FIR Filter Design Using Windowing Method

Finite Impulse Response(FIR) Filters are always stable and are therefore preferred for design of filters. one of the methods for design of FIR filters is using Window Function. In this method, we begin with the desired frequency response specification Hd (W) and determine the corresponding unit sample response hd(n). The hd(n) is infinite in duration and must be truncated at some point to yeild an FIR filter of length M.

In this experiment, we have designed an FIR filter using Hanning Window Function. This window function has significantly lower sidelobes as compared with the rectangular window. The phase plot observed was linear and the output was a delayed version of the input preventing distortion.


https://drive.google.com/drive/folders/0B9Ily3Urp8vgalRlVWhZb2lpUmc

Signal Processing Application

This was a group experiment. The aim of this experiment was to study a signal processing application and to develop an application around it. The application that we selected was Siesmic signal processing. We collected information from various published papers and patents. The group members are as follows Kanchan Sawant, Nivedita Petkar and Ankita Dhavale.

With reference to the Seismic signal processing, I selected the paper titled "Signal Processing in Ocean Bottom Seismographs for Refraction Seismology". My review is as follows:

The aim of the paper was to show the results regarding the signal acquisition and subsequent processing. The experiments were designed to extract information about the earth's crust at the ocean bottom, from the refracted waves obtained through an active seismology process.

The challenges faced were the development of a system of continuous data acquisition as the Ocean Bottom Seismographs(OBS) are autonomous systems submerged for long periods of time. The solutions adopted were wavelet techniques and refraction seismology.

The patent which I selected for study is Seismic signal processing machine and method for noise removal

US 4314347 A. This patent provides a new and improved process and method of controlling the operation of a data processing machine.

DSP Processor

We studied the DSP Processor TMS320F28375 in this lab session. Our senior provided a demonstration of how to perform this experiment using the programming software Code Composer Studio. The code was implemented using the software.

Basic arithmetic operations like addition, subtraction, multiplication, division were performed. Various Shifting instructions like LSL, LSR, ROR, ROL were used. 
 

FIR Filter Design Using Frequency Sampling Method

Frequency sampling method allows us to design FIR filter for standard frequency selective filters such as lowpass, highpass, bandpass, etc. filters with arbitrary frequency resopnse.In this experiment, we designed an FIR filter using Frequency Sampling method for low pass and high filters.

We took the input specifications similar to the expt performed using Window method. We observed that as the order increases the, the number of lobes in the stop band increases.The major advantage of FSM lies in the efficient frequency-sampling structure which is obtained when most of the frequency samples are zero.

https://drive.google.com/drive/folders/0B9Ily3Urp8vgb3NSemVRS3k4bms

Digital Chebyshev Filter

The digital Chebyshev filter was designed using the same procedure as the Butterworth Filter using Scilab. The observed specifications from plot matched the theoretical ones.

The characteristics show the ripple behavior in pass band and monotonic in stop band. The number of valleys and peak in the pass band determined the order of the filter.

The major difference between butterworth and Chebyshev Filter is that the poles of butterworth filter lie on the circle, while the poles of Chebyshev Filter lie in ellipse. Also, the Chebyshev filter meets the specifications with fewer poles i.e. with lesser order than the corresponding Butterworth filter.

https://drive.google.com/drive/folders/0B9Ily3Urp8vgVWlxVDFMNHJLUXc 

Digital Butterworth Filter

The aim of this filter was to design a Digital Butterworth Filter using the input specifications like Attenuation in pass band Ap, Attenuation in stop As, Pass band Frequency Wp, Stop band Frequency Ws, and Sampling Frequency Fs.

The magnitude and pole-zero plot was plotted for both low pass filter and high pass filter. The input specifications were verified both theoretically and graphically. Also, as the Order of the filter is increased the response becomes more accurate.Another observation is that, the poles of Butterworth filter lie on the circle, while the poles of Chebyshev Filter lie in ellipse.

https://drive.google.com/drive/folders/0B9Ily3Urp8vgaENSN21GN0Rtc00

Overlap Add and Overlap Save Method for calculating Linear Convolution

After studying the DFT and FFT algorithms, the next experiment is to perform linear convolution using Overlap Add Method and Overlap Save Method. Either of the two methods used along with FFT technique, are used to implement convolution faster than the direct method.

In OAM, the input sequence is decomposed into smaller blocks and then these are convolved using FFT and then the overlapping segments are added to them to get a continuous output.

OSM is another method for find linear convolution in which the input is divided into overlapping blocks which are circularly convolved with the impulse response of the system to give linear convolution.

https://drive.google.com/drive/folders/0B9Ily3Urp8vgeFVHWGdaVjd5aGc

Fast Fourier Transform

The aim of this experiment is to perform Fast Fourier Transform of a signal. The fast Fourier transform (FFT) is a discrete Fourier transform algorithm which reduces the number of computations needed for points from 2N^2 to 2logN of DFT.

In this experiment, we calculated the FFT of a signal with N=4. The FFT algorithm was developed in C language and the output was obtained. The number of computations for DFT and FFT were compared. FFT reduces the computation time because of decomposition techniques and hence is preferred over DFT.

You can refer to code for FFT and IFFT by clicking on the link below. 

https://drive.google.com/drive/folders/0B9Ily3Urp8vgVTZ3cTdrdzA3RTg

Discrete Fourier Transform

The aim of this experiment is to perform Discrete Fourier Transform of an N-point signal. This experiment was performed using C programming language.

The DFT transforms time-based data into frequency-based data. The IDFT performs the reverse process. For an N-point signal, first the DFT of signal with N=4 and with N=8 was calculated. It was observed that as N increases, the approximation error decreases and hence the resolution of the spectrum increases.

The link for the code for DFT and IDFT is given below:

https://drive.google.com/drive/folders/0B9Ily3Urp8vgR19FY3pEc1BabkE

Convolution and Correlation

The first experiment performed in DSPP lab session was implementing an algorithm for linear convolution, circular convolution and correlation. The experiments were performed using C programming language. 

The first step was to take the inputs. The inputs were the length L of the signal x (n), length M of the signal h (n), and the N-point output signal. Then a function to perform Linear Convolution was written. The output y (n) was computed using this function and printed on the screen. Similar method was followed for circular convolution and correlation. 

We found that, if the length of the output signal in circular convolution i.e. N is less than the length of output signal for linear convolution i.e. N=M+L-1 then we get aliased output. So in order to find linear convolution using circular convolution, we have to select N>L+M-1.

Correlation is a measure of similarity between two signals.Auto correlation function is a measure of similarity between a signal & its time delayed version.

Given below is the link for the codes of Linear convolution, Circular convolution, correlation.

https://drive.google.com/drive/folders/0B9Ily3Urp8vgWkstZGpBcGZ0aDA