Convolution and Correlation

This was a great experience learning Convolution and Correlation. First we will talk about convolution. There are 2 types of convolution one is Linear and the other is Circular. In Linear Convolution the length of output signal is always sum of the length of the inputs minus one. Also if both the input signals are causal then resultant output is also causal. But in circular convolution the length of output signal is the length which is maximum between both the input signals. Also circular convolution gives aliased output.

Now we will talk about correlation. In correlation there are 2 types one is auto correlation and the other one is cross correlation. Auto correlation signal is always an even signal. Auto correlation of delayed input signal is same as auto correlation of original signal. Cross correlation of input signal with delayed input signal is same as advanced auto correlated signal. Correlation is used to find degree of similarity between 2 signals.