Assignment Fall 2016
Module: Digital Signal Processing (ELEC 30001) ID NUMBER
Level: 3 Max. Marks: 100
Session: All
Assignment Outcomes
Represent a signal in a discrete time form and to be able to understand how to process it;
Characterize a DT system in DSP and its transfer function;
Analyze the system in Time plane, Z plane and frequency plane;
Guidelines:
Please add front title page with your answers uploaded on Moodle.
Each question carries 20 marks.
Assignment answers must be computer typed. Please do not write question statement. Just mention the question number.
Font - Times New Roman
Font – Style - Regular
Font - Size - 12
Softcopy is to be submitted through Moodle Turntin.
Explain with suitable diagrams wherever required.
The final assignment must have a Title Page, table of contents, references/ bibliography and page number.
Heading should be with Font Size 14, Bold, and Underline.
Each student has to do the assignment individually.
You can refer books in Library or use internet resource. But you should not cut and paste material from internet nor provide photocopied material from books. The assignment answers should be in your own words after understanding the matter from the above resources.
Rules & Regulations
If any coursework assessment is found to be copied from other candidates using unacceptable means, then it shall be cancelled and the total marks awarded will be zero. No chance of resubmission or appeal will be given*.
Your source of information should be mentioned in the reference page clearly. (For example: If it’s from book, you have to mention the full details of the book with title, author name, edition and publisher’s name. If it is from the internet you have to mention the correct URL). Otherwise the assignment will be considered as plagiarized*.
The students may be asked to appear for a viva voce to validate the assignment solutions submitted. The viva voce does not carry any marks.
Title Page must have Assignment Name, Module name, your name, ID, Section and the name of the faculty.
For late submission, 5% of the awarded marks will be deducted for each working day.
For plagiarism, please refer to student guide and clarification uploaded on Moodle.
Refer MIG for feedback dates on assignment.
No assignment will be accepted after one week from the date of submission*.
Date of submission 26.12.2016
* Refer to the MIG for MEC policy on academic integrity and late submission.
1. Consider a casual system with input x[n]and output y[n]. If the input is given by
x[n]=3^(1-n) u[n]-4^(n+1) u[-n-1],
The output has a z-transform given by
Y(z)=(1+z^(-1)-z^(-2))/(1-1/3 z^(-1) )(1-4z^(-1) )
Determine the z-transform of the input x[n]. (10 Marks)
Find all possible choices for the impulse response of the system. (10 Marks)
2. In an image processing application a digital signal processing system is represented by
y(n)=med{x(n-3),x(n-2),x(n-1),x(n),x(n+1),x(n+2),x(n+3)}; where the operation med{} is given by the algorithm: arrange values in the ascending order and the answer is the middle value. For eg: med(5,3,9}=5. Whether the system is
Causal (3 Mark)
Linear (10 Marks)
time invariant system (7 Marks)
Justify your answers.
3. Two causal filters having frequency response H1(?)=1/(1-0.5e^(-j?) ) and H2(?)= (sin2?/sin0.5? e^(-j1.5?) )^2 . Compute the coefficients of h (n) where h (n) is the inverse DTFT of H(?). Let H(?)=1/2p [H1(?)*H2(?)]. (20 Marks)
4. a. The basic radix-2 FFT algorithms based on decimation-in-time are indicated in the text, Figures 5 and 6. For each of these eight flow-graphs indicate whether or not each of the following properties is true or not with necessary justifications.
Represents an in-place computation
Input is in normal order
Output is in normal order
Coefficients should be stored in bit-reversed order
Accessing of the data is identical for every array. (10 Marks)
b. If x(n)=[1,2,3,2,1,0,1,2] calculate FFT using the flow graph given in Figure 5. (10 Marks)

Figure 5

Figure 6
5. Consider the given sequences:
m[n]=u[n]-u[n-6],
p[n]=d[n]+2d[n-2]+d[n-4],
h[n]=m[n]*p[n]
Determine and sketch the sequence h[n]. (7 Marks)
Determine and sketch the sequence r[n] such that r[n]*m[n]=?_(k=-8)^(n-1)¦h[k] , (6 Marks)
Is h[-n]=m[-n]*p[-n]? Justify your answer. (7 Marks)