Systems. Formatting Textual Data (Character Coding). Messages, Characters, and Symbols. Formatting Analog Information. Sources of Corruption. Pulse Code Modulation. Uniform and Nonuniform Quantization. Baseband Modulation. Correlative Coding.
ECE 6640 10
Course/Text Overview (2)3. Baseband Demodulation/Detection.
Signals and Noise. Detection of Binary Signals in Gaussian Noise. Intersymbol Interference. Equalization.
4. Bandpass Modulation and Demodulation/Detection.
Why Modulate? Digital Bandpass Modulation Techniques. Detection of Signals in Gaussian Noise. Coherent Detection. Noncoherent Detection. Complex Envelope. Error Performance for Binary Systems. M-ary Signaling and Performance. Symbol Error Performance for M-ary Systems (M>>2).
Exam #1
ECE 6640 11
Course/Text Overview (3)5. Communications Link Analysis.
What the System Link Budget Tells the System Engineer. The Channel. Received Signal Power and Noise Power. Link Budget Analysis. Noise Figure, Noise Temperature, and System Temperature. Sample Link Analysis. Satellite Repeaters. System Trade-Offs.
ECE 6640 12
Course/Text Overview (4)6. Channel Coding: Part 1.
Waveform Coding. Types of Error Control. Structured Sequences. Linear Block Codes. Error-Detecting and Correcting Capability. Usefulness of the Standard Array. Cyclic Codes. Well-Known Block Codes.
7. Channel Coding: Part 2.
Convolutional Encoding. Convolutional Encoder Representation. Formulation of the Convolutional Decoding Problem. Properties of Convolutional Codes. Other Convolutional Decoding Algorithms.
Exam #2
ECE 6640 13
Course/Text Overview (5)8. Channel Coding: Part 3.
Reed-Solomon Codes. Interleaving and Concatenated Codes. Coding and Interleaving Applied to the Compact Disc Digital Audio System. Turbo Codes.
Appendix 8A. The Sum of Log-Likelihood Ratios.
9. Modulation and Coding Trade-Offs.
Goals of the Communications System Designer. Error Probability Plane. Nyquist Minimum Bandwidth. Shannon-Hartley Capacity Theorem. Bandwidth Efficiency Plane. Modulation and Coding Trade-Offs. Defining, Designing, and Evaluating Systems. Bandwidth-Efficient Modulations. Modulation and Coding for Bandlimited Channels. Trellis-Coded Modulation.
Final Exam
ECE 6640 14
Course/Text Overview (6)Advanced Topics (as time permits)
11. Multiplexing and Multiple Access.
Allocation of the Communications Resource. Multiple Access Communications System and Architecture. Access Algorithms. Multiple Access Techniques Employed with INTELSAT. Multiple Access Techniques for Local Area Networks.
12. Spread-Spectrum Techniques.
Spread-Spectrum Overview. Pseudonoise Sequences. Direct-Sequence Spread-Spectrum Systems. Frequency Hopping Systems. Synchronization. Jamming Considerations. Commercial Applications. Cellular Systems.
Final Exam
ECE 6640 15
Text AppendicesA. A Review of Fourier Techniques.
Signals, Spectra, and Linear Systems. Fourier Techniques for Linear System Analysis. Fourier Transform Properties. Useful Functions. Convolution. Tables of Fourier Transforms and Operations.
B. Fundamentals of Statistical Decision Theory.
Bayes' Theorem. Decision Theory. Signal Detection Example.
C. Response of a Correlator To White Noise.
D. Often-Used Identities.
E. s-Domain, z-Domain and Digital Filtering.
F. List of Symbols.
G. SystemView by ELANIX Guide to the CD.
Comments from 2006 Offering
• A strong focus on themes and critical results for each chapter covered is needed. The text author provides his own list of critical elements, they can be incorporated into the instructors set.
• Matlab simulations of all significant concepts should be available. They allow the students to perform theoretical computations and then observe what the computations mean, particularly as it relates to bit-error rate performance, digital modulation and coherent and non-coherent demodulation, and channel encoding and decoding.
• The software that comes with the text provides demonstrations, but it is not user friendly and the software is very out-of-data (no longer supported).
ECE 6640 16
ECE 6640 17
Chapter 1
1. Signals and Spectra.1.1 Digital Communication Signal Processing.1.2 Classification of Signals. 1.3 Spectral Density. 1.4 Autocorrelation. 1.5 Random Signals. 1.6 Signal Transmission through Linear Systems. 1.7 Bandwidth of Digital Data.
A review of prerequisite material that is critically important when studying digital communication systems.
ECE 6640 18
Sklar’s Communications System
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
ECE 6640 19
Simplified Communications System• Format: making the message compatible with digital processing• Source Coding: efficient descriptions of information sources• Channel Coding: signal transformation enabling improved reception
performance after expected channel impairments• Modulation: formation of the baseband waveform• RF Mixing: frequency domain translation of baseband signal• Transmit/Receive: RF Amplifiers and Filters
Information Message Format Source
EncodeMod-
ulation RF Mixing Transmitter
Reformat Source Decode
Demod-ulation RF Mixing Receiver
Antenna
AntennaInformation Message
RF Signal
Noise
Interference
Channel Encode
Channel Decode
Bits Symbols Signals
ECE 6640 20
Communication Channel
• The channel greatly effects received RF signals– Frequencey, Bandwidth, Transmitted Signal Power, RF Propagation– Attenuation, Nonlinear Distortion, Multipath, Range, Direction– Signal-to-Noise Ratio (SNR) and Signal-to-Interference Ratio (SIR)– Minimum Detectable Signal Level (MDS), Noise Floor
TransmittingAntenna
ReceivingAntenna
RF Communication Channel
Noise
Interference
Linear Filtering
NonlinearDistortion
Atten-uation
ECE 6640 21
Received Signal
• The receiver must extract the original message as best possible!
• Multiple signals with similar channel characteristics may be present
• The RF channel(s) must be allocated and efficiently utilized. – Frequency band assignments and regulations (power, direction, etc.)– Signal modulation structures have different characteristics
tnthtsthtsthtstr NNc 22
ECE 6640 22
Why Digital?1. Noise, Interference, Path Loss, and Channel Impairments
(signal environment)2. Cost3. Inherent Availability4. Reliability and Reconfigurability
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
ECE 6640 23
Terminology
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
• Information Source• Textual Message• Character• Binary Digit (Bit)• Bit Stream• Symbol• Digital Waveform• Data Rate
Signal Processing Functions
ECE 6640 24Notes and figures are based on or taken from materials in the course textbook:
Bernard Sklar, Digital Communications, Fundamentals and Applications, Prentice Hall PTR, Second Edition, 2001.
Classification of Signals
• Deterministic and Random
• Periodic and Non-periodic
• Analog and Discrete/Digital
• Energy and Power Signals
ECE 6640 25
SKLAR DSP Tutorial
• The CD that comes with the text includes a “Concise DSP Tutorial” in pdf format
• Table of Contents:– Frequency Domain Analysis – critical importance– General Digital Filters – important– Finite Impulse Response (FIR) Filters – critical importance– Infinite Impulse Response (IIR) Filters – useful but …– Filter Design Techniques – will be discussed and provided– Adaptive Filters – saved for Dr. Bazuin’s ECE6950 course
• Also see Appendix B: Fundamentals of Statistical Decision Theory– Specific material from probability and statistics is required.
(ECE 3800 or ECE5820 material)ECE 6640 26
ECE 6640 27
Spectral Density
• Energy Spectral Density
• Power Spectral Density
dttxE 2X
2
T
2T
2
0X
0
0
dttxT1P
*X fXfXf
*TTTX fXfX
T1limfG
ECE 6640 28
Autocorrelation
• of an Energy Signal
dttxtxR XX
• Properties:1. Energy
2. Symmetry
3. Maximum
4. Transform Pair
220 XXERXX
XXXX RR
0XXXX RR
fR XXXX
ECE 6640 29
Autocorrelation
• of a Power Signal
• Properties:1. Energy
2. Symmetry
3. Maximum
4. Transform Pair
2
T
2T
2
0XX
0
0
dttxT10
XXXX
0XXXX
fGXXXX
2T
2T
TXX dttxtxT1lim
ECE 6640 30
Random Signals
1 Distribution Functions Probability Distribution Function (PDF) or Cumulative Distribution Function (CDF) [preferred]
xforxFX ,10 0XF and 1XF XF is non-decreasing as x increases 1221Pr xFxFxXx XX
For discrete events For continuous events
ECE 6640 31
Random Signals
2. Density Functions Probability Density Function (pdf)
xforxf X ,0
1
dxxf X
duufFx
XX
dxxfxXx
x
xX
2
1
21Pr
Functions of random variables
dydxxfyf XY
Probability Mass Function (pmf)
xforxf X ,0
1
dxxf X
duufFx
XX
dxxfxXx
x
xX
2
1
21Pr
ECE 6640 32
Random Signals
Mean Values and Moments 1st, general, nth Moments
dxxfxXEX X or
x
xXxXEX Pr
dxxfXgXgE X or
x
xXXgXgE Pr
dxxfxXEX Xnnn or
x
nnn xXxXEX Pr
Central Moments
dxxfXxXXEXX X
nnn
x
nnnxXXxXXEXX Pr
Variance and Standard Deviation
dxxfXxXXEXX X
2222
x
xXXxXXEXX Pr2222
ECE 6640 33
Random Signals
The Gaussian Random Variable
xforXxxf X ,2
exp2
12
2
where X is the mean and is the variance
dvXvxFx
vX
2
2
2exp
21
Unit Normal
duuxx
u
2
exp21 2
xx 1
XxxFX or
XxxFX 1
The Q-function is the complement of the normal function, : (Appendix B)
duuxQxu
2
exp21 2
ECE 6640 34
Random Processes
5. Random Processes 5.1. Introduction
Ensemble
5.2. Continuous and Discrete Random Processes
5.3. Deterministic and Nondeterministic Random Processes
5.4. Stationary and Nonstationary Random Processes
5.5. Ergodic and Nonergodic Random Processes A Process for Determining Stationarity and Ergodicity
a) Find the mean and the 2nd moment based on the probability b) Find the time sample mean and time sample 2nd moment based on time
averaging. c) If the means or 2nd moments are functions of time … non-stationary d) If the time average mean and moments are not equal to the probabilistic mean
and moments or if it is not stationary, then it is non ergodic.
From: George R. Cooper and Clare D. McGillem, Probabilistic Methods of Signal and System Analysis, 3rd ed.,Oxford University Press Inc., 1999. ISBN: 0-19-512354-9
ECE 6640 35
Random Processes: Continuous, Discrete and Mixed
Continuous and Discrete Random Processes A continuous random process is one in which the random variables, such as ntXtXtX ,, 21 , can assume any value within the specified range of possible values. A more precise definition for a continuous random process also requires that the cumulative distribution function be continuous. A discrete random process is one in which the random variables, such as ntXtXtX ,, 21 , can assume any certain values (though possibly an infinite number of values). A more precise definition for a discrete random process also requires that the cumulative distribution function consist of numerous discontinuities or steps. Alternately, the probability density function is better defined as a probability mass function … the pdf is composed of delta functions. A mixed random process consists of both continuous and discrete components. The probability distribution function consists of both continuous regions and steps. The pdf has both continuous regions and delta functions.
From: George R. Cooper and Clare D. McGillem, Probabilistic Methods of Signal and System Analysis, 3rd ed.,Oxford University Press Inc., 1999. ISBN: 0-19-512354-9
ECE 6640 36
Random Processes: Deterministic and Nondeterministic
Deterministic and Nondeterministic Random Processes A nondeterministic random process is one where future values of the ensemble cannot be predicted from previously observed values. A deterministic random process is one where one or more observed samples allow all future values of the sample function to be predicted (or pre-determined). For these processes, a single random variable may exist for the entire ensemble. Once it is determined (one or more measurements) the sample function is known for all t.
From: George R. Cooper and Clare D. McGillem, Probabilistic Methods of Signal and System Analysis, 3rd ed.,Oxford University Press Inc., 1999. ISBN: 0-19-512354-9
ECE 6640 37
Random Processes: Stationary and Nonstationary (1)
Stationary and Nonstationary Random Processes The probability density function for random variables in time as been discussed, but what is the dependence of the density function on the value of time, t, when it is taken? If all marginal and joint density functions of a process do not depend upon the choice of the time origin, the process is said to be stationary (that is it doesn’t change with time). All the mean values and moments are constants and not functions of time! For nonstationary processes, the probability density functions change based on the time origin or in time. For these processes, the mean values and moments are functions of time. In general, we always attempt to deal with stationary processes … or approximate stationary by assuming that the process probability distribution, means and moments do not change significantly during the period of interest.
From: George R. Cooper and Clare D. McGillem, Probabilistic Methods of Signal and System Analysis, 3rd ed.,Oxford University Press Inc., 1999. ISBN: 0-19-512354-9
ECE 6640 38
Random Processes: Stationary and Nonstationary (2)
Stationary and Nonstationary Random Processes The requirement that all marginal and joint density functions be independent of the choice of time origin is frequently more stringent (tighter) than is necessary for system analysis. A more relaxed requirement is called stationary in the wide sense: where the mean value of any random variable is independent of the choice of time, t, and that the correlation of two random variables depends only upon the time difference between them. That is
XXtXE and
XXRXXttXXEtXtXE 00 1221 for 12 tt You will typically deal with Wide-Sense Stationary Signals.
From: George R. Cooper and Clare D. McGillem, Probabilistic Methods of Signal and System Analysis, 3rd ed.,Oxford University Press Inc., 1999. ISBN: 0-19-512354-9
ECE 6640 39
Random Processes: Ergodicity
Ergodic and Nonergodic Random Processes Ergodicity deals with the problem of determining the statistics of an ensemble based on measurements from a sample function of the ensemble. For ergodic processes, all the statistics can be determined from a single function of the process. This may also be stated based on the time averages. For an ergodic process, the time averages (expected values) equal the ensemble averages (expected values). That is to say,
T
T
nT
nn dttXT
dxxfxX21lim
Note that ergodicity cannot exist unless the process is stationary!
From: George R. Cooper and Clare D. McGillem, Probabilistic Methods of Signal and System Analysis, 3rd ed.,Oxford University Press Inc., 1999. ISBN: 0-19-512354-9
ECE 6640 40
Random ProcessesThe power spectral density is the Fourier Transform of the autocorrelation:
diwtXtXERwS XXXX exp
For an ergodic process,
txtxdttxtx
T
T
TT
XX 21lim
diwdttxtx
TtXtXE
T
TT
XX exp21lim
dtdtiwtxiwttxT
T
TT
XX
expexp21lim
dtwXiwttxT
T
TT
XX
exp
21lim
dttwitxT
wXT
TT
XX
exp
21lim
2wXwXwXXX From: George R. Cooper and Clare D. McGillem, Probabilistic Methods of Signal and System Analysis, 3rd ed.,Oxford University Press Inc., 1999. ISBN: 0-19-512354-9
ECE 6640 41
Binary Sequence, Low Bit Rate
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
ECE 6640 42
Binary Autocorrelation and PSD
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
ECE 6640 43
Bandwidth Consideration
• The first spectral null occurs are 1/T. Therefore one measure of bandwidth could be the null.
• Are there others bandwidth measures? – 3dB bandwidth– 99% Power– If it were a rectangle with Gx(0) given, how wide would it be
(Noise Equivalent Bandwidth)– Etc.
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
ECE 6640 44
Bandwidth Consideration
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
ECE 6640 45
White Noise
Noise is inherently defined as a random process.
You may be familiar with “thermal” noise, based on the energy of an atom and the mean-free path that it can travel.
As a random process, whenever “white noise” is measured, the values are uncorrelated with each other, not matter how close together the samples are taken in time.
Further, we envision “white noise” as containing all spectral content, with no explicit peaks or valleys in the power spectral density.
As a result, we define “White Noise” as
tSRXX 0
0SwS XX
This is an approximation or simplification because the area of the power spectral density is infinite!
From: George R. Cooper and Clare D. McGillem, Probabilistic Methods of Signal and System Analysis, 3rd ed.,Oxford University Press Inc., 1999. ISBN: 0-19-512354-9
ECE 6640 46
Band Limited White Noise
Thermal noise at the input of a receiver is defined in terms of kT, Boltzmann’s constant times absolute temperature, in terms of Watts/Hz. Thus there is kT Watts of noise power in every Hz of bandwidth.
For communications, this is equivalent to –174 dBm/Hz or –144 dBW/Hz.
For typical applications, we are interested in Band-Limited White Noise where
fW
WfSwS XX 0
0
The equivalent noise power is then:
002 20 SWdwSRXE
W
WXX
For communications, we use kTB.
How much noise power, in dBm, would I say that there is in a 1 MHz bandwidth?
dBmBdBkTdBkTBdB 11460174
ECE 6640 47
White Noise in Comm.
• From the text
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
ECE 6640 48
Noise as A Gaussian Random Process
• What is so special about a Gaussian Distribution?– Result of summing a large number of random variables– Linear systems produce Gaussian Outputs– Well know/studied characteristics– Used to define the characteristics of numerous natural, real-world signals
A Gaussian Random Variable
xforXxxf X ,2
exp2
12
2
where X is the mean and is the variance
dvXvxFx
vX
2
2
2exp
21
ECE 6640 49
Linear Systems
Linear transformation of signals:
txthty
sXsHsY
Convolution Integrals
0
dhtxty
or
t
dxthty
where for physical realizability and stability constraints we require
00 tforth
dtth
ECE 6640 50
Transfer Function
• For linear systems: A sinusoidal input results in sinusoidal output modified in magnitude and phase.
fjexpfHfH
fHRefHImtanf 1
tf2cosAtx 0
txthty
000 ftf2cosfHAty
ECE 6640 51
Filtering a Random Process
• The PSD of a filtered response is
0222
0111 dhtxdhtxERYY
021212
01 XXYY RhhddR
021212
01 exp diwRhhddRwS XXYYYY
wHwHwSRwS XXYYYY
2wHwSRwS XXYYYY
ECE 6640 52
Distortionless Transmission and the Ideal Filter
• To receive a signal without distortion, only changes in the magnitude and/or a time delay is allowed.
0ttxKty
0tf2expfXKfY
• The transfer function is
0tf2expKfH
• A constant gain with a linear phase KfH 0tf2f
ECE 6640 53
Ideal Filter (1)
• For no distortion, the ideal filter should have the following properties:
fjexpfHfH
u
u
fffor,0
fffor,1fH
u
u0
fffor,arbitrary
fffor,tf2f
• The impulse response is
u
u
u
u
f
f0
f
f0
dfttf2jexpth
dftf2jexptf2jexp1th
ECE 6640 54
Ideal Filter (2)
0uu
0
0u
0
0u
0
0u
f
f0
0
f
f0
ttf2sincf2thtt2
ttf2sin2th
tt2jttf2jexp
tt2jttf2jexpth
tt2jttf2jexpth
dfttf2jexpth
u
u
u
u
• Continuing
• The sinc function– A non-causal filter
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
ECE 6640 55
Ideal Filters in the Freq. Domain
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
ECE 6640 56
Realizable Filters, RC Network
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
1st order Butterworth
Filter
ECE 6640 57
White Noise in an RC Filter
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
• The noise PSD has been modified • The autocorrelation is spread in time
ECE 6640 58
Signal Filtering in the Real World
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
ECE 6640 59
Signal Filtering in the Real World (2)
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
ECE 6640 60
Bandwidth Considerations, Easy
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
ECE 6640 61
Bandwidth Considerations, Harder
• If the spectrum extends to infinity, where do you assume that it can be cut off?
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
ECE 6640 62
Bandwidth Considerations
• Note 1 that as soon as time is limited, the signal has been multiplied by a rect function in the time domain.– A rect in the time domain creates an infinite sinc convolution in the
frequency domain!
• Note 2 that a bandlimited frequency domain signal can be generated by multiplying by a rect function in the frequency domain.– A rect in the frequency domain results in a non-causal, infinite
time convolution in the time domain!
• For mathematicians, a real signal can not be both time limited and frequency band limited?!
ECE 6640 63
Bandwidths that are Used
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
ECE 6640 64
Bandwidth Definitions
(a) Half-power bandwidth. This is the interval between frequencies at which Gx(f ) has dropped to half-power, or 3 dB below the peak value.
(b) Equivalent rectangular or noise equivalent bandwidth. The noise equivalent bandwidth was originally conceived to permit rapid computation of output noise power from an amplifier with a wideband noise input; the concept can similarly be applied to a signal bandwidth. The noise equivalent bandwidth WN of a signal is defined by the relationship WN = Px/Gx(fc), where Px is the total signal power over all frequencies and Gx(fc) is the value of Gx(f ) at the band center (assumed to be the maximum value over all frequencies).
(c) Null-to-null bandwidth. The most popular measure of bandwidth for digital communications is the width of the main spectral lobe, where most of the signal power is contained. This criterion lacks complete generality since some modulation formats lack well-defined lobes.
ECE 6640 65
Bandwidth Definitions (2)
(d) Fractional power containment bandwidth. This bandwidth criterion has been adopted by the Federal Communications Commission (FCC Rules and Regulations Section 2.202) and states that the occupied bandwidth is the band that leaves exactly 0.5% of the signal power above the upper band limit and exactly 0.5% of the signal power below the lower band limit. Thus 99% of the signal power is inside the occupied band.
(e) Bounded power spectral density. A popular method of specifying bandwidth is to state that everywhere outside the specified band, Gx(f ) must have fallen at least to a certain stated level below that found at the band center. Typical attenuation levels might be 35 or 50 dB.
(f) Absolute bandwidth. This is the interval between frequencies, outside of which the spectrum is zero. This is a useful abstraction. However, for all realizable waveforms, the absolute bandwidth is infinite.
Spectrum and Time Domain of a Band-limited Bandpass Signal
ECE 6640 66Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
Summary
• Communication must consider a number of aspects– Time and Frequency Domain Signals– Discrete and Continuous Time Signal Constructs– Deterministic and Random Signal Properties– Models of Signal Propagation
• Simple time and amplitude changes• Complex channel impairments
– Models of Other Signals in the Environment• Noise (white, Gaussian, or more complex)• Interference• Multipath
• To successfully model and analyze modern communication systems, there is a lot of prerequisite knowledge required.
ECE 6640 67