LTI Image Interpretation

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lauritachris
 
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LTI Image Interpretation

Post by lauritachris »

How would you interpretate this image about LTI systems and convolution?
Image

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adafruit_support_mike
 
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Re: LTI Image Interpretation

Post by adafruit_support_mike »

I'd interpret it as the standard convolution of a system whose impulse reponse is exponential decay and a square wave input, all done in discrete time.

h[X0] is how the system would respond to an impulse of size X at time 0. At time=0 the output is X, at time=1 the output is X/2, at time=2 the output is X/4. h[X1] is how the system would respond to an impulse of size X at time 1. At time=1 the output is X, at time=2 the output is X/2, at time=3 the output is X/4.

In general, the impulse response says the output to an impulse X at time=N will be X at time=N, X/2 at time=N+1, and X/4 at time=N+2.

The convolution (the last graph in the series) is the sum of all the impulse responses at specific times.. at time=2, we have the X/4 part of the impulse response to the impulse at time=0, the X/2 part of the response from the impulse at time=1, and the X part of the impulse response to the impulse at time=2.

For an LTI system whose impulse response is exponential decay, the output that corresponds to a square wave will be a rising curve that asymptotically approaches some value until you reach the last impulse in the square wave, then a falling curve that asymptotically approaches zero.

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