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when we know the impulse response of LTI system, by convolving the input with the impulse response of the system we can find the response of the system for that input (similarly you can find the response for any input with the convolution).
this is the mathematical function to find the similarities between the two signals (EX: in the RADAR correlation is used to comapre the transimited and echo signal of the target)
correlation is convolution of mirror image of the one signal with the other signal
for more details refer Digital Signal Processing by Oppenhium & Schaffer