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Assignment and marking criteria included in thatAssignment 2 and Submission Guidelines   School  School of Information Technology and Engineering   Course Name  Master of Engineering (Telecommunications)   Unit Code  ME606   Unit Title  Digital Signal Processing   Assessment Author  Dr. Reza Berangi   Assessment Type  Assignment 2 (Individual)   Assessment Title  z-Transforms, Filters  Concepts   Unit Learning  Outcomes covered  in this assessment   a. Develop and implement signal processing algorithms in Matlab   b. Undertake in-depth design of digital filters      Weight  15%   Total Marks  100   Word/page limit  N/A   Release Date  Week 7   Due Date  Week 11 (31 May 2019, 11:55 pm)   Submission  Guidelines   • All work must be submitted on Moodle by the due date along with a completed  Assignment Cover Page.    • The assignment must be in MS Word format, single line spacing, 11-pt Calibri  (Body) font and 2 cm margins on all four sides of your page with appropriate  section headings.     • Reference sources must be cited in the text of the report, and listed appropriately  at the end in a reference list using IEEE referencing style for School of Business and  School of Information Technology and Engineering respectively.   Extension   If an extension of time to submit work is required, a Special Consideration  Application must be submitted directly through the AMS.  You must submit this  application three working days prior to the due date of the assignment. Further  information is available at:    http://www.mit.edu.au/about-mit/institute-publications/policies-proceduresand- guidelines/specialconsiderationdeferment    Academic   Misconduct         Academic Misconduct is a serious offence. Depending on the seriousness of the  case, penalties can vary from a written warning or zero marks to exclusion from  the course or rescinding the degree. Students should make themselves familiar  with the full policy and procedure available at:  http://www.mit.edu.au/aboutmit/institute-publications/policies-procedures- and-guidelines/PlagiarismAcademic-Misconduct-Policy-Procedure. For further  information, please refer to the Academic Integrity Section in your Unit  Description. http://www.mit.edu.au/about http://www.mit.edu.au/about http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/special-considerationdeferment http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/special-considerationdeferment http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/special-considerationdeferment http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/special-considerationdeferment http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/special-considerationdeferment http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/special-considerationdeferment 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http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure http://www.mit.edu.au/about-mit/institute-publications/policies-procedures-and-guidelines/Plagiarism-Academic-Misconduct-Policy-Procedure  © MIT/SITE | ME606 Digital Signal Processing Assignment 2    Page 2 of 9 ME606 Assessment 2   Introduction     The objective of this assessment is for each student to demonstrate understanding of the  contents of lecture materials in the unit by applying the principles and concepts in lecture  notes. Concepts covered by this assignment include z-transforms, and FIR filter design. Section 1.  FIR filter design  In general, we have 3 commonly used FIR filter design techniques   (1) Windowed Fourier series approach   (2) Frequency sampling approach   (3) Computer-based optimization methods In this assignment we practice the first and the second methods in designing FIR filters 1-1 Designing a low pass FIR filter using Windowed Fourier Series approach The amplitude frequency response of an ideal low pass filter is shown in Figure. 1.  Its  impulse response can be found from its inverse Fourier transform as:  h = ( ω? π ) ∗ sinc ( nω? π ) , n =. . , −2, −1,0,1,2, … , 0

Kshitij · Accepted Answer

Ans.1 
MATLAB code  
wp=pi/8; % lowpass filter bandwidth 
M=121; 
n=-(M-1)/2:(M-1)/2; % selection time window 
h0=(wp/pi)*sinc((wp/pi)*n); % truncated impulse response 
h=h0.*rectwin(M)'; % windowing 
% h=h0.*hamming(M)';% windowing 
% h=h0.*hanning(M)';% windowing 
% h=h0.*bartlett(M)';% windowing 
% h=h0.*blackman(M)';% windowing 
figure;plot(h) 
ylabel('Impulse response') 
xlabel('Samples') 
% spectrum 
FFTsize=512; 
pxx=20*log10(abs(fft(h,FFTsize))); 
fxx=(0:(FFTsize/2)-1)*(pi/(FFTsize/2)); 
figure;plot(fxx,pxx(1:FFTsize/2)); 
ylabel('Amplitude[dB]'); 
xlabel('frequency [Radian]');grid on
1) Plot the impulse response and the amplitude spectrum of the filter:-
2.Frequecy measured at  wp= pi/8 = 0.3927, is approximate -5.91 db which is very close to expected 
value of -6 DB.
Maximum ripple is -85.45 db at  frequency 1.559  
3. 
The ratio of the transient band to the pass band is approximate 3
4. 
When we increases impulse response length m= 255  ,its ripple amplitude increase to -152.5
5. 
When  we are using  Hanning window with the filter impulse response length, M=121
Maximum ripple value we obtaines is -173.7 db  
When we are using hamming window with the filter impulse response length ,M=121
Maximum ripple measured value= 122.4 
6.
When we have taken wp =pi/4
7. 
MATLAB Program 
%% 
wp=pi/16; % lowpass filter bandwidth 
M=121; 
n=-(M-1)/2:(M-1)/2; % selection time window 
h0=(wp/pi)*sinc((wp/pi)*n); % truncated impulse response 
h1=h0.*rectwin(M)'; % windowing 
w0=pi/4; % BPF center frequency 
h=h1.*exp(j*w0*n); % Lowpass to bandpass conversion 
figure; 
subplot(211);plot(real(h));ylabel('Real part of impulse response') 
xlabel('samples') 
subplot(212);plot(imag(h));ylabel('imag part of impulse response') 
xlabel('samples') 
% spectrum 
FFTsize=512; 
pxx=20*log10(abs(fft(h,FFTsize))); 
fxx=(0:(FFTsize/2)-1)*(pi/(FFTsize/2)); 
figure;plot(fxx,pxx(1:FFTsize/2));ylabel('Amplitude[dB]');xlabel('frequency 
[Radian]');grid on
Ans7.
Ans.8 
the passband edges wp1=0.5522 , wp2= 1.

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Assignment 2 and Submission Guidelines School School of Information Technology and Engineering Course Name Master of Engineering (Telecommunications) Unit Code ME606 Unit Title Digital Signal...

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