OAM And OSM

Overlap-Add and Overlap-Save method is used to perform linear convolution and circular convolution of long data sequences respectively. They are called as block processing techniques as the input signal is divided into blocks and then analysed.  The OAM was performed by linear convolution using DITFFT and OSM by Circular Convolution using DITFFT.  In case of OSM the input signal was modified and the final output signal was obtained by discarding few initial values from all the convolved outputs.

FFT

In order to overcome the slow computation drawback of DFT , Fast Fourier Transform(FFT) method was invented which performs the same task in less number of steps ,thereby increasing the speed. In this method the input sequence is broken down into two equal parts. This breaking down of the signal was continued till no further decomposition was possible. Radix-2 algorithm is used to perform the experiment. The counter was then added in the code to check the total number of calculations and it was proved that less steps are required to perform the task as compared to DFT.
The difference in the number of steps required goes on increasing as the length of input signal increase.

Convolution and correlation

In todays experiment we studied Convolution which gives the output of the system and Correlation which gives the degree of similarity between the 2 signals which are being compared.
In linear convolution we found that if both the input signals are causal then the output signal is also causal . Also Aliased output was obtained in circular convulation . The length of output signal in case of linear convolution was found to be always greater than or equal to the that of the circular convolution.
In case of Auto correlation we found that the same output was produced even if the signal was delayed and always the ouput signal was an even signal. Also the Cross correlation of a signal with its delayed signal was same as that of the  autocorrelation of input signal

DFT

In this experiment we learned to obtain DFT signal from DTFT signal.DFT signal is basically obtained by sampling DTFT signal at w =2πk/N.
We also found that DFT gives approximated spectrum and as we increase the number of samples the approximation error decreases which in turn increase the resolution.This was achieved by doing zero padding. Also DFT produce priodic result with period equal to N.