ECE 538 Digital Signal Processing I: Fall 2023

Meets Live MWF, 12:30 - 1:20 PM (ET), WANG 2599

Announcements:



Final Home Exam: currently set to open up at Brightspace at 12:01 am on Monday, Dec. 11 and will remain open until 11:59 pm on Tuesday night. It is a 2 hour exam. It is 20 Multiple Choice, including one fun question. Be sure to have some scrap paper available. There will be some questions very similar to questions on Exams 1 and 2. There will be some fundamental questions on Perfect Reconstruction Filter Banks. There will be some questions on Frequency Domain Sampling and Time-Domain Aliasing, similar to those on old Exam 3's and some old finals AND similar to the examples we worked through in class in Lectures 43 and 44. Reminder: collaboration on the final is strictly prohibited.
VIP Sinc Function Products Handout for Continuous TimeHandout on Sinc Function Products
Useful Sinc Function Results for Discrete-Time UsefulSincFunctionResults.pdf

Key PRFB Notes for Exam 3 ; Key PRFB Notes for Exam 3 ; Add'l Key PRFB Notes for Exam 3 ; Key PRFB Notes for Exam 3 ;
Helpful Matlab code for Prob. 3: PR3DFTchan.m ; PR5DFTchan.m
Summary Notes on (a) Efficient implementation of Zero Inserts followed by Filtering and (b) Efficient implementation of Filtering by Decimation Efficient Implementation

Matlab Hmwk #3: P&M Prob. 7.29, 7.30. DUE DATE: Friday, Dec. 8 (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.
Notes relevant to Prob. 7.30: DFT of a Finite-Length Sinewave.
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.

Matlab Hmwk #2 Due: Tuesday, Nov. 21 at Brightspace by 11:59 pm. MatlabHmwk2F23.pdf .
QMF (M=2 subbands) using SRRC Halfband Filter PRRC2chan.m;
Noble's Identities. Proofs of Noble's Identities ;
Help converting Tree-Structure to Regular Structure: Tree Structure Conversion for 8-Channel Case ;
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
Key PRFB Notes for Exam 3 ; Key PRFB Notes for Exam 3 ; Add'l Key PRFB Notes for Exam 3 ; Key PRFB Notes for Exam 3 ;
Wiki Page on Subband Coding for Compression
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

Exam 2 Topics: (1) CTFT Properties/Pairs, (2) DTFT Properties/Pairs, (3) CTFT-DTFT Relationship, (4) Signal Reconstruction from Samples (Sampling Theory, Ideal D/A Conversion), (5) Aliasing, (6) VIP Multirate Formulas: (a) Zero-Inserts and (b) Decimation, (7) Digital Upsampling, (8) Fractional Time-Shift Filters (Ideal), (9) Digital Subbanding, (10) Single Sideband Modulation.

Exam 2 is scheduled for Monday, Oct. 30. Opens at like 9 am on Monday, Oct 30 and closes on Tuesday, Oct 31 at 10 pm. I am leaning toward 90 mins this time, rather than 75 mins. I want it go well :)


Matlab Hmwk #1: *NEW*: Wednesday, Oct. 4. This homework is modeled after 2.65 in the 4th Ed of 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 ; Old Prob 2.25 showing MLSR Circuits ; 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.

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.
Convolution video: Convolution

Exam #1: Friday, Sept 29 through Brightspace ; Weeks 1-3 below. Text Chaps 1-5. Look over Exam 1's from the like the past 10 years or so. No CDMA problem. Allowed single, double-sided crib sheet either handwritten or typed, no photocopying BUT important for you to have some blank sheets of paper to do workout on. Open book. NO PROCTOR NEEDED.

Format for Exam 1 ( Friday, Sept. 29) 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 time-window the exam will be open. Note on Finding n=o Point in Cross-Correlation

Exam 1 Material: Chaps 1,2 plus 3,4,5. I would recommend prioritizing these sections from Chaps 3-5 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


VIP Sinc Function Products Handout Handout on Sinc Function Products

Link for Purdue University Calendar for the 2023-2024 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: Qinbo Bai
TA email: bai113@purdue.edu
TA Office: ??

Prof. Zoltowski's Tentative On-Campus Walk-In Office Hours: MWF 11:30-12:20 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 29, online via Brightspace.
Exam 2: *NEW* October 30, online via Brightspace.
Exam 3: December 2(??), Take Home; Upload to Brightspace
Finals Week: December 11-16. Have Final open Dec. 11-12? 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.

Course Info

Professor: Mike Zoltowski
General Course Info for Fall 2023: pdf.
Course Syllabus for Fall 2023: pdf.

Exam Dates:
Exam 1: September 29, online via Brightspace.
Exam 2: NEW October 30, online via Brightspace.
Exam 3: December 2 (??), Take Home; Upload to Brightspace
Finals Week: December 11-16



Related Info and Links

Purdue ECN link for downloading MATLAB MathWorks

Module Notes and Demos

getspeech.m Needed for course M-files, 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. Discrete-Time Signals and Systems Basics

Module 1a: Module 1a; Matlab demo: aliaseg.m,
Discrete-Time 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 Cross-Correlation

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 Cross-Correlation:
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 Newton-Raphson 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.Z-Transform (Chap 3) & DT Fourier Transform (Chap 4); Frequency Response of LTI Systems (Chap 5)

Z-Transform Basics Basics of Z-Transform
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 Z-Transform Undergrad Review

Chap 4: Effect of Pole-Zero 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, All-Pass Filters
Module 5: Module 5 Chap. 5 Notch Filters (pdf) ; zpgui3.m,
Note on All-Pass Filters; AllPassFilter.m,
Difference Equation for All-Pass Filters

Exam 1 Problems on Notch Filter as Parallel Combination of Two All-Pass Filters NotchFilterAllPassFilter.pdf ; AllPassNew.m,
Exam 1 Problems on Pole-Zero Cancellation ;
VIP Pole-Zero Cancellation Summary Notes Summary Notes for Pole-Zero Cancellation; DTFT_DT_Rectangle.pdf ; PoleZeroCancellation.pdf ; Addl Notes on Pole-Zero Cancellation

Chap. 5: Autocorrelation/Cross-Correlation 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; CTFT-DTFT 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 CTFT-DTFT Relationship;
Analyzing Sampling Theory When Sampling Points do not include t=0. Sample Time Invariance
Handout on CTFT-DTFT Relationship from Undergrad Course with CTFT frequency variable in units of radians/s: CTFT-DTFT Relationship
CTFT_DTFT_Upsample.m CTFT-DTFT 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 ; upsample3eg1.m, upsamplex3eg2.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 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 ; Illustration of Binary Encoding 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,
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 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 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*: Monday, Oct. 2. 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 Homework 2 = Matlab Hmwk #2 Due: Monday, Nov. 20 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 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=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 #3: P&M Prob. 7.29, 7.30. DUE DATE: Friday, Dec. 10 (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


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 All-Pass Filters/Signals Notes on All-Pass Filters
Notes on Autocorrelation/Cross-Correlation (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 All-Pass Filters NotchFilterAllPassFilter.pdf
Exam 1 Problems on Pole-Zero Cancellation ;
VIP Pole-Zero Cancellation Summary Notes Summary Notes for Pole-Zero Cancellation; PoleZeroCancellation.pdf ; Addl Notes on Pole-Zero 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 Pole-Zero Cancellation Summary Notes Summary Notesfor Pole-Zero Cancellation

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

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 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 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


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


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 ;

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, 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