Discrete Convolution and Correlation

Linear convolution ,Circular convolution and Linear using circular convolution were performed using mathematical formula.Length of the output signal in L.C. is N=L+M-1.In C.C, N is max(L,M) whereas in L.C. using C.C., N >=L+M-1.Circular convolution gives aliased output that means depending upon the length of x[n] and h[n], last few values of L.C. output are getting overlapped with first values of the same result and addition gives circular convolution output.Auto correlation output is even signal and the middle value is maximum.The auto correlation of delayed signal is same as auto correlation of original signals. Coefficient of correlation is maximum (i.e. 1) when two signals are exactly same.