window function

In this experiment,we used Hanning window for LPF and HPF filter Design ,by taking Pass band Attenuation (Ap), Stop band Attenuation (As), Pass band Frequency (Fp) in Hz, Stop band Frequency (Fs) in Hz, Sampling Frequency in Hz as an input. we plotted magnitude spectrum and phase spectrum and verified the value of Ap and As in pass band and stop band from the magnitude spectrum.

winspec

FIR Filter Design Using Frequency Sampling

The digital filter is designed  using frequency sampling method. For LPF and HPF filter Design we have taken Pass band Attenuation (Ap), Stop band Attenuation (As), Pass band Frequency (Fp) in Hz, Stop band Frequency (Fs) in Hz,  Sampling Frequency in Hz as an input.  I have plotted Magnitude Spectrum and Phase Spectrum and verified the value of Ap and As in pass band and stop band from the spectrum. From magnitude response it is clear that number of lobes increases with increase in order.

fir-fsm

DESIGN OF CHEBYSHEV FILTER

In this experiment, we have implemented design of Digital Chebyshev filter from Analog Chebyshev filter using BLT method.Taking Pass band Attenuation (Ap), Stop band Attenuation (As), Pass band Frequency (Fp) in Hz, Stop band Frequency (Fs) in Hz, Sampling Frequency in Hz as an input. magnitude spectrum was plotted and verified the value of Ap and As in pass band and stop band from the spectrum.

Chebyshev

DESIGN OF BUTTERWORTH FILTER

We implemented Butterworth filter using attenuation and frequency in stop and pass band and sampling frequency.By using blt method we got the normalised filter for it and denormalised according to the filter .Thus filter was designed after taking its ZT. From the graph we concluded that there are no ripples found in either stop or pass band and with increase in order the slope becomes sharper.

BUTTERWORTH

FILTERING OF LONG DATA SEQUENCE

 Execution of Long Input Sequence using Overlap Add Method and overlap save method,the length of input signal and input signal values as an input are taken from user.Taking length of impulse response and signal values of impulse response as an input from user. Here long input sequence is broken down into small sequences of equal length, then using zero padding and FFT corresponding X[K] is obtained. Then all these X[K] are added to get final output. Overlap add method is used to process real-time signal which have no defined end. overlap save method is used to evaluate discrete convolution between a very long signal X(n) and a finite impulse response h(n).

OAM

OSM

FFT

In this experiment  FFT of 8 point signal was performed and here the length of input signal and signal values were taken from user. X[K] using FFT and x(n) by IFFT was calculated. In FFT calculations takes place in parallel manner. Also there are less number of complex additions and multiplication, hence the number of calculations is drastically reduced. Therefore FFT is much faster than DFT.

FFT-1

FFT-2

IFFT-1

IFFT-2

DFT

In this experiment DFT of 4 and 8 point signal,I also studied it was concluded effect of zero padding on magnitude spectrum and the length of input signal and signal values were taken from user were calculated X[K] by DFT and x(n) by IDFT and plotted magnitude spectrum of the signal. Change in 4 point signal by appending 4 zeros at end.Change was observed in X[K] and magnitude response. Hence it was conclude that as the number of points increases, the resolution of magnitude spectrum increases.

DFT

IDFT

DISCRETE CONVOLUTION AND CORRELATION

In this experiment ,I used mathematical tools for linear convolution , circular convolution and linear convolution using circular convolution functions and the obtained results were verified with the results obtained from mathematical formulation.In linear convolution if both the signals are causal then the output result is also causal,circular convolution gives aliased output.

Correlattion is mathematical tool used to find similarity between two signal and the output signal is in the form of pallindrome,Hence when signals are same this can be used to find erroe in a signal .

Cirular

Linear

Correlation