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.
Take-Exam 3 coming soon. Tentative window for which it will be open: Nov. 24- Dec. 1. It should only take a few hours to do.
Prob. 1. OFDM. Prob. 2. Noble Identities. Prob. 3. Perfect Reconstruction Filters Banks. Two sets of notes for PRFB
with orthogonal filters of length equal to the number of channels: PRFB Key Notes Pt 1 PRFB Key Notes Pt. 1. ;
PRFB Key Notes Pt 2 PRFB Key Notes Pt. 2. ;
Matlab Hmwk #3 Due: Sunday, Dec. 1 by 11:59 PM at Brightspace MatlabHmwk3F24.pdf .
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
Very Helpful Handout: Conversion for 8-channel Case ; Convert from Tree Structure to Regular Structure Using Noble's Identities
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
Matlab Hmwk #2: 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 time-shift 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 4-6 material at course web site. Chaps 6, 11. (see syllabus for relevant sections.)
(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 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 cross-correlation --
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 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.
CDMAeg1.m, cdmaeg.m, gold1.m,
gold2.m; gold3.m.
Exam #1:
Exam 1: Monday, Sept 30 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. 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 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
Link for Purdue University Calendar for the 2024-2025
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 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 30, online via Brightspace.
Exam 2: October 30, online via Brightspace.
Exam 3: December 2, Take Home; Upload to Brightspace
Finals Week: December 9-13. Have Final open Dec.
10-11? 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 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 ;
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 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.
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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 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*: 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 time-shift 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 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
- Conversion for 8-channel Case ; Convert from Tree Structure to Regular Structure Using Noble's Identities
- 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=4 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^|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.
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