Filtering of long data sequence

Overlap add method and overlap save method are used for filtering long data sequence. These methods are used in practical world for multipying two signals. The input signal x(n) is divided into equal lengths and convoluted with h(n). Depending on which method is used, decomposed y(n) for both OAM and OSM was calculated.  Though FFT yield  faster results it cannot be used in practice as it requires the entire length of input signal which isn't possible as it would introduce large delay and memory requirements of the system will also increase. Hence OAM and OSM are preffered.

https://drive.google.com/open?id=0B8Ks3rz0S_nzUDFfQjFLQWkwOGs

Fast Fourier Transform

The aim of this experiment was to perform FFT of N point signal (N=4).
It was observed that though fast fourier transform leads to faster results in practice by butterfly diagram,  it takes same computational time as DFT but complex algorithm while implementing using a program. For multiplying two complex values we use the method as directed by sir of multiplication of complex variables. For eg: (a+ib)(c+id)=(ac-bd)+i(ad+bc) which leads to simpler code logic.

https://drive.google.com/open?id=0B8Ks3rz0S_nzby1Xb01OOC1IZms

Discrete Fourier Transform

The objective of this experiment was to develop a function for calculating DFT of  N-point signal.
This experiment was performed in C. Two separate code were written, one for 4point and one for 8 point DFT. 8point  DFT was calculated using 4point DFT code.
A signal for N=4, was taken and its DFT was found. Same signal was converted to N=8 using zero padding.
The DFT output H[k] was same, as that for N=4 for even values of k.
Also H[k] is periodic due to nature of twiddle factor.
Magnitude spectrum for N=4 and N=8 were drawn.
https://drive.google.com/open?id=0B8Ks3rz0S_nzMmlUZGw3aV9wbXM

Discrete convolution and correlation

Part 1:
The aim of the experiment was to study mathematical operations like convolution, circular convolution and linear convolution using circular convolution (studied in the course of signals and systems, semester V)
A code was developed in  C language for the above three  operations.
We were supposed to calculate the convolution results and verify them. Aliasing effect in circular convolution was noted when we compared the output of linear convolution with circular convolution.
Linear convolution using circular convolution was also performed.

Part 2:
The aim was to study correlation and measure the degree of correlation. We implemented a code for auto correlation and cross correlation.
Auto correlation is the correlation of a signal with itself. The output signal has length of 2M-1 (M being the length of original signal) and follows the pallindrome pattern.
Cross correlation is the correlation between two signals to measure the degree of similarity.
https://drive.google.com/open?id=0B8Ks3rz0S_nzZ21PMTlscjQyR1k

Signal Processing Application

This experiment was performed in groups of four. Our group topic was Comb filter.
Group Members: Natasha Choudhary, Umesh Gawale, Pranav Ghaisas, Tejashree Gore

Problem definition: To implement a comb filter to eliminate noise signal

Individual experiment was to review one IEEE paper and one patent on the above topic.

IEEE paper review:
Published in: International Conference of Microelectronics, Communication
Tittle: Design of cascaded integrator comb filter using single adder and subtractor.
Authors: Gourav Sarkar, Debjyoti Mallik, H.S. Jatana, Department of Space, Mohali, India.
Summary: The paper proposed two architectures of a cascaded integrator comb(CIC) filter, one using tri-state buffers, other with multiplexers. These architectures were shown to occupy lesser areas on chip than compared to the traditional design. This can be used in ASIC designs.

Patent review 
Application no: 09/317,761
Patent no: 6,034,628
Date of Patent: May 24,1999
Inventor: Dieter Daxelmayr , Villach, Austria
Summary: The comb filter model proposed consists of three series connected integrators such that the first and last integrator receive digital data stream at high sampling frequency in order to yeild digital data stream at low sapling frequency. This is also known as a decimation comb filter.

Implementation of above problem definition was done on scilab as a group experiment.

Note:
1. IEEE paper was downloaded from sci-hub.io
2. Patent was downloaded from freepatentsonline.com

https://drive.google.com/open?id=0Byo4VUtNmtKBTGVIMWI0eHlSdk0

To perform operations using DSP processor

In this experiment we were given a general overview of programming on a dsp kit in assembly level language. This experiment was performed in the class and was demonstrated by a senior. The dsp kit used was TMS320f28375. Arithmetic, logical and shifting operations were studied here. The instructions for above operations were implemented and register values before and after execution were observed and noted down.
DSP kits are used for real time signal analysis(i.e output is obtained as soon as input is provided). In the demonstration, emulation using dsp was carried out. One way to program a DSP is using Code composer studio. It is a software by TI. A code developed by the senior was pre-loaded into the board and. Input was given using a mic and output was given to the speakers. 

FIR filter design using frequency sampling method

The objective of this experiment was to design a digital filter for the given input specifications using frequency sampling method. In this method the desired frequency response Hd(w) is sampled at w=2*pi*k/N ( where N = length of  the signal) The frequency samples are thus obtained are taken as DFT coefficients H[k]. FIR filter response is found by taken IDFT of H[k]. Manitude and phase spectrum were plotted for this. Pass band and stop band attenuation values were verified. 

https://drive.google.com/open?id=0B8Ks3rz0S_nzVE1ZRlItVFl4Qlk

Linear phase FIR filter using window function

The objective of this experiment was to design digital filter using windowing technique and study the spectrum of filter.
This experiment was implemented in two stages:
1.C code: in the first part of the experiment we calculated impulse response h(n) of the filter by multiplying desired impulse response hd(n) with window funtion W(n). Input specifications as mentioned in the lab manual were entered and the opuput of the code was h(n). This impulse response obtained was noted down and used in stage 2.
2. Scilab code: The values obtained from stage one were used to find magnitude and phase plot for the required impulse response.
Thus FIR filter was designed by truncating infinite samples of hd(n) using windowing method. The implulse response of FIR filter obtained was symmetric in nature. Hence its phase spectrum was linear(i.e phase response varies linearly with frequency)

https://drive.google.com/open?id=0B8Ks3rz0S_nzbXZXTU8zMWp4OG8

Design of analog and digital Butterworth filter

This was the first experiment implemented on scilab. Scilab's help browser was used to get acquainted with the functions available in scilab. The objective of this experiment was to design a digital butterworth filter from analog filter. Analog filter was designed by the same method as studied in class, i.e calculation of normalized and denormalized filter and then using BLT to find digital filter trnasfer function. magnitude response of Digital low pass filter and digital high pass filter was plotted. Pole-zero diagram for both were observed and concluded that since the poles lie within the unit circle, filter must be stable. (hence implementable)
Input specifications as mentioned in the lab manual were obtained from the users and values of pas band and stop band attenuation were verified. 

https://drive.google.com/open?id=0B8Ks3rz0S_nzN25zQy1TaDBxSG8

Design of analog and digital Chebyshev filter

The objective of this experiment was to design a digital chebyshev filter from analog chebyshev filter. Here we take inputs like pass band attenuation, stop band attenuation, pass band, stop band and sampling frequencies in hertz. We implemented calculations of all parameters of the chebyshev filter in scilab. 

After plotting the digital filter, the values of pass band and stop band attenuation were verified. As the values were not matching, it was concluded that after increasing the order of the filter, we get better matching between input and output values. 

https://drive.google.com/open?id=0Byo4VUtNmtKBbDJLUkJDZlJULTQ