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convolution sum

The formula y[n] = sum_k x[k]h[n-k], computing an LTI system's output from its input and impulse response.

The convolution sum $y[n] = x[n]*h[n] = \sum_k x[k]\,h[n-k]$ computes an LTI system's output $y[n]$ from its input $x[n]$ and impulse response $h[n]$ , derived from the sifting property together with linearity and time-invariance.

See also

impulse response LTI system

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