Overlap Add and Overlap Save Method

In this experiment we learn Overlap Add method (OAM) and Overlap Save method (OSM).

Both Overlap Add method and Overlap Save method are block processing techniques to process large data sequences. These large data sequences are decomposed into smaller sequences and then computed individually.

Overlap Add method (OAM) involves the decomposing of the signal into smaller signals and then using liner convolution and the overlapped part of the sequences are added to find the output.

Overlap Save method (OSM) involves the decomposing of the signal into smaller signals and then using circular convolution and the convoluted part of the sequences are discarded to find the output.

Both of these methods are equally computationally fast and use memory equally.

Fast Fourier Transform

In this experiment we learnt Fast Fourier Transform (FFT)

This is also a computational method like Discrete Fourier Transform (DFT) but is faster than it, hence the name Fast Fourier Transform (FFT)

The calculation of odd and even parts are done parallely and this reduces the total number of operations of addition and subtraction of real and imaginary parts. We performed FFT of 4pt and 8pt signals using Radix 2 algorithm which accounts for parallel computation and hence increases efficiency and faster calculation time.

Discrete Fourier Transform

In this experiment the aim was to study and understand Discrete Fourier Transform (DFT) using C language and manual verification.

Discrete Fourier Transform is used to transform time domain signals into frequency domain signals by sampling. More is the number of samples the greater is the degree of realisation of the original signal in the transfer domain.

We observed the magnitude spectrum of 4 pt and 8 pt signals. Also, by adding zeros to the 4 pt signal, the magnitude spectrum of the signal was more defined as we had more samples to plot.

We also observed that the transformed signal achieved from the time domain is compressed and also that DFT is computationally slow as the number of real and imaginary additions and multiplications is high.

Discrete Convolution and Correlation

The aim of this experiment was to study and understand Convolution and Correlation of Discrete signals in Signal Processing which was coded with C and verified manually.

Convolution can be defined as the integral of the product of the two functions after one is reversed and shifted. The output function can we viewed as a modified version of one of the original signals.

The length of the output signal(N) is one less than the sum of the lengths of the two signals (L & M)

N=L+M-1

Aliasing effect can be observed in case of Circular Convolution.

Correlation can be defined as the measure similarity between two signals. When measured for the same delayed signal, it is called as autocorrelation and when measured between two different signals, it is called crosscorrelation.