Spring 2023

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 Ed for announcements and communications with the course staff.

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: 30%

• Midterm 2: 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 Friday and due the next Friday at 11:59pm with a grace period of 2 days.

• 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. 

• 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 1/27/23 at 11:59pm

Homework 2, due 2/3/23 at 11:59pm

Homework 3, due 2/10/23 at 11:59pm

Homework 4, due 2/17/23 at 11:59pm

Homework 5, due 2/24/23 at 11:59pm

Homework 6, due 3/10/23 at 11:59pm

Homework 7, due 3/17/23 at 11:59pm

Homework 9, due 4/14/23 at 11:59pm

Lecture Notes: 

Lecture Playlist

01/17/23  Lecture1a (Intro)  Lecture1b (Discrete Signals review).

01/19/23 Lecture1b contd (LTI systems & Properties), Lecture2 Notes (DTFT intro)

01/24/23 Lecture 3b DTFT Properties & Convergence

01/26/23 Lecture 4  Z-Transform, notes

01/31/23 Lecture 5 DFT, notes

02/02/23 Lecture 6, DFT Properties, Circulant Convolutions

02/07/23 Lecture 7,  FFT, Notes

02/09/23 Lecture 8, Spectral Analysis using DFT 

02/14/23 Lecture 9, Time-Frequency Tiling, Gatspar Notes

02/16/23 Lecture 10, Intro to Wavelets

02/21/23 Lecture 11, Discrete Wavelet Transform

02/23/23 Lecture 12, Sampling

02/28/23 Lecture 13 Resampling

03/07/23 Lecture 14 Polyphase decomposition

03/09/23 Lecture 15 Filter Banks

03/4/23 Lecture 16 Filter Banks 

03/14/23 Lecture 17 Perfect reconstruction Filterbanks derivation etc.

03/16/23 Lecture 18 Practical ADC/DAC

03/21/23 Lecture 19 Practical ADC/DAC, Quantization

03/23/23 Lecture 20 Practical ADC Oversampling (finish), Transform Analysis of LTI systems

04/02/23 Lecture 21 Transform Analysis of LTI Systems (contd.)

04/04/23 Lecture 22 Transform analysis (finished)

04/11/23 MT2 review

04/13/23 Midterm 2

Discussion:

1. PDF, Solutions, Slides

2. PDF, Solutions Slides 

3. PDF, Solutions, Slides

4. Jupter Notebook (check ed)

5. Discussion Slides, Lab Slides

6. To be posted

7. To be posted

8. Slides