Convolution and Correlation

Convolution and Correlation

Convolution

This experiment focussed on calculating the linear convolution, circular convolution and linear convolution using circular convolution of an input signal x[n] with the impulse response h[n] and storing the output in y[n].

For linear convolution, the length of output signal is (N = L+M-1) where L is length of x[n] and M is length of h[n].

For circular convolution, the length of output signal is N = Max(L,M) where L and M have same meaning as above.

For linear convolution using circular convolution, the length of output signal is (N>= L+M-1).

Convolution finds its application in design and implementation of finite impulse response filters and image processing.

Correlation

Correlation is used to find the degree of similarity between two input signals.

This experiment focussed on calculating auto-correlation and cross correlation of two input signals.

If a signal is correlated with itself, the resulting signal is called an Auto-correlated signal. This was the first case. The results showed that autocorrelation signal is an even signal. The value of autocorrelated signal at n=0 gives the energy of the signal. The second case was auto-correlation of a delayed input signal. The result showed that auto-correlation of delayed input signal is same as autocorrelation of original input signal. The third case was cross-correlation of two signals.