This document is a compilation of my notes for ELE 632: Signals and Systems II at TMU. All information comes from my professor’s lectures, as well as the course textbook Linear Systems and Signals by B.P. Lathi.

Adam Szava - 2tor.ca

W2023

Table of Contents

Chapter 3: Discrete Signals and Systems

This is the same chapter we studied in ELE532, in this course we consider the same ideas but with discrete signals. For this reason, these notes will only include the new content and will not review previous content if it is left unchanged from ELE532.

What is a Discrete Signal?

A discrete signal is one which only exists at integer values of time $n$. For example, below:

Notice that:

• Discrete signals are denotes by $x[n]$ instead of $x(t)$ like in the previous course.
• Lines are drawn from the horizontal axis, up to the value of the signal at every point, but the value of the function is the tip of the line.
• The signal is still analog (meaning $x[n]$ can still be any continuous value, just the input time has to be an integer). Digital signals would require the signal to have a discrete output.
• We assume that if there is no point at $n = n_0$ that $x[n_0]=0$. So, this means there are infinitely many zero points in each direction which have a value of $0$ for this signal.

Obtaining a Discrete Signal

Discrete signals are often obtained by performing a uniform sampling of a continuous time signal. If you have some continuous signal $x(t)$ then the discrete signal based off of $x(t)$ sampled every $T_s$ seconds is:

$$ x[n]=x(nT_s) $$

Signal Operations

As with continuous signals, there are signal operations we can perform on discrete signals:

• Time-Shifting (no change from continuous case)