Announcements:
It may be helpful to review material from the
undergraduate junior level course on signals and systems:
ECE 301 Signals and Systems We will look at notes posted there, especially towards the beginning of the course.
Matlab Hmwk #2: *NEW*: Due: Friday, Nov. 15. Take my code
for Single Sideband Modulation based Digital Subbanding for 4 signals below
and generalize it for 5 signals. We will provide the 5 signals to you,
as everyone's program will be run to make sure they work, i.e., play back
the correct 5 original signals. So you will need to upload your code
so that we can run it. You will also need to plot the phase of each of the
4 fractional timeshift filters, and the magnitude as well. ALSO: plot the "before" DTFT and "after" DTFT for each signal as in my code.
"Before" means DTFT of original signal. "After" means DTFT after each signal has been separated and restored back to
its original sampling rate (and centered back at omega =0). Put together all the plots in a brief report  no need to write conclusions.
Multiplex4SigsColor.m Matlab code for multiplexing 4 Signals using SSB Modulation
VIP Sinc
Function Products Handout for Exam 2Handout on Sinc
Function Products
Exam 2 Topics: Weeks 46 material at course web site. Chaps 6, 11. (see syllabus for relevant sections.)
(1) CTFT Properties/Pairs, (2) DTFT
Properties/Pairs, (3) CTFTDTFT Relationship, (4) Signal
Reconstruction from Samples: Sampling Theory, Ideal D/A
Conversion, (5) Aliasing, (6) VIP Multirate Formulas: (a)
ZeroInserts and (b) Decimation, (7) Digital Upsampling,
(8) Fractional TimeShift Filters (Ideal), (9) Digital
Subbanding, (10) Single Sideband Modulation.
Exam 2 is scheduled for Wednesday, Oct. 30.
I am leaning toward 90 mins this time, rather than 75
mins. I want it go well :)
Matlab Hmwk #1: *NEW*: Friday, Oct. 4. This homework
is modeled after 2.65 in the textbook but 2.65 is only
referred to now for how to create the Maximal Length
Shift Register Sequence of length 127:
ACTUAL HOMEWORK PROBLEM ; M15.m .
Textbook Prob. 2.65 ;
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 and directly below: 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.
CDMAeg1.m, cdmaeg.m, gold1.m,
gold2.m; gold3.m.
Exam #1:
Exam 1: Monday, Sept 30 through Brightspace ; Weeks 13 below.
Text Chaps 15. Look over Exam 1's from the like the
past 10 years or so. No CDMA problem. VIP: important for you to have blank
sheets of paper to do workout on. Open book. NO PROCTOR
NEEDED. VIP: collaboration is strictly prohibited and will result in a failing grade.
Format for Exam 1 ( Monday, Sept. 30) will be 15
multiple choice questions in 75 minutes. The exam is
open book BUT I think a crib sheet is more important:
you learn a lot through the effort of summarizing key
points and key equations in a concise, condensed and
ordered fashion. Plus, you don' have time to be paging
through the book during the exam, although you can
demarcate certain tables in your book. I don't plan to
use Examity or Respondus. You will take the exam online
through Brightspace. The only thing we need to discuss
is the timewindow the exam will be open. Note on Finding n=o
Point in CrossCorrelation
Exam 1 Material: Chaps 1,2 plus 3,4,5. I would recommend
prioritizing these sections from Chaps 35 in the
textbook: Chap 3: 3.2, 3.4.3, 3.5.3, 3.5.4; Chap 4: 4.2.3,
4.4; Chap 5: 5.2, 5.3, 5.4
Link for Purdue University Calendar for the 20242025
Academic Year
Link to Amazon Listing for Required Textbook ; Textbook_Cover
PDF of 4th Edition of Text: pdf
; Proakis
& Manolakis 4th Ed Solutions Manual ; Textbook_Cover
PDF of 3rd (OLD) Edition of Text: pdf.
TA Info: Hashan Kavinga
TA email: hweeraso@purdue.edu
TA Office: ??
Prof. Zoltowski's Tentative OnCampus WalkIn Office
Hours: MWF 11:3012:20 pm in WANG EE Lobby Area (right
before class.)
Prof. Zoltowski Info: Office: MSEE 318. email:
(PREFERRED) michael.zoltowski@gmail.com or
mikedz@purdue.edu
Exam Dates:
Exam 1: September 30, online via Brightspace.
Exam 2: October 30, online via Brightspace.
Exam 3: December 2, Take Home; Upload to Brightspace
Finals Week: December 913. Have Final open Dec.
1011? 90 mins
It may be helpful to review material from the
undergraduate junior level course on signals and systems:
ECE 301 Signals and Systems We may occasionally look at
notes posted there, especially towards the beginning of
the course.
Your primary homework assignment is to solve my old
exams (posted below) without looking at the solutions in a
timed setting. You can look at the solutions before and
after attempting the exam, but it is important to work
through them without looking at the solution. A few
students have asked for homework problems out of the
textbook, but I think the best homework, in terms of
preparing for the exam, is to work through my old exams.
Some history and miscellaneous course information:
This course emphasizes applications of Digital Signal
Processing (DSP) in compact disc (CD) players, wireless
communictions including OFDM and CDMA, radar, and speech
processing. Professor Zoltowski has taught this course the
Fall of every year since 1990.

Module Notes and Demos
 getspeech.m Needed for
course Mfiles, this is the platform independent way to
read the .wav files here.
 Link to lots of wave files TI
Wav Files
 Blank PDF Pages: Blank PDF
pages
 "WAV"files : [ enter(female)
enter(male) erase(female) help(female) w(female) zero(female) one(male) ]

Weeks 1. DiscreteTime Signals and Systems Basics
 Module 1a: Module 1a;
Matlab demo: aliaseg.m,
DiscreteTime Signal
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);
 DT
Convolution Derivation: Visuals;
 For additional examples on DT convolution, see my old
Exam 1's from ECE 301 Signals and Systems at the link
above. The 2nd problem on recent Exam 1's dealt with DT
convolution, e.g., see Prob. 2 on Exam 1 from SP15.
 Supplementary Material on LTI Systems from Undergrad
Course:
 Matlab Convolution Example: CleverConv.m
 Impulse
Properties Plus Convolving with Delta Function (301);
 Implications of
Linearity and TI as Pertaining to Convolution (301);
 Impulse Response
of Nonrecursive Difference Eqns;
 Approximate CT
Convolution via DT Convolution;

Weeks 2. Autocorrelation and CrossCorrelation
 Basics of
Autocorrelation ; Text
Chap. 2 Part 2 Scan ;
 Module 2: Autocorrelation
Example: PN Sequence ;
 Matlab for Barker Codes: BarkerCodes.m
 Matlab for MLSR and Frank Codes: FrankCodeVsMLSR.m
 AutocorrelationProperties
 Autocorrelation
Pet Problem on many old exams
 VIP Pet Problem on Complementary Sequences Example
Autocorrelation Problem
 Mixed_CT_DT_Autocorrelation.pdf
Autocorrelation: CT Signal formed from DT Signal
 Supplementary Material on Applications of
CrossCorrelation:
 Application To CDMA
; Application to CDMA Wireless Communications
 CDMAeg1.m, cdmaeg.m, gold1.m,
gold2.m; gold3.m.
 Synchronous CDMA Matlab Example: walsh_cdma_eg.m;
 GPS Basics with Key Figures: GPS Basics
 Link for how to use NewtonRaphson Search to Solve
GPS Equations Newton Method for GPS ;
 Link for Various Amplifier Classes Amplifier
Classes ;
 Link for GPS Tutorials: GPS
Tutorial ; GPS
Tutorial 2
Week 3.ZTransform (Chap 3) & DT Fourier
Transform (Chap 4); Frequency Response of LTI Systems
(Chap 5)
 ZTransform Basics Basics of ZTransform
 ZT Basics Part 2: Connection to
Laplace Transform
 Module 3: Module 3
 Supplementary Material on ZT below will not be
covered in class.
 Addendum: Module 3
Addendum
 ECE
438 Notes on ZTransform Undergrad Review

 Chap 4: Effect of PoleZero Locations on Frequency
Response
 Basics: Sinewave Input to LTI System
 Module 4: Module 4
 Chap. 5
Graphical Frequency Response (pdf); notcheg2.m

 Chap. 5: Notch Filters, AllPass Filters
 Module 5: Module 5 Chap. 5 Notch Filters
(pdf) ; zpgui3.m,
Note on AllPass Filters;
AllPassFilter.m,
 Difference
Equation for AllPass Filters

 Exam 1 Problems on Notch Filter as Parallel
Combination of Two AllPass Filters NotchFilterAllPassFilter.pdf
; AllPassNew.m,
 Exam 1 Problems on PoleZero Cancellation ;
 VIP PoleZero Cancellation Summary Notes Summary
Notes for PoleZero Cancellation; DTFT_DT_Rectangle.pdf
; PoleZeroCancellation.pdf
; Addl Notes on
PoleZero Cancellation

 Chap. 5: Autocorrelation/CrossCorrelation Redux
 DT Fourier
Transform: Properties Pairs: Text Tables 4.5, 4.6
 Energy Density Spectrum: Energy Density
Spectrum.
 VIP Pet Problem on Complementary Sequences Example
Autocorrelation Problem

Week 4. Properties of CTFT; CTFTDTFT Relationship;
Ideal D/A Conversion
 CT Fourier
Transform: Properties/Pairs
 Dirac Delta
Function Properties;

FourierTransformEgs.m ;
FourierTransformExamples.m
 DT Fourier
Transform: Properties/Pairs;
 ECE 301
Handout on DTFT
 DT Fourier
Transform: Properties Pairs including Sinewaves
 The two sets of notes below will be covered in
parallel.
 Ideal D/A
Conversion ; Derivation
of CTFTDTFT Relationship;
 Analyzing Sampling Theory When Sampling Points do not
include t=0. Sample
Time Invariance
 Handout on CTFTDTFT Relationship from Undergrad
Course with CTFT frequency variable in units of
radians/s: CTFTDTFT
Relationship
 CTFT_DTFT_Upsample.m
CTFTDTFT Illustration
 SampleSinewave.m ;
SampleSincProduct.m
; SampleGaussian.m ; SampleSincProductAboveNyquist.m
aliaseg2.m, aliaseg3.m


Week 5. D/A Conversion Featuring Digital Upsampling
 Digital Upsampling Introduction Initial Insights
into Digital Upsampling ; Note on Fractional Time
Shift
 Module 8: Intro to Digital
Upsampling upsamplex2eg1.m;
upsamplex2eg2.m;
 VIP Multirate Formulas: VIP_MultirateFormulas.pdf
 Module 9: Module 9 ;
upsamplex3eg1.m ;
upsamplex3eg2.m ;
upsamplex4eg2.m ;
 Insights on Efficient Upsampling: Final Words
on Efficient Upsampling; , ZOHeg2.m

Week 6: Digital Subbanding and SSB Filtering
 VIP Multirate Formulas: VIP_MultirateFormulas.pdf
 Efficient Digital Subbanding: Key Insights Post Upsampling
Modulation
 Multiplex3Sigs.m ; Multiplex3SigsR.m ; Multiplex4SigsAlt.m ;
 Hilbert
Transform and SSB modulation; hilbert301eg.m
 Undergrad Notes on SSB
Modulation in Analog Domain; hilbert301eg.m

Bandlimited Hilbert Transformer
 SSB Based Digital Subbanding: SSB Based Digital
Subbanding ;
 Multiplex3SigsReal.m
; Multiplex4SigsReal.m
; Multiplex4SigsColor.m
 Transmultiplexers: Digital Subbanding Efficient
Digital Subbanding of 3 Signals,
 Final Words on Digital Subbanding: Final Words on
Digital Subbanding

End of Lecture 2 Material for Exam 2 Fall 2023

 Below are Supplemental Notes FYI: Not Covered in
Class
 Supplemental Notes on
Single Sideband Modulation

SupplementalNotes on VSB modulation;
 VSB
Modulation with Complex RaisedCosine Filter;


Week 7: Perfect Reconstruction Filter Banks
 Perfect Reconstruction Filter Banks (PRFB): Introductory Notes
on PRFBs ; Efficient Implementation of Analysis
Side: Efficient
Implementation of Analysis Side inc Ideal Case ;
Efficient Implementation: PRFB4chanNewEff2017.m
 Notes on TwoChannel PR
Filter Bank ; Summary
Page 2Channel PRFB ;
 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 ;
 Wkipedia
Page on JPEG 2000 (Digital Cinema)
 Wkipedia
Page on Subband Coding (Compression)
 Image_compression_wavelets_jpeg2000.pdf



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

 Module 13: Analysis of
Quantization Error ; Illustration of Binary
Encoding 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

Week 9. Sampling in the Frequency Domain.
 My notes on
Frequency Domain Sampling Notes (Chap 7) ;
 Module 22: Module 22 timealias.m;
 SpectrumReconstruction.m
VIP Help for Matlab Hmwk 3
 Exam3Test.m VIP Help for
Exam 3 for nice DFT problems exploiting timedomain
aliasing
 Ultimate DFT Pair ;
 Text notes on
Properties of the DFT.
 Notes on DFT
Based Processing.
 DFT of a
FiniteLength Sinewave.
 sineDFTeg1.m sineDFTeg2.m, sineDFTeg3.m,
 Basic DFT Pair.; Observations on
DFT based processing of finitelength sinewaves
; CosineAliasing.m
 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
 Fourier
Transform of Finite Length Sinewaves
 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 for Previous Offering
 Matlab Hmwk #1: *NEW*: Friday, Oct. 4. This homework
is modeled after 2.65 in the textbook but 2.65 is only
referred to now for how to create the Maximal Length
Shift Register Sequence of length 127: ACTUAL HOMEWORK PROBLEM ; 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: *NEW*: Friday, Nov. 15. Take my code
for Single Sideband Modulation based Digital Subbanding for 4 signals
and generalize it for 5 signals. We will provide the 5 signals to you,
as everyone's program will be run to make sure they work, i.e., play back
the correct 5 original signals. So you will need to upload your code
so that we can run it. You will also need to plot the phase of each of the
4 fractional timeshift filters, and the magnitude as well. More details to come.

 Matlab Hmwk #3 Due: Monday, Nov. ?? by 11:59 PM at Brightspace MatlabHmwk2F23.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
 Conversion for 8channel Case ; Convert from Tree Structure to Regular Structure Using Noble's Identities
 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=3 subbands PR Filter Bank Using Length 4 sinewaves
as subband filters: PR4DFTchan.m,
 M=5 subbands PR Filter Bank Using Length 5 sinewaves
as subband filters: PR5DFTchan.m
 SubbandCoding
 Wavelet Based Compression
 Wavelet Denoising

 Matlab Hmwk #4: P&M Prob. 7.29, 7.30. May be Optional of Extra Credit 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 ; VIP: use Matlab code below

SpectrumReconstruction.m Key Matlab code for
Prob. 7.29
 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.

VIP Information for Exam 1

 Useful Sinc Function Results UsefulSincFunctionResults.pdf
 Add'l Table of DTFT Pairs Including Sinewaves
DT Fourier
Transform: Properties Pairs inc. Sinewaves
 Sinewaves thru LTI System Sinewaves Thru LTI
Systems (covered) ; Sinewave Input to
LTI System

 Notes on AllPass Filters/Signals Notes on AllPass Filters
 Notes on Autocorrelation/CrossCorrelation
(covered)
Autocorrelation Properties/Proofs ; VIP Pet
Problem on Complementary Sequences Example
Autocorrelation Problem ; Energy Density
Spectrum

 Exam 1 Problems on Notch Filter as Parallel
Combination of Two AllPass Filters NotchFilterAllPassFilter.pdf
 Exam 1 Problems on PoleZero Cancellation ;
 VIP PoleZero Cancellation Summary Notes Summary
Notes for PoleZero Cancellation; PoleZeroCancellation.pdf
; Addl Notes on
PoleZero Cancellation

Fall 2019 Exam Information

 Final Exam: Final Exam
2019
 Exam 1: Exam 1 Blank Copy
; Exam 1 Tentative Solution
 Exam #2: Exam 2 Blank Copy
; Exam 2 Solution ; Multiplex4Cosines.m,
 Exam #3 Exam 3 Blank Copy
; Exam 3 Solution ;
Exam 3 Stats: Exam 3
Stats

Fall 2018 Exam Information

 Final Exam: Final Exam
2018
 Exam 1: Exam 1 Blank Copy
; Exam 1 Student
Solution
 VIP PoleZero Cancellation Summary Notes Summary
Notesfor PoleZero Cancellation

 Exam 2: Exam 2 Blank Copy
; Exam 2 Solution ;SampleGaussianNew.m,

 Exam 3: Nov. 30, Friday, inclass. Exam 3 Blank Copy ; Exam 3
Solution Exam 3 Solution
; Exam 3 Statistics Exam
3 Stats

 VIP Sinc Function Products Handout Handout on Sinc
Function Products

Fall 2017 Exam Information

 Final Exam Fall 2017: Final
Exam 2017 ; Final Exam
Solution;
 Exam 1: Exam 1 ; Exam 1 Solution; Exam 1 Statistics;
Addendum Notes;

 Exam 2: Exam 2 ; Exam 2 Solution; Exam 2 Statistics

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

Fall 2016 Exam Information

 Final Exam Fall 2016: Final
Exam 2016 ; Final
Exam Solution;
 Final Exam: 4.5 problems :) OFDM, efficient digital
upsampling, frequency domain sampling and timedomain
aliasing, aspects of the bilinear transform
 Final Exam: Tuesday, Dec. 13, 79 pm, PHYS 223
 Example of Bilinear Transform Problems: Final Fall
2008, Exam 2 Fall 2005, Exam 3 Fall 2004, Exam 2 Fall
2002, Exam 2 Fall 2001, Exam 2 Fall 2000
 Exam 3: Exam 3; Exam 3
Solution: Exam 3 Solution
; Exam 2 Statistics:
Exam 3 Statistics
 Exam 2: Exam 2; Exam 2
Solution: Exam 2 Solution
; Exam 2 Statistics: Exam 2 Statistics
 Exam 1: Exam 1 ; Exam 1 Solution; Exam 1 Statistics;

Fall 2015 Exam Information


 Final Exam Fall 2015: Final
Exam 2015; Final
Exam Solution 2015; FinalExamProb.m;
FinalExamProb2.m; FinalExamAliasing.m;

 Final Exam Fall 2015: Final
Exam 2015; Final
Exam Solution 2015; FinalExamProb.m;
 Final Exam Fall 2015: Final
Exam 2015;
 Exam 3: Exam 3 ; Exam 3 Solution; Exam 3 Statistics;
 Exam 2: Exam 2 ; Exam 2 Solution; Exam 2 Statistics;
 Exam 1: Exam 1 ; Exam 1 Solution; Problem 1 Addendum;


Fall 2014 Exam Information

 Final Exam Fall 2014: Final
Exam 2014;
 Final Exam Solution;

 Exam 3: Blank Exam 3; Exam 3 Solution; Exam 3 Statistics; Exam 3 Statistics;
 Partial Final Exam
Solution;

 New Handout on Basic Sampling Theory Sample Time
Invariance
 Exam 2: Exam 2 Blank; Exam 2 Solution; Exam 2 Statistics;

 Exam 1 Exam 1 Solution:
Exam 1 Solution



Fall 2013 Exam Information

 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

 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 ;


Fall 2011 Exams plus Solutions

 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
 Final Exam: Monday, Dec. 10, at 1 pm in MSEE B012.
Partial Solution to 2017 Final Exam:Final Exam Soln 2017
 Exam 3: November 30, Friday, inclass
 Exam 3: Nov. 30, Friday, inclass. Exam 3 Blank Copy ; Exam 3
Solution Exam 3 Solution
; Exam 3 Statistics Exam
3 Stats


 Matlab Hmwk #3: P&M Prob. 7.29, 7.30. DUE
DATE: Friday, Dec. 7 (last day of classes) 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 ; VIP: use Matlab code below

SpectrumReconstruction.m Key Matlab code for
Prob. 7.29
 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.

 Exam 2: Exam 2 Blank Copy
; Exam 2 Solution ; Exam 2 Statistics
 VIP Sinc Function Products Handout Handout on Sinc
Function Products

 Matlab Hmwk #2.**VIP** Due: Monday, Nov. 19. MatlabHmwk2F18.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

 Exam 1: September 28, Friday, inclass. Exam 1 Cover Sheet
 VIP PoleZero Cancellation Summary Notes Summary
Notesfor PoleZero Cancellation

 Matlab Hmwk #1: *VIP Assigned*: Friday, Oct. 5.
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
; 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.

