lecture8 - EE313 Linear Systems and Signals Spring 2009...

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EE313 Linear Systems and Signals Spring 2009 Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin Discrete-Time Convolution
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8 - 2 Linear Time-Invariant System Any linear time-invariant system (LTI) system, continuous-time or discrete-time, can be uniquely characterized by its Impulse response : response of system to an impulse Frequency response : response of system to a complex exponential e j 2 π f for all possible frequencies f Transfer function : Laplace transform of impulse response Given one of the three, we can find other two provided that they exist
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8 - 3 Example Frequency Response System response to complex exponential e j ϖ for all possible frequencies ϖ where = 2 π f Passes low frequencies, a.k.a. lowpass filter ϖ | H ( ϖ )| ϖ p ϖ s s p passband stopband stopband ϖ H ( ϖ )
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8 - 4 Discrete-time Convolution Output y [ n ] for input x [ n ] Any signal can be decomposed into sum of discrete impulses Apply linear properties Apply shift-invariance Apply change of variables y [ n ] = h
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lecture8 - EE313 Linear Systems and Signals Spring 2009...

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