OSM and OAM

Overlap Add Method (OAM) and Overlap Save Method (OSM) are the techniques used for filtering of long input data sequence x[n] with finite impulse response h[n].In OAM the output sequence is found in which the input sequence is divided in 'L' point blocks. Whereas in OSM block length ='N'. As the input signal is processed block by block , they are also called as Block Processing techniques. This also reduces the delay of processing.Both the techniques require same computational time

Fast Fourier Transform

Fast Fourier Transform (FFT) and DFT produces the same results. FFT is considered to be a fastest algorithm as it implements the Decomposition of the input sequence which reduces calculation.One more reason of being faster is that the input is applied in parallel fashion. Radix-2 algorithm was used for implementation of N (length of input signal)=4,8.The output index  is in bit reversal order with that of the input.

Discrete Fourier Transform

Discrete Fourier Transform (DFT) is basically the frequency sampling of Discrete Time Fourier Transform (DTFT). It was observed that the resolution of the frequency spectrum improves when zero padding is done.It basically gives the expanded view of the spectrum over the same range which also reduces the approximation error.The spectrum gets compressed , also becomes periodic when input signal is expanded in time domain.Expansion was implemented by adding zeroes in between. DFT is computationally slow.

Discrete Convolution and Correlation

Linear convolution ,Circular convolution and Linear using circular convolution were performed using mathematical formula.Length of the output signal in L.C. is N=L+M-1.In C.C, N is max(L,M) whereas in L.C. using C.C., N >=L+M-1.Circular convolution gives aliased output that means depending upon the length of x[n] and h[n], last few values of L.C. output are getting overlapped with first values of the same result and addition gives circular convolution output.Auto correlation output is even signal and the middle value is maximum.The auto correlation of delayed signal is same as auto correlation of original signals. Coefficient of correlation is maximum (i.e. 1) when two signals are exactly same.