EE123: Digital Signal Processing, Spring 2025

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, 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: 25% 

• Midterm 2: 25% 

• Project: 25% 

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.

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

Homework:

HW1

HW2

HW3

HW4

HW5

HW6

HW7

HW8

HW9

Midterm Schedules:

Midterm 1: Tuesday, March 11th during class

Midterm 2: Thursday, April 17th during class

Lecture Notes: 

01/21/25 Lecture 1 Intro, DT Signals, Systems & Properties

01/23/25 Lecture 2 LTI Systems & DTFT, Class Notes

01/27/25 Lecture 3 DTFT Convergence & Z Transform, Class Notes

01/29/25 Lecture 4 Inverse Z- Transform Notes

02/04/25 Transform Analysis of LTI System

02/06/25 Transform Analysis, Generalized Linear Phase

02/11/25 Discrete Fourier Transform

02/13/25 Properties of DFT, Block Convolutions, Notes

02/18/25 FFT, Decimation in Time

02/20/25 Spectral Analysis using DFT, Notes

02/25/25 Time Frequency Tiling

03/04/25  Intro to Wavelets 

03/06/25 Discrete Wavelets

03/13/25 Sampling

03/18/25 Resampling

03/20/25 Polyphase Decomposition

04/01/25 Filter banks

04/08/25 Practical ADC/DAC

04/22/25 Image Compression

Discussion:

Disc1, Disc1_sol

Disc2, Disc2_sol

Disc3, Disc3_sol

Disc4, Disc4_sol

Disc5, Disc5_sol

Disc6, Disc6_sol, STFT_demo

Midterm1 Review, Disc7, Disc7_sol

Disc8, Disc8_sol

Disc9, Disc9_sol

Disc10, Disc10_sol

Midterm2 Review

Guest Lecture: