EE 313 Linear Systems and Signals - Lecture 8

Before Lecture

• Spring 2026 courses
  • Machine Learning and Communication Systems
  • Speech and Audio Processing

Announcements

• Homework #5 is due on Friday, Oct. 17, 2025, by 11:59pm

Lecture

• Lecture slides on Discrete-Time Convolution in PowerPoint format.
  
  • Notes: Part 1 and Part 2
  • Demo: Signal Processing First Discrete-Time Convolution

• Fall 2018: Lecture notes by Mr. Houshang Salimian (TA): Part 1 and Part 2

Supplemental

• Part 1
  • Review of FIR Filters
  • Squaring Block, Not Linear
  • Ideal Delay, Homogeneity Property Part I and
  • Part II
• Part 2
  • Review of LTI Properties: Part I and Part II
  • FIR Filters and Role of Initial Conditions on LTI Properties
  • Decomposing a Discrete-Time Signal into Weighted Sum of Impulses
• Part 3
  • Demo. Demo two-point averaging filter
  • Demo. Signal Processing First Discrete-Time Convolution

• Part 1:
  • Time invariance system property
  • Linearity system property
  • Linearity under observation
  • FIR filter initial conditions for linearity and time invariance to hold
  • Time Invariance Under Observation -- when observing signals for n ≥ 0, initial conditions must be zero as a necessary but not sufficient condition for time invariance to hold
• Part 2:
  • Review of LTI properties
  • Discrete-Time convolution formula
  • Demo: SP First Discrete-time Convolution
  • Handout: Convolution of two rectangular pulses (the discrete-time example is after the continuous-time example)

• Linearity and shift-invariance properties
• Unit delay system properties when observing for n ≥ 0: homogeneity and additivity
• Initial conditions for LTI FIR properties to hold
• Derivation of discrete-time convolution
• Highest discrete-time frequency

Last updated 10/27/25. Send comments to Prof. Evans at bevans@ece.utexas.edu