Module Notes and Demos
 getspeech.m Needed for
course Mfiles, this is the platform independent way to
read the .wav files here.
 "WAV"files : [ enter(female)
enter(male) erase(female) help(female) w(female) zero(female) one(male) ] The only useful
information on the front page of each module below is
the relevant sections in the P&M Text and the
relevant Matlab demo files. The rest of the front page
of each module should be ignored. The goal is to work
through three modules per week, or 1.5 modules per
lecture, on average. Additional modules will be added on
material towards the end of the course coverage.

Weeks 1 and 2.
 Module 1a: Text Outline
Scan; Text Chap. 1
Scan; Module 1a;
Matlab demo: aliaseg.m,
DiscreteTime Signal
Basics (301);
DiscreteTime System Basics (301)
 Module 1b: Module1b;
Matlab Demo on Simple Difference Equation: notcheg.m
 Module 2: Supplemental
Notes on DT Convolution (301);
Convolution Examples from
Undergradate Text (301);
Impulse
Properties Plus Convolving with Delta Function (301);
Implications of
Linearity and TI as Pertaining to Convolution (301);
 P&M Text Chap. 2,
Part 1 Scan ; P&M
Text Chap. 2 Part 2 Scan ;
 Autocorrelation and CrossCorrelation: Sect 2.6
 Basics of
Autocorrelation ; Text
Chap. 2 Part 2 Scan ; Module2
;
Autocorrelation
Properties: Proofs
 Additional
Properties
of Autocorrelation See Parts (c), (d) of Prob. 1
from Exam 1 for Fall 2006.
 Autocorrelation
Pet
Problem On many old exams :)
 Link for GPS Tutorial on use of Gold Codes: GPS
Tutorial
 Another GPS Tutorial: GPS
Tutorial 2
 CDMAeg1.m, cdmaeg.m, gold1.m,
gold2.m; gold3.m.
 Add'l CDMA Matlab Example: walsh_cdma_eg.m;

Week 3. ZTransform
 Link
for
ECE 438 Notes on ZTransform Undergraduate Review
 ZTransform Basics Basics
of ZTransform
 Module 3: Module 3
Text Chap. 3, Part 1 Scan
(pdf) Text Chap. 3,
Part 2 Scan (pdf)
 Module 4: Module 4, Graphical
Frequency Response Example ; Chap. 5
Graphical Frequency Response (pdf); notcheg2.m,
 Module 5: Session10Roadmap.pdf
; Module 5 Chap. 5 Notch Filters
(pdf);
zpgui.m, zpgui3.m,
Note on AllPass Filters;
AllPassFilter.m,
 Autocorrelaton Revisited: Energy Density Spectrum: Energy Density
Spectrum.

Week 4. Properties of DTFT; CTFTDTFT Relationship
 CT Fourier
Transform: Properties & Pairs; DT Fourier Transform:
Properties & Pairs;
 DT Fourier
Transform: Properties Pairs including Sinewaves
 Basics: Sinewave
Input
to LTI System
 Alternative Derivation
of CTFTDTFT Relationship;
 CTFTDTFT
relationship for Sampled Sinewave
 SampleSinewave.m
 SampleSincProduct.m
 SampleSincProductAboveNyquist.m
 Scan of First
Section of Text Chap. 6; Scan of Undergrad 301
Text Chap. 7;
 aliaseg2.m, aliaseg3.m,
 Development of
Ideal D/A Conversion;
 The 3 modules below cover the textbook's derivations
of Sampling Theory and Ideal A/D Conversion that
essentially avoids the use of Dirac Delta functions. We
will not cover these modules in class. Review them on
your own while reading Chap. 6 of the textbook.
 Module 6, Module 7a, Module 7

Week 5. D/A Conversion Featuring Digital Upsampling
 D/A Conversion:
Quick Review of Ideal D/A Conversion;
 Module 8: Intro to Digital
Upsampling upsamplex2eg1.m;
 VIP Multirate Formulas: VIP_MultirateFormulas.pdf
 Module 9: Module 9 ; upsample2eg2.m, upsamplex2eg2.m, ZOHeg2.m,
 Insights on Efficient Upsampling: Final Words
on Efficient Upsampling;
 Efficient Upsampling by 3 with Polyphase Filters: upsamplex3.m,


Week 6: Digital Subbanding and SSB/VSB Filtering
 VIP Multirate Formulas: VIP_MultirateFormulas.pdf
 Module 11: Efficient
Downsampling and Frequency Division Multiplexing,
subbandeg3.m
 Module 12: Digital
Subbanding: Transmultiplexers Multiplex3Sigs.m
 Transmultiplexers: Efficient Digital Subbanding: Efficient
Digital Subbanding of 3 Signals, Multiplex3Sigs.m
 Additional Insights Into Efficient Digital
Subbanding:
Post Upsampling Modulation
 Final Words on Digital Subbanding: Final Words on
Digital Subbanding, Multiplex3SigsAlt.m
; Multiplex4SigsAlt.m
 Supplemental
Notes on Hilbert Transform; hilbert301eg.m
 Supplemental
Notes on VSB modulation; VSB Modulation
with Complex RaisedCosine Filter;


Week 7: Perfect Reconstruction Filter Banks
 Notes on TwoChannel PR
Filter Bank ; Summary
Page for TwoChannel PR Filter Bank ;
 Notes on SquareRoot RaisedCosine Spectrum: ContinuousTime
SquareRoot RaisedCosine Spectrum ; To get
evenlength symmetric halfband filter, replace time
variable t by T_s /4 + n T_s /2
 PRRC2chan.m
 Solve Problem 1 from Final Exam Fall 2012 to see why
these work: PR3DFTchan.m ; PR5DFTchan.m
 Noble's Identities. Proofs of Noble's
Identities ;
 Powerpoint presentation on TwoChannel (Halfbands)
Perfect Reconstruction Filter Bank:
PPT file on Quadrature Mirror Filter Bank ; PDF file on Quadrature Mirror Filter
Bank ;
 Image_compression_wavelets_jpeg2000.pdf



Special Topics Week.
 OFDM Day: OFDM Lecture
; OFDM_SimpleEg.m, OFDM Exam Example ;
 The NxN DFT Matrix
 Chap4_DFTsinewaves.pdf

 Module 13: Analysis of
Quantization Error quantizeb2.m.


Week 8. DFT and FFT: Fast Fourier Transform.
 The DFT Matrix: The NxN DFT
Matrix
 Module 20: DecimationinTime Radix 2 FFT: Module 20;
 DFT_Matrix8.jpg, DFT_Matrix16.jpg, dftmatrix8.jpg, dftmatrix8.pdf, dftatrix16.jpg, dftatrix16.pdf,
 DFT_MatrixColors.m,
DFT_MatrixColors.fig
; dftcolor.m,
 Text: Radix 2 FFTs Sect.
8.1.3
Radix 2 FFTs
 Use FFT to Compute IDFT FFT
to Compute Inverse DFT
 Text: Divide and Conquer Chap 8: Divide &
Conquer Approach
 Module 21: Module 21 DivideConquer.m, sineDFTeg1.m sineDFTeg2.m, sineDFTeg3.m,
 Module 22: Module 22 timealias.m,

Week 9. Sampling in the Frequency Domain.
 My notes on
Frequency Domain Sampling Notes (Chap 7) ;
 Text notes on
Properties of the DFT.
 Notes on DFT
Based Processing.
 DFT of a
FiniteLength Sinewave.
 Basic DFT Pair.; Observations on
DFT based processing of finitelength sinewaves
 Text notes on
DFT based Linear Filtering.
 Time Domain
Aliasing of MultiPole Causal Signals.
 Text
notes on overlapadd and overlapsave AND DFT "tricks"
for realvalued signals ; Computation Count for DFT
Based Linear Filtering.
 Mfile for efficient Computation of DFT of two
realvalued sequences plus efficient computation of
2Npt DFT of realvalued sequence. EFF_FFT_Real.m
 Illustration of overlapsave method using FFT's: OverlapSaveEff.m
 Text notes on radix 2
FFT's Also Divide and Conquer Appraoch
 Spectrogram Examples: voweleg.m
; voweleg2.m ; vowelwin.m . 0af1s1t0.wav ; 0ef1s1t0.wav
 Module 23: Module 23 windowseg.m, trunceffects.m, windowseg2.m, windowedsines.m,

Week 10. IIR Digital Filter Design.
 Module 14: Module 14 ;
Classic Analog Filter Designs Analog Filter Designs
 EllipticFilters,
Butterworth
Filters, Chebyshev
Filters,
 Module 15: Module 15
 Module 16: Module 16 buttereg.m, chebyeg1.m, chebyeg2.m, ellipeg.m;

Week 11. FIR Digital Filter Design.
 Note on Linear Phase FIR Filters Linear Phase FIR
Filters
 Module 18: pdf , Text: Equiripple FIR Filter
Design FIRlowpasseg.m,
FIRbandpasseg.m,
 Module 19: Module 19 deriveg.m, deriveg2.m,
hilberteg.m,

Week 12. Parametric Spectral Estimation.
 Module 24: Module 24
 Speech Models and Linear Predictive Coding SpeechLPC.
 Module 25: Condensed Overview/Derivation of AR and
ARMA spectral estimation methods: pdf. Illustrative
Example of Linear MMSE estimation: pdf. Module 25 SOSextrap.m, SOSviaAR.m, ARspecest.m.
 Link
for
Last lecture of LPC Compressions for Speech ; LPC Lecture


Week 13.
 Module 26: Module 26 SOSestviaAR.m, ARMAviaAR.m.
 Module 28: Modul 28
Derivation of LevinsonDurbin Algorithm: pdf. Minus sign on RHS of
last eqn at bottom of last page should be plus sign.

Week 14.
 Module 29: Module 29
Notes on MA(q) random process: pdf.
YWvsULS.m, ARMA2stepest.m,
 Module 30: Module 30 MinVarforSOS.m, MinVarforARMA.m.
 Derivation of LevinsonDurbin Algorithm. pdf. Minus sign on RHS of
last eqn at bottom of last page should be plus sign.

Week 15.
 Module 28: Adaptive Filtering. pdf
 Module 29: pdf NoiseCancel.m.

Week 16.
 Module 29: pdf AdaptCancel.m.
 Module 30: pdf MinVarforSOS.m.
 Module 31: pdf CancelTone.m.
 Module 32: pdf FIRequalizer.m. Prob529.m.
 Module 33: pdf AdaptEqualize.m.
You need Adobe Acrobat Reader 2.1 or later to view PDF
files. The latest version is available freely at www.adobe.com. 
Homeworks and Solutions

Homework Problems from Proakis Text
 Hmwk #1: Problems: 1.6, 1.7, 1.8, 1.9, 1.11, 2.10,
2.11, 2.13, 2.45, 2.46, 2.61. Solution: pdf

 Hmwk #2: Problems: 3.43, 3.49, 3.51, 7.3, 7.4, 7.7.
Solution: pdf

 Hmwk #3: Problems: 4.51, 4.32  change input to
x[n]=sin(pi n /4) / (pi n), 4.47, 4.49, 4.50, 4.76(a),
4.93, 4.100. Solution: pdf

Matlab Based Homeworks
 Matlab Hmwk #1: Due date: Wednesday, Sept. 30.
Oncampus students MUST turn in a paper printout.
Offcampus students can email me a pdf file or word doc.
The problem is 2.65 in the textbook with several
modifications to the problem as it is posted in the
textbook: Problem 2.65
Statement, Modifications
, Prob2_62.txt. M15.m . Recommend against using the
matlab command "xcorr" to do the crosscorrelation 
just use convolution to do correlation as in the CDMA
examples posted at the course web site: ryx =
conv(y,x(end:1:1)) and throw away the first first M1
values of ryx (where M is the code length) since those
correspond to negative timeshifts and the problem only
asks you to plot for positive timeshifts.

 Matlab Hmwk #2.**VIP** Due: Monday, Nov. 16. MatlabHmwk2F14.pdf .
 QMF (M=2 subbands) using SRRC Halfband Filter PRRC2chan.m;
 Noble's Identities. Proofs of Noble's
Identities ;
 M=4 subbands based on RootRaised Cosine Halfband
Filter and TreeStructure PRRC4chan.m
 M=4 subbands based on TwoTap {1,1} Halfband Filter
and Tree Structure PR4chan.m
 Summary Page for
TwoChannel PR Filter Bank ;
 QMF using SRRC Halfband
Filter
 Analog RootRaisedCosine(SRRC)Spectrum: CT SRRC Spectrum ;
To get halfband filter, replace time variable t by T_s
/4 + n T_s /2
 M=3 subbands PR Filter Bank Using Length 3 sinewaves
as subband filters: PR3DFTchan.m,
 M=5 subbands PR Filter Bank Using Length 5 sinewaves
as subband filters: PR5DFTchan.m
 Image_compression_wavelets_jpeg2000.pdf

 Matlab Hmwk #3: P&M Prob. 7.29, 7.30. DUE
DATE: Friday, Dec. 4 Matlab 3: Two text
Problems from Chap. 7. .
 Note: Prob. 7.30. f_1 = 1/128 NOT 1/18  typo!
 Also, plot magnitude of DFT in each case.
 Note: Prob. 7.29. For parts (b) and (c), use
 reconstruction formula (7.1.13) on pg. 453.
 Prescription for
what to plot ;
 My notes on
Frequency Domain Sampling Notes (Chap 7) ;
 (b) Use N=21 rather than N=20, and use the sequence
x[n]=a^nD, n=0,1,...21, where D=(N1)/2=10. Multiply
X(w) in problem statement by linear phase term exp(jDw)
with D10.
 (c) Use N=101 rather than N=100, and use the sequence
x[n]=a^nD, n=0,1,...100, where D=(N1)/2=50. Multiply
X(w) in problem statement by linear phase term exp(jDw)
with D=50.
 (e) Use the timedomain aliasing formula in (7.1.4)
on page 450. Use three terms: x[nN] + x[n] + x[n+N],
for n=0,1,...N1. Plot what this formula yields on the
same graph as a plot of the IFFT of N samples of the
original spectrum in the interval from 0 to 2pi.
 Prescription for
what to plot ;



VIP Information for Exam 1

 Example Autocorrelation Problem: Example
Autocorrelation Problem ; CTFTDTFT for Sampled
Sinewaves

 Useful Sinc Function Results UsefulSincFunctionResults.pdf
 Add'l Table of DTFT Pairs Including Sinewaves
DT Fourier
Transform: Properties Pairs inc. Sinwaves
 Sinewaves thru LTI System Sinewaves Thru LTI
Systems (covered) ; Sinewave Input to
LTI System
 CTFTDTFT for
Sampled Sinewaves
 Notes on AllPass Filters/Signals Notes on AllPass Filters
 Notes on Autocorrelation/CrossCorrelation
(covered)
Autocorrelation Properties/Proofs ; Additional
Properties of Autocorrelation ; Example
Autocorrelation Problem ; Energy Density
Spectrum

 Exam 1 Problems on Notch Filter as Parallel
Combination of Two AllPass Filters NotchFilterAllPassFilter.pdf
 Fall 2008, Prob. 2.
 Fall 2004, Prob. 2.
 Fall 2002, Prob. 2.
 Exam 1 Problems on PoleZero Cancellation PoleZeroCancellation.pdf
; Addl
Notes on First Order Difference Equations
 Fall 2001, Prob. 2.
 Fall 1998, Prob. 2.
 Exam 1 Problems on Sampling a CT Digital
Communications Signal to obtain a DT System: CT_Signal_to_DT_System.pdf
 Fall 2007, Prob. 3.
 Fall 2006, Prob. 2.
 Fall 2005, Prob. 3.
 Fall 2000, Prob. 3.
 Fall 1999, Prob. 3.
 Old Exam 1 Problems on Autocorrelation and
CrossCorrelation
 Fall 2009, Prob. 2.
 Fall 2008, Prob. 3.
 Fall 2006, Prob. 1. Key problem. Additional
Properties of Autocorrelation
 Fall 2004, Prob. 1. part (g)
 Exam 1 Problems on CrossCorrelation for CDMA
 Fall 2007, Prob. 1. OVSF
 Fall 2005, Prob. 1. 4PAM.
 Fall 2003, Prob. 1. 4PAM.
 Fall 2002, Prob. 1. QPSK, complex codes
 Fall 2000, Prob. 1. BPSK, basic problem.


Fall 2014 Exam Information

 Final Exam Fall 2014: Partial
Final Exam Solution;

 Exam 3: Exam 3 Solution;
Exam 3 Statistics; Exam 3 Statistics;

 Exam 2: Exam 2 Solution;
Exam 2 Statistics;

 Exam 1 Exam 1 Solution:
Exam 1 Solution



Fall 2013 Exam Information

 Final Exam Final Exam

 Exam 3 Exam 3 Solution:
Exam 3 Solution

 Exam 2 from Fall 2013. Exam
2 Solution: Exam 2
Solution.

 Exam 1 from Fall 2013: pdf
; Soln: Exam 1 Solution
; ; OnCampus Stats: Exam
1 Histogram ;


Fall 2012 Exams plus Solutions
 Final Exam for Fall 2012: pdf

 Exam 3 from Fall 2012: pdf
; Soln: Exam 3 Solution

 Exam 2 from Fall 2012: pdf
; Soln: Exam 2 Solution
; OnCampus Stats: Exam
2 Histogram ;

 Exam 1 from Fall 2012: pdf
; Soln: Exam 1 Solution;
OnCampus Stats: Exam 1
Histogram

Fall 2011 Exams plus Solutions

 Final Exam from Fall 2011: pdf

 Exam #3 from Fall 2011: pdf
Soln: Exam 3 Solution.

 Exam #2 from Fall 2011: pdf
Soln: Exam 2 Solution.
Histogram of scores: Histogram
 KEY MATERIAL FOR EXAM 2: Efficient
Digital Subbanding of 3 Signals, Multiplex3Sigs.m
 Final Words on Digital Subbanding: Final Words on
Digital Subbanding, Multiplex3SigsAlt.m

 Exam #1 from Fall 2011: pdf
Soln: Exam 1 Solution.
Histogram of scores: Histogram


Fall 2010 Exams plus Solutions

 Final Exam from Fall 2010: pdf

 Exam #3 from Fall 2010: pdf
Soln: Exam 3 Solution.
Histogram of scores: Histogram

 Exam #2 from Fall 2010: pdf
Soln: Exam 2 Solution.
Histogram of scores: Histogram

 Exam #1 from Fall 2010: pdf
Soln: Exam 1 Solution.
Histogram of scores: Histogram


Fall 2009 Exams plus Solutions

 Final Exam from Fall 2009: pdf

 Exam #3 from Fall 2009: pdf
and Exam 3 Solution ;
jpg.

 Exam #2 from Fall 2009: pdf
and Exam 2 Solution

 Exam #1 from Fall 2009: pdf
Soln: pdf.



Fall 2008 Exams plus Solutions

 Final Exam from Fall 2008: pdf.

 Exam #3 from Fall 2008: pdf
Soln: pdf. Histogram: jpg.

 Exam #2 from Fall 2008: pdf
Soln: pdf.

 Exam #1 from Fall 2008: pdf
Soln: pdf.



Fall 2007 Exams plus Solutions

 Final Exam from Fall 2007: pdf.

 Exam #3 from Fall 2007: pdf
Soln: pdf.

 Exam #2 from Fall 2007: pdf
Soln: pdf.

 Exam #1 from Fall 2007: pdf
Soln: pdf.


Fall 2006 Exams plus Solutions

 Final Exam from Fall 2006: pdf.

 Exam #3 from Fall 2006: pdf
Soln: pdf.

 Revised Exam #2 from Fall 2006: pdf Soln: pdf.

 Exam #1 from Fall 2006: pdf,
Soln: pdf. Histogram: pdf.


Fall 2005 Exams plus Solutions

 Final Exam from Fall 2005: pdf. Soln: pdf. Or: pdf.

 Exam #3 from Fall 2005: pdf,
Soln: pdf.

 Exam #2 from Fall 2005: pdf,
Soln: pdf. Histogram: pdf.

 Exam #1 from Fall 2005: pdf,
Soln: pdf. Histogram: pdf.


Fall 2004 Exams plus Solutions

 Final Exam from Fall 2004: pdf.

 Exam #3 from Fall 2004: pdf,
Soln: pdf.

 Exam #2 from Fall 2004: pdf,
Soln: pdf.

 Exam #1 from Fall 2004: pdf,
Soln: pdf.



Fall 2003 Exams plus Solutions

 Final Exam from Fall 2003: pdf.

 Exam #3 from Fall 2003: pdf,
Soln: pdf. Histogram
& Score Stats: pdf

 Exam #2 from Fall 2003: pdf,
Soln: pdf. Histogram
& Score Stats: pdf

 Exam #1 from Fall 2003: pdf,
Soln: pdf. Histogram
& Score Stats: pdf


Fall 2002 Exams plus Solutions

 Final Exam from Fall 2002: pdf.

 Exam #3 from Fall 2002: pdf,
Soln: pdf. Alternative
Soln to Problem 3 (c): pdf. Extra
Review Problem from recent QE: pdf. Only look
at 1st problem; second problem relevant to Final

 Exam #2 from Fall 2002: pdf,
Soln: pdf. Supplemental
Soln: pdf.

 Exam #1 from Fall 2002: pdf.
Solution to Prob. 2: pdf;
Supplemental Notes: pdf;
For Problem 3, see soln to Prob 1 of Exam 2 from Fall
99: pdf. Histogram of
Scores for Exam 1: E1Hist_Off.pdf;
E1Hist_On.pdf


Fall 2001 Exams plus Solutions

 Final Exam from Fall 2001: pdf.

 Exam #3 from Fall 2001: pdf
ps, Solution: pdf.

 Exam #2 from Fall 2001: pdf
ps, Solution: pdf

 Exam #1 from Fall 2001: pdf
ps, Solution: pdf

Fall 2000 Exams plus Solutions

 Final Exam from Fall 2000: pdf.
 Exam #3 from Fall 2000: pdf
ps, Solution: pdf Histogram: pdf

 Exam #2 from Fall 2000: pdf
ps, Solution: pdf Histogram: pdf

 Exam #1 from Fall 2000: pdf
ps Solution: pdf Histogram: pdf


Additional Practice Exams
 Final Exam from Fall 1999: pdf
ps Solution: pdf
 Final Exam from Fall 1998: pdf
ps Solution: pdf
 Exam #3 from Fall 1999: pdf
ps Solution: pdf
 Exam #3 from Fall 1998: pdf
ps Solution: pdf
 Exam #3 from Fall 1995 (only Probs 3 and 4 are
relevant to our Exam 3): pdf ps Solution: pdf
 Exam #3 from Fall 1996: pdf
ps Solution: pdf

 Exam #2 from Fall 1999: pdf
ps Solution: pdf
 Exam #2 from Fall 1998: pdf
ps Solution: pdf
 Exam #3 from Fall 1996: pdf
ps Solution: pdf
 Exam #2 from Fall 1995 (only Probs 1 and 3 are
relevant to our Exam 2): pdf ps Solution: pdf
 Exam #3 from Fall 1995 (only Probs 3 and 4 are
relevant to our Exam 2): pdf ps Solution: pdf

 Exam #1 from Fall 1998: pdf
ps Solution: pdf
 Exam #1 from Fall 1999: pdf
ps, Solution: pdf, pdf
