Butterworth Filter

After completing methods of finding output of filter,we moved towards the design part of filter.In this experiment ,we have studied butterworth filter,low pass and high pass.we observed that butterworth filter have monotonic amplitude response in both pass band and stop band.Quick roll-off around the cut-off frequency,which improves with increasing order.Analog LPF poles lie on LHS of s-plane and digital poles lie inside the circle.These conditions denote stability of filter.

Chebyshev filter

Chebyshev filters are analog or digital filters having a steeper roll-off and more passband ripple than Butterworth filters. Chebyshev filters minimize the error between the idealized and the actual filter characteristic over the range of the filter but with ripples in the passband.The Chebyshev filter has a smaller transition region than the same order Butterworth filter, at the expense of ripples in its pass band. Because of the passband ripple inherent in Chebyshev filters, the ones that have a smoother response in the passband but a more irregular response in the stopband.This filter requires less hardware than butterworth filter.

OVERLAP ADD METHOD AND OVERLAP SAVE METHOD

OSM (Overlap Save Method) and OAM(Overlap Add Method) are linear filtering method. In this practical, we have performed OSM and OAM using 13 point input sequence x(n) and 4 point h(n). The obtained output of OSM and OAM method is same for given input sequence.In OAM, the input signal was decomposed into non overlapping blocks and their corresponding y(n) was calculated using linear convolution and then these signals are combined to obtain the final output.
In OSM, the input is decomposed into overlapping blocks and their corresponding y(n) is calculated through circular convolution and then these signals are concatenated to give the final output.

FAST FOURIER TRANSFORM

Fast fourier transform is fast method of computation than discrete fourier transform(DFT).It requires less number of calculation than Discrete Fourier Transform(DFT), which includes real addition and multiplication. FFT uses parallel processing hence it has high operation efficiency.In this experiment , we have taken cases of 4 point and 8 point sequence. The output of FFT is in bit reversed format. we have perfomed this experiment using C program of DITFFT(Decimation in time FFT).

DISCRETE FOURIER TRANSFORM

In this experiment,first 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 and further 4 point sequence was expanded by adding alternate zeros between two samples.It's DFT output was found out using C code of DFT. Magnitude spectrums were plotted for each case.As value of N increases, frequency spacing and approximation error decreases as well as resolution of the spectra increases.Expansion of signal in time domain giver compressed spectrum in frequency domain.

CONVOLUTION AND CORRELATION

our first practical of semester six was convolution and correlation.The program for this practical was given in C language. I have substituted the values of x(n) and h(n) in program .Final output length of y(n) for linear convolution is equal to L+M-1. For circular convolution it is maximum value from L(length of x(n)) and M(length of h(n)).Circular convolution gives aliased output.
Auto correlation of signal is even signal and cross-correlation of input signal with delayed signal is same as advanced auto correlated input signal.Correlation was used to test the degree of similarity between two signals.