Correlation is a statistical measure of how similar or different two waveforms , signals or random processes are. Correlation is used to compare the similarity of two signals, the result is a signal that shows this similarity and reaches its maximum at the time when the two signals match best. Correlation can be used to measure the delay of a certain system. From mathematical point of view correlation is:
E[x(t)y(t)]=∫x(Θ)y(t+Θ)dΘ
Convolution is the operation / transformation that governs the input and output relationship in Linear and Time Invariant system. It is an integral that expresses the amount of overlap of one function as it is shifted over another function. It is used to compute the output of a certain LTI system when a certain input signal is applied to it and its impulse response is known. So we can also say that convolution is kind of a filtering operation. The convolution of two function is:
x(t)*y(t)=∫x(Θ)y(t-Θ)Dθ
Convolution is specifically used for the multiplication of continuous and discrete time signal in time domain and valid for LTI system but correlation is matching and comparison of signal. In the case of a matched filter, correlation and convolution becomes the same.
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