Design of Chebyshev Filter

In this experiment we used the same technique as we did for butterworth filter. We performed this experiment on SCILAB and same input parameters were given as in butterworth filter for LPF and HPF.
From this experiment we observed that, ripples were present in passband and on the other hand it was monotonic in stopband for LPF and it was vice versa for HPF.For LPF we get exact zero at -1 and for HPF we get exact zero at +1.

Design of Butterworth Filter

In this experiment, we designed a butterworth filter using SCILAB for implementation of the code.Input parameters such as As,Ap,Fs,Fp and F were used to design the filters.With the help of this parameters order of the filter,cutoff frequency,normalized filter and denormalized filter was calculated.
Graph was observed between Mag(in db) vs Frequency (in Hz).From the output we observed that the magnitude response is monotonic and poles lies inside unit circle which is the condition of stablilty.We used BLT method for design of filter,

Convolution and Correlation

In this experiment, we explored about two important parts of digital signal processing i.e convolution and correlation . Convolution was carried in three ways i.e linear convolution,circular convolution and linear convolution using circular convolution.Correlation was also performed in two ways i.e auto correlation and cross correlation.

All this was performed with the help of the C programming.We observed that circular convolution gives aliased output .For auto correlation, the middle value of the output signal denotes the energy of the signal.  Auto correlation of delayed input signal is equivalent to auto correlation of original signal. The significance of correlation is used to find the degree of similarity between two signals.

Discrete Fourier Transform

Discrete Fourier Transform(DFT) is used to transform time domain signals into frequency domain signals with the help of sampling. DFT is frequency sampling of Discrete time fourier transfrom (DTFT).In this experiment 4 point and 8 point appended sequence DFT was calculated. DFT results are periodic with length equal to the input signal.
Magnitude spectrum for the same was plotted.We observed that if signal is expanded,the spectrum is compressed and its more accurate compared to 4 point. DFT is computationally slow because large number of multiplications and additions.

Fast Fourier Transform

Fast Fourier Transform(FFT) has less number of addition and multiplication.Therefore,it is faster than Discrete fourier Transform (DFT).Cooley and Tuckey's radix-2 Decimation In Time Fast Fourier Transform ( DITFFT)  was performed,where the term decimation means nothing but sampling.

The FFT algorithm divides the N point signal into 2 parts i.e even and odd.Decomposition reduces the calculation.FFT of 4 point and 8 point sequences was calculated using radix 2 algorithm.Bit reversal technique was observed.

Filtering of Long Data Sequence

Overlap Add Method(OAM) and Overlap Save Method(OSM)  are algorithms to calculate DFT of very large length Input signals.OAM is calculated by decomposing the input sequence and applying linear convolution to this signal,where as in OSM instead of dividing the input,we divide the output and apply only those input values which are required to calculate this output.
We observed that both methods gave the same output.Both methods requires same amount of computations.These methods are block processing techniques.