EXP4: Overlap Add and Overlap Save

Output of FIR filter is convolution of input signal, x[n] and impulse response of filter, h[n]. Practically length of input signal is very long and and convolution becomes complicated. Therefore for filtering real time input signal there are two methods.
1. Overlap Add Method (OAM) 2. Overlap Save Method (OSM)
In both the methods the input signal is decomposed into small parts. In OAM ,length of decomposed signal is L,where L=N-M+1. Linear convolution of decomposed input signal and h[n] is carried out and final output is found out by shifting and adding individual outputs. In OSM ,input is decomposed by adding some preceding values. Circular convolution is done with h[n] after zero padding h[n].Final output of OSM is obtained after discarding the extra preceded values. Thus, OAM and OSM are block processing techniques.

EXP3: Fast Fourier Transform

As DFT is computationally is slow, in order to reduced the calculations and increase the speed drastically, Fast Fourier Transform i.e FFT was introduced. In theory sessions,we learnt Radix-2 FFT algorithms.
In this lab session we studied and executed FFT of 4pt and 8pt sequence using DITFFT. We also calculated the no. of computations required to find out FFT of a sequence. Comparing it with no.of computations required of DFT we concluded that FFT is much faster compared to DFT.

EXP2: Discrete Fourier Transform

Discrete Fourier Transform (DFT) is frequency sampled version of Discrete Time fourier transform(DTFT). DFT gives periodic results.
In this experiment,we performed 4-point and 8-point DFT. First we performed 4pt DFT. Later we appended the 4pt signal with 4 zeros and performed 8-point DFT. We also added zeros at even places of 4pt signal and performed 8pt DFT. We plotted the approximate magnitude spectrum of all the DFT signals.
We observed that expansion of signal in time domain gives compressed signal in frequency domain.
We also calculated the no.of computations required to get DFT of a signal and concluded that DFT is computationally slow.

EXP1: Convolution and Correlation

Convolution and correlation are very important from signals and systems point of view. Linear Convolution gives output of the system whereas correlation tells us about the similarity of two signals.
In theory sessions we implemented these mathematically. In lab session we are learning its practical implementation using C programming. We thoroughly studied the codes of linear convolution,linear using circular convolution,correlation. While studying the codes we revised the concepts of C programming learnt in first year especially the concept of call by reference which has been used in all the codes.

We compiled and executed the codes using terminal window of ubuntu. For linear convolution,we first entered the length of input signals,L=length of first signal and M=length of second signal and then entered the values.We found out that length of output signal i.e N=L+M-1. Similarly we performed linear using circular convolution and correlation.We concluded that auto correlation of delayed signal is same as original signal and the value of auto correlation at n=0 is the energy of the signal.