Overlap Add Method and Overlap Save Method

Overlap Add Method and Overlap Save Method

This experiment focussed on filtering of a long input data sequence. Overlap Add and Overlap Save methods are block processing techniques. These methods are used to decrease the delay in obtaining the output for real time signals.

These methods decompose the input signal into smaller blocks of finite length. Overlap Add method performs Linear Convolution on the blocks of data using FFT. The overlapped values are added to obtain the output signal. Overlap Save Method performs Circular Convolution on the blocks of data using FFT. The overlapped values are not taken.   

Fast Fourier Transform

Fast Fourier Transform

The result of Fast fourier transform of a signal is same as that of discrete fourier transform of the same input signal. But, the computational part is reduced in FFT as it uses Cooley and Tuckey's algorithm to compute the result. The algorithm used in FFT computation divides the N point sequence in 2 sequences : even and odd. Thus decomposition reduces calculations.

In this experiment, FFT of 4 point and 8 point sequence was calculated using DITFFT. The comparison of number of real and complex additions and multiplications required for FFT and DFT showed that FFT required less calculations due to parallel processing.

Discrete Fourier Transform

Discrete Fourier Transform

Using DFT, discrete time data is converted into a discrete frequency representation. The experiment focussed on finding the DFT of input signal x[n]. In the first case, the input signal was a N point sequence, so the output of DFT was also a N point sequence. In the second case, the length of input signal was increased by zero padding. The result showed that, frequency spacing for output signal decreased. As a result, approximation error decreased.

DFT gives an approximate spectrum and is computationally slow.

Convolution and Correlation

Convolution and Correlation

Convolution

This experiment focussed on calculating the linear convolution, circular convolution and linear convolution using circular convolution of an input signal x[n] with the impulse response h[n] and storing the output in y[n].

For linear convolution, the length of output signal is (N = L+M-1) where L is length of x[n] and M is length of h[n].

For circular convolution, the length of output signal is N = Max(L,M) where L and M have same meaning as above.

For linear convolution using circular convolution, the length of output signal is (N>= L+M-1).

Convolution finds its application in design and implementation of finite impulse response filters and image processing.

Correlation

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

This experiment focussed on calculating auto-correlation and cross correlation of two input signals.

If a signal is correlated with itself, the resulting signal is called an Auto-correlated signal. This was the first case. The results showed that autocorrelation signal is an even signal. The value of autocorrelated signal at n=0 gives the energy of the signal. The second case was auto-correlation of a delayed input signal. The result showed that auto-correlation of delayed input signal is same as autocorrelation of original input signal. The third case was cross-correlation of two signals.