L10-11+Notes

L10-11+Notes - Barrett - CS450 Winter 2011 Lecture 10-11...

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Barrett - CS450 Winter 2011 Lecture 10-11 http://www.jhu.edu/signals/convolve/ ) 1. Linear shift-invariant systems: • What is the superposition principle? The multiplicative property? The additive property? Show it graphically. Show it mathematically. • Is the system y ( n ) = nx ( n ) linear? Is the system y ( n ) = Ax ( n ) + B linear? • What is shift-invariance? Show it graphically. Show it mathematically. • In a particular system, Π ( π t ) -> cosech (2 t ) and ( ( t-a )) -> cosech (2 πα t ). Is the system shift-invariant? • What is a Dirac delta function (Impulse)? Define it graphically and mathematically. • Define the “impulse response” of a system. • Why is the impulse response important in terms of being able to characterize a system. 2. Harmonic Functions • How do we represent harmonic functions (sines and cosines) as complex exponentials? • What is the transfer function K ( ω )? Is it dependent or independent of space/time - and why is this significant in terms of being able to characterize a system using K ( ω )? • If I input a harmonic signal into a system, will it always produce a harmonic output?
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L10-11+Notes - Barrett - CS450 Winter 2011 Lecture 10-11...

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