Convolution and Correlation Algorithms

Experiment 1

In this experiment  Convolution (Linear Convolution, Circular Convolution and Linear Convolution using Circular Convolution) and Correlation (Auto Correlation and Cross Correlation) has been performed.
Convolution is a mathematical way of combining two signals to form a third signal. It is the single most important technique in Digital Signal Processing. Using the strategy of impulse decomposition, systems are described by a signal called the impulse response. Convolution is important because it relates the three signals of interest: the input signal, the output signal, and the impulse response. 

Linear Convolution is used for non-periodic signals and Circular Convolution is used for periodic signals. The output of Circular Convolution is aliased. Application of Convolution is to find output of the system. We observed that for Linear Convolution the length of output signal is N=L+M-1 and For the circular that length is N= MAX(l,M).

The output of Auto Correlation is the value of the output at n=0 gives the energy of the signal. Auto Correlation of delayed signal is same as that of original signal. The output was both-sided.