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== Question 3. == | == Question 3. == | ||
* An LTI system has unit impulse response h[n] =u[-n]. Compute the system's response to the input <math>x[n] = 2^{n}u[-n].</math> Simplify your answer until all <math> \sum</math> signs disappear.) | * An LTI system has unit impulse response h[n] =u[-n]. Compute the system's response to the input <math>x[n] = 2^{n}u[-n].</math> Simplify your answer until all <math> \sum</math> signs disappear.) | ||
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| + | == Answer == | ||
| + | <math> y[n] = x[n] * h[n] , where * is convolution,\</math> | ||
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| + | <math> \sum^{\infty}_{k=-\infty} 2^{k}u[-k]u[-n+k]</math> | ||
Revision as of 13:22, 10 October 2008
Question 3.
- An LTI system has unit impulse response h[n] =u[-n]. Compute the system's response to the input $ x[n] = 2^{n}u[-n]. $ Simplify your answer until all $ \sum $ signs disappear.)
Answer
$ y[n] = x[n] * h[n] , where * is convolution,\ $
$ \sum^{\infty}_{k=-\infty} 2^{k}u[-k]u[-n+k] $
