OAM and OSM

 
     The Fast Fourier Transform Algorithm had an important limitation in which it required all input                 values to be available for obtaining an output.

For a real world signal which can be arbitrarily long, waiting for the entire signal to arrive and get stored would result in massive delays and also increase the cost of storage equipment. Here OAM and OSM come into picture. The inputs are very large in these methods. They are used for decreasing the output delay. 

 A long input data sequence was taken and the impulse response was taken of a smaller length i.e. 3. The length of decomposed signal came to be 5 whereas the length of output decomposed signal came to be 8.

 We concluded that for inputs having large lengths OAM and OSM are useful for getting outputs with reduced delay.This experiment took some time as the concept was new to us.

Link for code:https://drive.google.com/drive/folders/0B076kcYDr0DCbzZndW5SMGdjMmM

DFT

The aim of this experiment was to perform Discrete Fourier Transform.

We observed that as the value of N (length of signal) increases, frequency spacing increases and error decreases.

We plotted the magnitude spectrum when N=4 and also after zero padding i.e when N=8. The magnitude spectrum was found to be symmetric.

Link for code:https://drive.google.com/drive/folders/0B076kcYDr0DCbzZndW5SMGdjMmM

FFT

The aim of the experiment was to perform fast fourier transform of a 4 point sequence. The program was written in C language.

In this experiment, we observed that the number of calculations in FFT are less than that in DFT. Thus, FFT is faster.The number of calculations to implement the DFT equation directly is proportional to N*N, where N is the number of data points. The FFT algorithm reduces this to a number proportional to NlogN where the log is to base 2.

Link for code:https://drive.google.com/drive/folders/0B076kcYDr0DCbzZndW5SMGdjMmM

Convolution and Correlation

The aim of the experiment was to study linear convolution, circular convolution and correlation. In circular convolution, aliasing effect i.e folding of sequence was observed. 

We concluded that in linear convolution, length of output signal N=L+M-1. For circular convolution, length N=max(L,M).

We studied auto-correlation and cross-correlation. For auto-correlation, the observation was that the output signal is a palindrome sequence and the output of correlation is both-sided.

Cross correlation is the correlation between two signals to measure the degree of similarity.

Link for code:https://drive.google.com/drive/folders/0B076kcYDr0DCbzZndW5SMGdjMmM