Discrete Convolution and Correlation

In this experiment,we learned linear convolution,circular convolution and linear convolution using circular convolution. We used the mathematical formula of convolution and observed the results. The length of the input signal in linear convolution was L=4 and M=4, the length of the output signal is N=L+M-1,therefore N=4+4-1=7 (the length of output signal is 7). In circular convolution as we increase the   length of signal, zeros are added to the output signal. The length of the signal was N=max(L,M).In circular convolution we get aliased output.For linear convolution using circular convolution N>= L+M-1. Zero padding was observed.We studied aliasing effect.We also performed cross and auto correlation. The second case was having the same input but delayed. In auto correlation the value at the center is largest and the signal is symmetric.The application of correlation is to find the degree of similarity of two signals.