Impulse Response and Convolution

: Signal ProcessingImpulse Response and ConvolutionMarch 10, 2020 The Signals and system AbstractionDescribe asystem(physical, mathematical, or computational) by the wayit transforms aninput signalinto anoutput is particularly useful for systems that arelinear and input into additive parts and sum the responses to the [n]y[n]n=++++=n 1 0 1 2 3 4 5nnnn 1 0 1 2 3 4 5nSuperpositionBreak input into additive parts and sum the responses to the [n]y[n]n=++++=n 1 0 1 2 3 4 5nnnn 1 0 1 2 3 4 5nSuperposition works because the system system is linear if its Response to a weighted sum of inputs is equal tothe weighted sum of its responses to each of the [n]y1[n]andsystemx2[n]y2[n]the system is linear ifsystem x1[n] + x2[n] y1[n] + y2[n]

If a system is linear and time-invariant (LTI), its input-output relation is completely speci ed by the system’s impulse response h(t). 1. One can always nd the impulse response of a system. δ (t)system h 2. Time invariance implies that shifting the input simply shifts the output. δ (t−τ)system h 3.

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  System, Response, Impulse, Output, Impulse response

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