Signals and System

In this experiment we got the frequency response of infinite and finite impulse response signals, we obtained the conditions for which they behave as different kinds of filters.For IIR filter , for pole on right it is low pass filter while for pole on left it is high pass filter.For FIR filter ,for input a = [1  6 5 2 5 6 1] it is band reject filter . For input b = [1 6 5 2 -5 -6 -1] it is band pass filter. 

In the application experiment we applied the concept of signals and system to a practical signal. We took a audio file as a input from a directory .Then applied the parametric equalization to it.Parametric equalizers are multi-band variable equalizers which allow users to control the three primary parameters: amplitude, center frequency and bandwidth.Practically they can be used to adjust the volume level of a frequency, or range of frequencies, within an audio signal. We displayed the input and output signals on Spectrum Analyzer and then the processed file was played.

This experiment was based on the Fast Fourier Transform Algorithm. This algorithm is different from the discrete Fourier transform, however the final result that we obtain is the same. This code was easier to understand since this chapter was taught in the class. The code though I found to be more  complex than DFT. We performed FFT on 4-point and 8-point sequence and displayed the output for the same. Also we plot the magnitude and phase spectrum for the same.

Linear Finite Impulse Response is implemented using any of the two algorithms of Overlap Save Method(OSM) and Overlap Add Method(OAM). Overlap Add & Overlap Save Methods are particularly used to perform convolution on longer input of data sequences by breaking actual input signal into smaller length of different signals and then performing convolution on individual data streams.In OAM method, the values which get overlap were added together. In OSM method, the values which get overlap were discarded.

The fourth lab was about  s ampling and reconstruction . An input signal is sampled at regular intervals. The sampling theorem needs to be satisfied. According the sampling theorem the sampling frequency needs to be greater than or equal to twice the maximum frequency present in the signal. If this is not taken care of then we observe aliasing effects. Reconstruction is not possible if this theorem is not satisfied. This experiment was performed on MATLAB. Also the graphs were plotted to illustrate the experiment.

The third lab was to perform Discrete Fourier Transform experiment. This topic was introduced in the class before the practical and hence was relatively easy to understand during the practical session. We understood the facts learned in theory. It is very important to understand the working of the code , only then can one be able to construct a function of his own . The session was a lengthy one as we had to take 5 set of outputs and had to also draw their magnitude spectrum's. 

In the second lab we had to performed Correlation. Correlation is a measure of similarity between two signals. The concept were taught in the class and based on that practicals are performed. There are two types of correlation: Auto correlation: It is defined as correlation of a signal with itself. Auto correlation function is a measure of similarity between a signal & its time delayed version. Cross correlation: Cross correlation is the measure of similarity between two different signals.

In first Experiment we learned about linear and circular Convolution. Convolution is the mathematical operation on two signals to produce the third signal that expresses how the shape of first signal is modified by the other.The length of the signal in the Linear convolution is N=L+M-1 and the length of the signal in Circular Convolution is Max(L,M). In Circular Convolution we get aliased output.We can solve linear and circular convolution using formula or tabular method. In linear convolution signal may not be periodic but in circular convolution signal is assumed to be periodic . Linear convolution is used in real life applications.