Overlap Add and Overlap Save Method

Overlap Add and Overlap Save Method are two methods which are helpful for finding discrete convolution of a very long input signal.

In Overlap Add Method, we use linear convolution and in Overlap Save Method we use circular convolution. F.F.T algorithm is used for computing the convolution.

Overlap Add and Overlap Save Method are known as block processing techniques because the input sequence is divided into different blocks and each block is processed separately.
These methods are suitable for processing of real time. 

Fast Fourier Transform

Fast Fourier Transform is implemented where fast response is required. F.F.T is fast implementation of D.F.T. In F.F.T then number of computations are reduced as a result it is computationally faster than D.F.T.

In this experiment, we computed the F.F.T of signals having N=4 and N=8.
Radix-2 algorithm is used for computing F.F.T of an input signal i.e the input signal must 2^N points. To achieve this zero padding of the input signal is done. The input and output sequence in radix-2 F.F.T algorithm is in bit reverse manner.

We also calculated the number of computations required to calculate the F.F.T of a given signal and thus verified that F.F.T is computationally faster than D.F.T. 

Discrete Fourier Transform

Discrete Fourier Transform (D.F.T) is the transform that deals with a finite discrete-time signal and a discrete number of frequencies. It is the frequency sampled version of D.T.F.T (Discrete Time Fourier Transform). D.F.T gives N coefficient values in frequency domain and it's spectrum is discrete.

In this experiment, we have performed D.F.T over signals of length N=4 and N=8 using C programming. We also determined the number of computations required to find the D.F.T of a signal. Thus we can conclude that D.F.T is computationally slow.

Convolution and Correlation

Convolution is used to find the response i.e output of an L.T.I system. In this experiment we have executed a program which computes the convolution of two signals. Thus we have verified the theoretical  results of the convolution using C program.

Correlation helps in finding the degree of similarity between two signals. After implementing the code for computing correlation we can conclude that auto correlation is an even signal and auto-correlation and cross-correlation of delayed signal is same as auto-correlation of original input signal.

Thus implementing the theoretical mathematical concepts using C programming helped in revising the programming concepts of C language.