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Unformatted text preview: (a) Is the system linear? (b) Is the system timeinvariant? (c) Is the system causal? (d) Is the system stable? (e) What is the impulse response of the system? (f) What does the impulse response tell us about stability and causality? 3. Consider a discretetime system H whose output, given input { x [ n ] } n = , is given by y [ n ] = x [ n ] + ay [ n2]. For parts (a)(d), prove your claim using the properties summarized on page 4 of the lecture notes. (Hint: The input/output relationship can be recursively deduced.) (a) Is the system linear? (b) Is the system timeinvariant? (c) Is the system causal? (d) Say  a  < 1. Is the system stable? (e) What is the impulse response of the system? (f) What does the impulse response tell us about stability and causality? P. Schniter, 2010 1...
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 Fall '08
 Clymer,B
 Digital Signal Processing, Signal Processing

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