EXP 4: Overlap Add Method and Overlap Save Method

When the data size and  rate is high e.g. video we filter the long data sequence using Overlap Add Method and Overlap Save Method.In OAM, convolution of smaller groups of input with the second input is obtained. So we get convolution for each group which gets overlap depending upon the length of the input signal. In OSM, we divide the output instead of input signals and use only limited input required to calculate that output. Hence the memory requirement is reduced. Both the methods require the same amount of computations and hence the same memory.

EXP 3: Fast Fourier Transform

For finding DFT for large signal we use FFT which divides N point signal into two equal parts with each part consists of alternate values. This division process was done till no further division could be possible. The output obtained was in bit reversal order which we arranged the so that no confusion should be made while reading the output. We perform this experiment for four point signal and eight point signal hence the algorithm used is radix-2. Later we checked the number of calculation using counter. The number of calculations were reduced.

EXP 2: Discrete Fourier Transform

To perform this experiment, we used C programming and three cases. We used four arrays two for inputs (real and complex) other two for output. We passed these four arrays to the second function which was used to calculate DFT. Length of the output is same as that of the input signal. When the length of a signal increased the resolution of the output magnitude spectrum improved.When the length is increased by adding zeros after each value, the spectrum gets contracted and, the spectrum was seen to be periodic. Hence we could say DFT, a periodic signal.

EXP 1: Discrete Convolution and Correlation.

In linear convolution, the length of the output signal obtained was the one less than the addition of the length of the two input signals. In circular the length of the output signal was same as that of the input with higher length. In circular, we found aliasing of last few values on initial few values. In Discrete Correlation, we learned how to find similarities between two signals. it was observed that the output for correlation is symmetric about the middlemost value which is also the magnitude of energy of the signal. In cross-correlation, when the input is scaled by some factor, the output also got scaled by the same factor.