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# Lecture 1: Useful Signal Models for Discrete-Time

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Schedule :: Intro :: Signal Models for Discrete-Time :: Signal Operations :: Difference Equations :: Zero-Input :: Zero-State :: Natural & Forced :: System Stability

### Some Useful Signal Models for Discrete-Time

Discrete-time unit impulse :

Discrete-time unit step :

Discrete-time exponential
.

grows when , and decays when . Plot on unit circle.

What about when ? We can write this as for some . This is a rotating phasor.

Discrete-time sinusoid .

Note: Not all discrete-time sinusoids are periodic (unlike in the continuous-time case):

This is only possible if is an integral multiple of :

iff

or

Must therefore have be a rational number.

Note: There is non-uniqueness of discrete-time sinusoids. For example:

All these frequencies 'look' the same!
Exponentially damped sinusoid
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 16). Lecture 1: Useful Signal Models for Discrete-Time. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/1_1node1.html. This work is licensed under a Creative Commons License