Experiment one : Discrete Convolution and Correlation

Part one: Convolution

Convolution is used to find output of the system.

We calculated 

1. Linear convolution
2. Circular convolution
3. Linear convolution using circular convolution.

Learnings from experiment:

• In linear convolution, length of output signal is one less than the addition of length of both input signals.
• In circular convolution:

1) Length of output signal is same as that of input signal with higher length.
2) Last few values are aliased on initial few values. Hence we get aliased output.


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

We calculated 

1. Autocorrelation
2. Cross-correlation

Learnings from experiment:

• Autocorrelation is an even signal.
• Autocorrelation of delayed input signal is same as that of autocorrelation of original input signal.
• Cross-correlation of input signal with delayed input signal is same as advanced autocorrelated input signal.
• In cross-correlation of scaled input signal, output is scaled by same factor as that of input signal.