DSPP Experiment No. 04

               Overlap Add Method and Overlap Save Method

We use overlap add method(OAM) and overlap save method(OSM) when input signal x(n) is given to digital FIR filter.OAM and OSM are linear filtering methods.In this practical,a 13 point input sequence is taken and output is found out using C program using OAM and OSM for same input sequence.The outputs obtained using both the methods are same.

In OAM method,input sequence is decomposed and then linear convolution is performed on these signals individually.The outputs obtained are then combined together and displayed.In OSM the signals are decomposed and then circular convolution is performed.The input is decomposed in OSM in such a way that there are some value from previous sequence.The outputs obtained are then combined inbto a single sequence by removing the repeated number of values.In this practical,x(n) was a 13 point sequence and h(n) was 4 point sequence.

DSPP Experiment No. 03

                            FAST FOURIER TRANSFORM 

Fast fourier transform(FFT) is a fast method of computation than Discrete fourier transform(DFT) as FFT has less number of additions(both real and complex) and multiplications(both real and complex) involved.Operational efficiency of FFT is high as it uses parallel processing.Also the output of FFT is in bit reversed form.In this practical,two cases were considered by taking 4 point and 8 point input sequences.The output was found using C program which implemented DITFFT(Decimation in time FFT) algorithm.

Experiment No. 02

                  DISCRETE FOURIER TRANSFORM

Discrete fourier transform(DFT) gives periodic results.It is frequency sampled version of discrete time fourier transform.DFT is a slow algorithm.

In this experiment,initially a 4 point sequence was taken and it's DFT was found out using C program.Then this same sequence was appended by 4 zeros to form a 8 point sequence.It's DFT output was found out.Then magnitude spectrum was plotted for both output sequence.It was observed that the magnitude spectrum of 8 point input sequence was more accurate than 4 point input sequence.It was because the resolution of magnitude spectrum of 8 point sequence was higher.

DSPP Experiment No. 01

                              Convolution and Correlation

Linear convolution is used to find output of the system whereas correlation is used to find degree of similarity of two signals.These concepts are given to us in theory of digital signal processing.In this experiment,for linear convolution,x(n) is taken as input along with impulse response h(n).The output is y(n).For length of output signal y(n) of convolution operation,we use the formula N>=L+M-1 .For length of output signal of correlation operation we use the formula N=max(L,M).In this practical,the codes for these operations were studied and then implemented.Linear convolution,circular convolution,linear convolution using circular convolution,auto-correlation and cross correlation were performed.The output obtained was then verified with the answers obtained by theoritical calculations.