Spring 2022

The purpose of this course website is to link to course documents, like lecture notes, homeworks, and labs, and to provide information about the course to the public. Always remember to check Piazza for announcements and communications with the course staff.

Instructor:

• Gopala Anumanchipalli

Office Hours

GSIs:

• Josh Sanz

• Suma Anand

Office Hours

Lab Assistant

• Ethan Guo

Lab Assistant Office Hours

Class Time and Location:

• M/W 4-6pm, Wheeler 222

GSI Section:

• F, 1:00 pm - 2:00 pm, Wheeler 102

Labs:

• 101: M, 10:00am - 11:00am, Cory 111

• 103: Tu, 5:00pm - 6:00pm, Cory 111

• 102: W, 1:00pm - 2:00pm, Cory 111

Tentative course outline:

A list of the topics that will be covered is given here, in the order that they will be covered. This may change based on time.

• Intro to DSP, discrete signals, LTI systems

• DTFT, properties, frequency response

• The z transform, properties, ROC, inversion, DFT

• Fast convolution, circular vs. linear convolution, overlap add/overlap save

• FFT, decimation in time/frequency, spectral analysis using the DFT

• Spectral analysis using the DFT, windowing, resolution tradeoffs, zero-padding

• STFT, T-F tiling, uncertainty principle

• Wavelets in continuous time, Haar expansions, Discrete Wavelet Transform using Haar basis

• T-F tilings of wavelet bases, Hilbert space view of signals, orthonormal bases

• Wavelets as multi-resolution ladder of spaces, connection to filters and filter banks

• Sampling, Aliasing, Reconstruction, DT processing of CT signals

• Resampling, CT processing of DT signals, interpretation of non-integer delays

• Filter design, FIR filters, windowing, intro to minimax optimal FIR filters (Parks-McLellan)

• Multirate identities, sampling rate conversions, polyphase decompositions and filter banks

• PRFBs, vector-space view of filter banks as orthonormal basis expansions

• Filter-banks and wavelets: Mallat’s Algorithm

• Transform analysis of LTI systems, Allpass, Min-Phase and Generalized Linear Phase

• Optimal FIR filters, Parks-McLellan Algorithm, Equiripple filters

• Oversampled ADC, noise shaping and quantization noise analysis

• Basics of image compression

• Sampling below the Nyquist Rate: finite rate of innovation sampling

• Compressed Sensing

• 2D-DFT

• Tomography

Approximate grading distribution:

• Homework (Weekly): 10%

• Labs: 15%

• Midterm 1 (March 2nd, during lecture): 30%

• Midterm 2 (April 13, during lecture): 30%

• Project: 15%

Homework Instruction:

• Weekly assignments consist of problem sets. In addition, there will be about 4-6 lab assignments consisting of programming using Jupyter notebook.

• Homework will be assigned each Wednesday and due the next Wednesday at 11:59pm.

• Homework submission will be in digital form through Gradescope. Here's a LaTeX template Miki_Lustig_hw01_sol.tex that produces this output after compilation. If you don't want to typeset, you can use a tablet computer or scan handwritten homework using a document scanning app for your smartphone.

• No late homework without prior consent from the instructor. Submission is time-stamped!

• Homework will be self graded. Self grading will be due the Monday after the solutions are released.

• Homework slip policy: the homework with the lowest grade will be dropped.

Homework:

Homework 1, due 1/26/22 at 11:59pm

Homework 2, due 2/4/22 at 11:59pm

Homework 3, due 2/9/22 at 11:59pm

Homework 4, due 2/16/22 at 11:59pm

Homework 5, due 2/23/22 at 11:59pm

Homework 6, due 2/28/22 at 11:59pm

Homework 7, due 3/10/22 at 11:59pm

Homework 8, due 3/17/22 at 11:59pm

Homework 9, due 3/31/22 at 11:59pm

Homework 10, due 4/7/22 at 11:59pm

Homework 11, OPTIONAL, "due" 4/11/22 at 11:59pm

Optional Compressed Sensing Exercise, due 5/6/22 at 11:59pm

Lecture Notes:

Lecture 1B and 1C, 1/19/22, Intro + DT Systems

Lecture 2, 1/24/22, LTI Systems

Lecture 3, 1/26/22, z-Transforms

Lecture 4a and 4b, 1/31/22, z-Transforms cont'd and DFT

Lecture 5a and 5b, 2/2/22, DFT

Lecture 6, 2/7/22, DFT + overlap-add

Lecture 7, 2/9/22, FFT

Lecture 8, 2/14/22, Spectral Analysis with the DFT

Lecture 9a and 9b, 2/16/22, Time frequency tiling and wavelets

Lecture 10, 2/23/22, Wavelets

Lecture 12, 2/28/22, Sampling

Lecture 13, 3/9/22, Resampling

Lecture 14, 3/14/22, Polyphase decomposition, Sampling example solution

Lecture 15, 3/16/22, Multirate Identities, Polyphase decomposition example

Lecture 16, 3/28/22, Filter Banks

Lecture 17, 3/30/22, Filter Banks (contd.)

Lecture 18, 4/4/22, Practical ADC/DAC

Lecture 19a, 19b 4/6/22, Practical ADC/DAC contd, Transform Analysis of LTI systems

Lecture 20a, 4/11/22, Transform Analysis (contd), Minimum Phase systems

Lecture 21a, 21b, 4/18/2022, Generalized Linear Phase, Filter Design

Lecture 22a, 22b, 4/20/2022, Optimal Filter Design, Image Compression

Lecture 23, 4/25/22, Compressed Sensing

Discussion Notes:

Discussion 1 Slides, Handout, Solutions, 1/21/22, LTI Systems

Discussion 2 Slides, Handout, Solutions, 1/28/22, z-Transforms

Discussion 3 Slides, 2/4/22, DFT

Discussion 4 Slides, 2/11/22, Lab 2, FFT, and DFT review

Discussion 5 Slides, 2/18/22, Spectrograms and STFT

Discussion 6 Slides, Lecture Notes, 2/25/22, Continuous and Discrete Wavelets

Midterm 1 Review Session, 2/28/22

Discussion 7 Slides, 3/4/22, Lab 3 Intro

Discussion 8 Slides, 3/11/22, Sampling

Discussion 9 Slides, 3/18/22, Resampling

Discussion 10 Slides, 4/1/22, Lab 4 & Polyphase Decomposition

Discussion 11 Slides, 4/8/22, Transform Analysis of LTI Systems and Midterm 2 Review

Midterm 2 Review Session, 4/11/22