Learning Experience on Overlap Add Method and Overlap Save Method

OAM and OSM are used when we want to filter a long data sequence.In this experiment, we have found the output of FIR filter using these methods.In OAM, an input signal is divided into smaller groups and which then used to find convolution with other input. So we get convolution for each group which the gets overlap depending upon the length of the input signal. In OSM, the only difference is that we modify the input sequence and append the next sequence with the previous inputs we have appended. OAM and OSM are block processing techniques since we divide the long input sequence into blocks and then calculate further.These methods are suitable for real-time signal processing.

Learning Experience On Fast Fourier Transform

In this experiment, we performed Fast Fourier transform of 4-point sequence and 8-point sequence.In FFT since all the calculations are done in a parallel manner it is fast.FFT is done in two ways using Decimation in Time and Decimation in Frequency.Here we performed DITFFT so the signal was decimated into parts using Radix-2 Algorithm since the signal is 4 and 8 point sequence using C-programming.Computations in FFT was also performed using a counter and we found that the number of calculation was reduced as compared to DFT so FFT is computationally fast. 

Learning Experience On Discrete Fourier Transform

In this experiment, we performed Discrete Fourier Transform of 4-point sequence, zero padded signal, and Expanded signal. Magnitude spectrum of each case was drawn and observed that DFT coefficients are defined for w=2k/n. Also the spectrum is discrete in the range 0 to 2.From the three cases when the signal was zero padded the length of the signal increased due to which frequency spacing got decreased which increases the Resolution the spectrum.Also, expansion of signal in time domain gives compressed spectra in Frequency domain.We also observed that DFT produces periodic Results.Computations in DFT which included real Multiplication and Additions was also Calculated and we found that Discrete Fourier Transform is slow.   

Learning Experience On Convolution and Correlation

This experiment was performed in two parts which included Discrete Convolution and Discrete Correlation..We observed that the length of Linearly Convolved output signal was N=L+M-1 while that of Circularly Convolved output signal was Max(L,M) where L & M are length of input signals.Also circular convolution gives aliased output.In Discrete Correlation when the input signals are delayed auto-correlation of delayed input signal is same as that of original signal while Cross-Correlation of input with delayed input signal is same as that of auto correlated  delayed input signal. The application of Convolution is to find the output of the system while that of Correlation is to find degree of similarity between two signals.