Learning Experience: Covolution and Correlation Algorithms

Experiment Performed:

 We studied mathematical operations such as linear convolution, circular convolution, liner convolution using circular convolution and also, correlation techniques such as auto and cross correlation using codes on C. 

Conclusions Inferred: 

We learnt plenty about the nature of the outputs of each of the techniques.

1) Linear Convolution: We performed convolutions of two signals, varying the lengths of the signal each time. We learnt that the length of the output signal (N) was always one less than the sum of the lengths of the two signals.

Therefore, N=L+M-1

where, L= length(x[n]); M= length(h[n])

2) Circular Convolution: We learned that the output of circular convolution will be aliased in nature. If the length of the output signal is N', where N' is the maximum length of either of the input signals (x[n] , h[n]); then from the output of LC, the first few values are aliased with the values beyond N'.

3) Correlation: We performed various correlations like auto-correlation, cross-correlation, delayed cross-correlation and inferred that correlation of a delayed input signal produces the same output and cross-correlation of a signal with its delayed version produces a delayed output.