# ECE 538 Digital Signal Processing I - Fall 2019

## Meets MWF, 12:30 - 1:20 PM (ET), WANG 2579

### Announcements:

Final Exam: Thursday, Dec. 12. 3:30-5:30 pm. PHYS 203. Allowed 3 crib sheets + open book. Four problems. One relatively long problem on Perfect Reconstruction Filter Banks. The final lecture was a good review for the final exam and is now posted. Good luck with all your finals!

No Matlab Assignment 3. Matlab Hmwks 1 & 2 will count for 7.5% each for a total of 15% of final numerical grade.
Exam #3: Monday, Nov. 25: Exam 3 Solution ; Exam 3 Stats: Exam 3 Stats

Exam #3: Exam 3 Blank Copy ; Exam 3 Solution ; Exam #3: Monday, Nov. 25. Weeks 7-9 below. Text Chaps 6,11. Topics: Perfect Reconstruction Filter Banks (PRFB), FFT, DFT, Sampling in the Frequency Domain and Time-Domain Aliasing. No OFDM problem and NO efficient implementation of a PRFB. Look over Exam 3's from the like the past 7 years or so. Allowed single, double-sided crib sheet either handwritten or typed, no photocopying. Also: open book.

Matlab Hmwk #2.**NEW** Due: MONDAY, Nov. 18. MatlabHmwk2F19.pdf .
QMF (M=2 subbands) using SRRC Halfband Filter PRRC2chan.m;
Noble's Identities. Proofs of Noble's Identities ;
M=4 subbands based on Root-Raised Cosine Halfband Filter and Tree-Structure PRRC4chan.m
M=4 subbands based on Two-Tap {1,1} Halfband Filter and Tree Structure PR4chan.m
Summary Page for Two-Channel PR Filter Bank ; QMF using SRRC Halfband Filter
Analog Root-Raised-Cosine(SRRC)Spectrum: CT SRRC Spectrum ; To get half-band filter, replace time variable t by T_s /4 + n T_s /2
Efficient M=4 subbands PR Filter Bank Using Ideal Polyphase Filters (Truncated): PRFB4chanEffIdeal.m,
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

Exam #2: Exam 2 Blank Copy ; Exam 2 Solution ; ; Exam 2 Stats: Exam 2 Stats PlotTime14.m ; Friday, Oct. 25. Weeks 4-6 below. Text Chaps 6,11. Topics: D/A Conversion, CTFT-DTFT Relationship, Digital Upsampling, Digital Subbanding. Look over Exam 2's from the like the past 7 years or so. Allowed single, double-sided crib sheet either handwritten or typed, no photocopying. Also: open book.

Exam #1: Exam 1 Blank Copy ; Exam 1 Solution ; Exam #1 Stats: Exam 1 Stats Friday, Sept. 27. Weeks 1-3 below. Text Chaps 1-5. Look over Exam 1's from the like the past 7 years or so. No CDMA problem and No problem on Sampling a CT signal to get a DT System. Allowed single, double-sided crib sheet either handwritten or typed, no photocopying. Also: open book.

Matlab Hmwk #1: *NEW*: Friday, Oct. 4. On-campus students MUST turn in a paper print-out. Off-campus students can email me a pdf file or word doc. The problem is modeled around Prob 2.65 in the textbook but now 2.65 is only referred to for generating the Maximal-Length Shift-Register Sequence of length M=127, ACTUAL HOMEWORK PROBLEM ; M15.m . Recommend against using the matlab command "xcorr" to do the cross-correlation -- 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 M-1 values of ryx (where M is the code length) since those correspond to negative time-shifts and the problem only asks you to plot for positive time-shifts.

Link to Amazon Listing for Required Textbook ; Textbook_Cover
PDF of 3rd (OLD) Edition of Text: pdf.

Mat
TA Info: Kyle Willstatter
TA email: kwillsta@purdue.edu
TA Office: ??

Prof. Zoltowski's Tentative On-Campus Walk-In Office Hours: MWF 1:30-2:30 pm in MSEE 318 (right after class.)
Prof. Zoltowski's Tentativ Off-Campus Phone-In Office Hours: TR 12:00-1:30 pm in MSEE 318 or by appt.
Prof. Zoltowski Info: Office: MSEE 318. email: (PREFERRED) michael.zoltowski@gmail.com or mikedz@purdue.edu

Exam Dates:
Exam 1: September 27, Friday, in-class.
Exam 2: October 25, Friday, in-class.
Exam 3: November 25, Monday, in-class
Finals Week: December 9-14

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.

### Course Info

Professor: Mike Zoltowski
General Course Info for Fall 2019: pdf.
Course Syllabus for Fall 2019: pdf.

Exam Dates:
Exam 1: September 27, Friday, in-class.
Exam 2: October 25, Friday, in-class.
Exam 3: November 25, Monday, in-class
Finals Week: December 9-14.

Get the MATLAB Student Version from MathWorks (\$99 for FULLY FUNCTIONAL version of MATLAB including Simulink, Signal Processing Toolbox, DSP Systems Toolbox, Image Processing Toolbox, Control Systems Toolbox, Optimization Toolbox, Statistics Toolbox, and Symbolic Math Toolbox.
The IEEE Signal Processing Society.

### Module Notes and Demos

getspeech.m Needed for course M-files, this is the platform independent way to read the .wav files here.
Blank PDF Pages: Blank PDF pages
"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. Discrte-Time Signals and Systems Basics

Module 1a: Text Outline Scan; Text Chap. 1 Scan; Module 1a; Matlab demo: aliaseg.m,
Discrete-Time Signal Basics (301); Discrete-Time 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);
DT Convolution Derivation: Visuals;
Matlab Convolution Example: ConvEg.m
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 ; Text Chap. 2 Part 2 Scan ;

### Weeks 2. Autocorrelation and Cross-Correlation

Basics of Autocorrelation ; Text Chap. 2 Part 2 Scan ; Module 2 ;
Autocorrelation Properties: Proofs ; Additional Properties of Autocorrelation
Autocorrelation Pet Problem On many old exams :)
Matlab for Barker Codes: BarkerCodes.m
Matlab for MLSR PN sequence: M15.m
PPT file on GPS Basics with Key Figures: GPS Basics ; GPS Basics (pdf)
Link for GPS Tutorials: GPS Tutorial ; GPS Tutorial 2
Application To CDMA ; Application to CDMA Wireless Applications
CDMAeg1.m, cdmaeg.m, gold1.m, gold2.m; gold3.m.
Mixed_CT_DT_Autocorrelation.pdf ; Autocorrelation of CT Signal formed from DT Sequence

### Week 3. Z-Transform and DT Fourier Transform (DTFT)

Z-Transform Basics Basics of Z-Transform ; Z-Transform Basics Part 2: Connection to Laplace Transform ; 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,
Basics: Sinewave Input to LTI System
DT Fourier Transform: Properties Pairs: Text Tables 4.5, 4.6
Module 5: Module 5 Chap. 5 Notch Filters (pdf) ; zpgui3.m,
Note on All-Pass Filters; AllPassFilter.m,
Difference Equation for All-Pass Filters
Autocorrelaton Redux: Energy Density Spectrum: Energy Density Spectrum.

### Week 4. Properties of DTFT; CTFT-DTFT Relationship

CT Fourier Transform: Properties/Pairs; 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 CTFT-DTFT Relationship;
New Handout on Basic Sampling Theory Sample Time Invariance
CTFT-DTFT relationship for Sampled Sinewave
SampleSinewave.m ; SampleSincProduct.m ; SampleGaussian.m ; SampleSincProductAboveNyquist.m
Scan of First Section of Text Chap. 6; Scan of Undergrad 301 Text Chap. 7;
aliaseg2.m, aliaseg3.m, ; CTFT_DTFT_Upsample.m CTFT-DTFT Illustration
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. If you want, you can review them on your own while reading Text Chap. 6. Module 6, Module 7a, Module 7

### 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;
VIP Multirate Formulas: VIP_MultirateFormulas.pdf
Module 9: Module 9 ; upsample2eg2.m, upsamplex2eg2.m
Insights on Efficient Upsampling: Final Words on Efficient Upsampling; , ZOHeg2.m
Efficient Upsampling by 3 with Polyphase Filters: upsamplex3.m ; upsamplex3R.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 ; Multiplex3SigsR.m
Additional Insights Into Efficient Digital Subbanding: Post Upsampling Modulation
Final Words on Digital Subbanding: Final Words on Digital Subbanding, Multiplex3SigsAlt.m ; Multiplex4SigsAlt.m
Final Notes on Digital Subbanding: More Final Notes on Digital Subbanding ;
Multiplex3SigsReal.m ; Multiplex4SigsReal.m
Supplemental Notes on Hilbert Transform;
Supplemental Notes on Single Sideband Modulation; hilbert301eg.m
Supplemental Notes on VSB modulation; VSB Modulation with Complex Raised-Cosine 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 Two-Channel PR Filter Bank ; Summary Page 2-Channel PRFB ;
Notes on Square-Root Raised-Cosine Spectrum: Continuous-Time Square-Root Raised-Cosine Spectrum ; To get even-length symmetric half-band 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 Two-Channel (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 quantizeb2.m.

### Week 8. DFT and FFT: Fast Fourier Transform.

The DFT Matrix: The NxN DFT Matrix
Module 20: Decimation-in-Time 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,
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
Module 22: Module 22 timealias.m,

### Week 9. Sampling in the Frequency Domain.

My notes on Frequency Domain Sampling Notes (Chap 7) ;
SpectrumReconstruction.m VIP Help for Matlab Hmwk 3
Exam3Test.m VIP Help for Exam 3 for nice DFT problems exploiting time-domain aliasing
Ultimate DFT Pair ;
Text notes on Properties of the DFT.
Notes on DFT Based Processing.
DFT of a Finite-Length Sinewave.
sineDFTeg1.m sineDFTeg2.m, sineDFTeg3.m,
Basic DFT Pair.; Observations on DFT based processing of finite-length sinewaves ; CosineAliasing.m
Text notes on DFT based Linear Filtering.
Time Domain Aliasing of Multi-Pole Causal Signals.
Text notes on overlap-add and overlap-save AND DFT "tricks" for real-valued signals ; Computation Count for DFT Based Linear Filtering.
M-file for efficient Computation of DFT of two real-valued sequences plus efficient computation of 2N-pt DFT of real-valued sequence. EFF_FFT_Real.m
Illustration of overlap-save 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: Equi-ripple 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 Levinson-Durbin 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 Levinson-Durbin Algorithm. pdf. Minus sign on RHS of last eqn at bottom of last page should be plus sign.

### Week 15.

Module 29: pdf NoiseCancel.m.

### Week 16.

Module 30: pdf MinVarforSOS.m.
Module 31: pdf CancelTone.m.
Module 32: pdf FIRequalizer.m. Prob529.m.

### 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: *NEW*: Friday, Oct. 4. On-campus students MUST turn in a paper print-out. Off-campus students can email me a pdf file or word doc. 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 cross-correlation -- 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 M-1 values of ryx (where M is the code length) since those correspond to negative time-shifts and the problem only asks you to plot for positive time-shifts.

Matlab Hmwk #2.**NEW** Due: Friday, Nov. 15. 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 Root-Raised Cosine Halfband Filter and Tree-Structure PRRC4chan.m
M=4 subbands based on Two-Tap {1,1} Halfband Filter and Tree Structure PR4chan.m
Summary Page for Two-Channel PR Filter Bank ;
QMF using SRRC Halfband Filter
Analog Root-Raised-Cosine(SRRC)Spectrum: CT SRRC Spectrum ; To get half-band 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. OLD 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^|n-D|, n=0,1,...21, where D=(N-1)/2=10. Multiply X(w) in problem statement by linear phase term exp(-jDw) with D-10.
(c) Use N=101 rather than N=100, and use the sequence x[n]=a^|n-D|, n=0,1,...100, where D=(N-1)/2=50. Multiply X(w) in problem statement by linear phase term exp(-jDw) with D=50.
(e) Use the time-domain aliasing formula in (7.1.4) on page 450. Use three terms: x[n-N] + x[n] + x[n+N], for n=0,1,...N-1. 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

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

Notes on All-Pass Filters/Signals Notes on All-Pass Filters
Notes on Autocorrelation/Cross-Correlation (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 All-Pass Filters NotchFilterAllPassFilter.pdf
Fall 2008, Prob. 2; Fall 2004, Prob. 2, Fall 2002, Prob. 2.
Exam 1 Problems on Pole-Zero Cancellation ;
VIP Pole-Zero Cancellation Summary Notes Summary Notes for Pole-Zero 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
F 2007, Prob. 3, F2006, Prob. 2, F 2005, Prob. 3, F 2000, Prob. 3, F 1999, Prob. 3.
Old Exam 1 Problems on Autocorrelation and Cross-Correlation
F 2009, Prob. 2. F 2008, Prob. 3. F 2006, Prob. 1. F 2004, Prob. 1.
Exam 1 Problems on Cross-Correlation for CDMA
Fall 2007, Prob. 1. OVSF
Fall 2005, Prob. 1. 4-PAM.
Fall 2003, Prob. 1. 4-PAM.
Fall 2002, Prob. 1. QPSK, complex codes
Fall 2000, Prob. 1. BPSK, basic problem.

### Fall 2019 Exam Information

Exam 1: Exam 1 Blank Copy ; Exam 1 Tentative Solution
Exam #2: Exam 2 Blank Copy ; Exam 2 Solution ; Exam 2 Stats: Exam 2 Stats
Exam #3 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 Pole-Zero Cancellation Summary Notes Summary Notesfor Pole-Zero Cancellation

Exam 2: Exam 2 Blank Copy ; Exam 2 Solution ; Exam 2 Statistics

Exam 3: Nov. 30, Friday, in-class. 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 2017: Final Exam 2017 Partial Solution to 2017 Final Exam:Final Exam Soln 2017

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 time-domain aliasing, aspects of the bilinear transform
Final Exam: Tuesday, Dec. 13, 7-9 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

Final Exam Final Exam
Final Exam Solution Final Exam Solution

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 ; ; On-Campus 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 ; On-Campus Stats: Exam 2 Histogram ;

Exam 1 from Fall 2012: pdf ; Soln: Exam 1 Solution; On-Campus 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

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, in-class
Exam 3: Nov. 30, Friday, in-class. 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^|n-D|, n=0,1,...21, where D=(N-1)/2=10. Multiply X(w) in problem statement by linear phase term exp(-jDw) with D-10.
(c) Use N=101 rather than N=100, and use the sequence x[n]=a^|n-D|, n=0,1,...100, where D=(N-1)/2=50. Multiply X(w) in problem statement by linear phase term exp(-jDw) with D=50.
(e) Use the time-domain aliasing formula in (7.1.4) on page 450. Use three terms: x[n-N] + x[n] + x[n+N], for n=0,1,...N-1. 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 Root-Raised Cosine Halfband Filter and Tree-Structure PRRC4chan.m
M=4 subbands based on Two-Tap {1,1} Halfband Filter and Tree Structure PR4chan.m
Summary Page for Two-Channel PR Filter Bank ;
QMF using SRRC Halfband Filter
Analog Root-Raised-Cosine(SRRC)Spectrum: CT SRRC Spectrum ; To get half-band 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, in-class. Exam 1 Cover Sheet
VIP Pole-Zero Cancellation Summary Notes Summary Notesfor Pole-Zero Cancellation

Matlab Hmwk #1: *VIP Assigned*: Friday, Oct. 5. On-campus students MUST turn in a paper print-out. Off-campus 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 cross-correlation -- 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 M-1 values of ryx (where M is the code length) since those correspond to negative time-shifts and the problem only asks you to plot for positive time-shifts.

Comments, questions & suggestions regarding this web site to: Mike Zoltowski mikedz@ecn.purdue.edu