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# Lecture 1: Zero-State Respone

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

The steps are similar to what we did before: introduce delta function, then the impulse response, then the convolution sum.

Discrete time impulse function:

(Plot). We have the discrete-time impulse response :

Then is the solution when initial conditions are all zero:

We can find a numerical solution by substitution.

Zero-state response : Observe that we can write

Now we add up the response of the system to each of these outputs:

Same sorts of properties as we had before:

Commutative
Distributive
Associative
Shifting
Convolution. with impulse
Width:
If has length points and has length points, then has length points. (Note length given in points .)

For causal systems with causal inputs

Total response = zero-input component + zero-state component.

Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 16). Lecture 1: Zero-State Respone. 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_5node5.html. This work is licensed under a Creative Commons License