Discrete Convolution & Discrete Correlation

Convolution is used to find the output of a system using input signal and impulse response. We have studied three cases: Linear convolution, Circular Convolution and Linear Convolution using Circular Convolution. The input signal x(n) and impulse response h(n) were entered to the computer program. The output signal y(n) was verified with the calculated values. It is observed that in LC, the length of output signal is N=L+M-1 where ‘L’ and ‘M’ are lengths of x(n) and h(n) respectively. While in CC, N=Max(L,M) and in case of LC using CC, N≥L+M-1.

Correlation is used to find the degree of similarity between two signals. In case 1, we analyse auto-correlation of a signal. Here output signal y(n) is an even signal and y(0) is the maximum value. Auto-correlation of delayed input signal produced the same result as auto-correlation of original signal. Cross-correlation of input signal with delayed signal was observed to be same as advanced auto-correlated signal. The degree of similarity was calculated using coefficient of correlation ‘r’ which is defined as covariance of the variables divided by the product of their standard deviations.

Originally Posted at: https://chaitanya33.wordpress.com/2017/03/09/discrete-convolution-discrete-correlation/