Reg. No:……………………………
KIGALI INSTITUTE OF SCIENCE AND TECHNOLOGY
INSTITUT DES SCIENCES ET TECHNOLOGIE
Avenue de l'Armée, B.P. 3900 Kigali, Rwanda
INSTITUTE EXAMINATIONS – ACADEMIC YEAR 2013
END OF SEMESTER EXAMINATION: MAIN EXAM
FACULTY OF ENGINEERING
COMPUTER ENGINEERING & INFORMATION TECHNOLOGY
THIRD YEAR SEMESTER II
CIT 3325 : DIGITAL SIGNAL PROCESSING
DATE: / /2013
TIME: 2 HOURS
MAXIMUM MARKS = 60
INSTRUCTIONS
1.
This paper contains Four (4) questions.
2.
Answer One compulsory question section A and any two (2) questions in section B
3.
Each question is 20 Marks
4.
No written materials allowed.
5.
Do not forget to write your Registration Number.
6.
Do not write any answers on this question paper.

SECTION A: Compulsory
Question 1: a) Distinguish between energy and power signals. Test whether the discrete-time signal
x[n] = (1/2) n u[n] is a power signal or energy signal.
[5 Marks] b) Using the property of z-transform, determine the z-transforms of the following signals and the corresponding pole-zero patterns. x [n] = (1 + n) u (n) [5 Marks] c) Compare finite-impulse response (FIR) filters with infinite-impulse response (IIR) filters in terms phase, flexibility, stability and noise of impulse response. Mathematical expressions are required to clarify your answers
[5 Marks] d) Compute 4-Point DFT of a sequence x[n] = {0, 1, 2, 3} using DIT algorithm and sketch
its butterfly diagram.
[5 Marks]
SECTION
B: Choose any two questions
Question 2 a) A discrete-time signal x [n] is defined as: i) Determine its values and sketch the signal x[n] ii) Give the sequential representations of x[-n], x[-n +4], x[-n -4] iii)
Can you express the signal x[n] in terms of δ[n] and u[n]? ( in one expression)
[6 Marks] b) Determine the causal signal x[n] if its z-transform is:
[6 Marks]
c) Make a comparison between analogue and digital filters. [4 Marks]
d)What is the speed improvement factor in calculating 64-point DFT of a sequence using direct computation DFT and FFT algorithms? Hints: use only number of multiplications! [ 4 Marks]

Question 3 a) List 4 disadvantages of digital filters compared to analog filters. [4 marks] b) State and prove the differentiation property in z-transform. [5 marks] c) What are the differences and similarities between Decimation-in-time (DIT) and Decimationin-frequency (DIF) algorithms? [5 Marks] d) Compute the Inverse DFT of:
[6 Marks]
Question 4 a) List any 5 advantages of digital filters over analog filters. [5 Marks] b) Compute 4-Point DFT of a sequence x[n] = {0, 1, 2, 3} using DIF algorithm and sketch its butterfly diagram. [6 Marks] c) Nowadays, there is a need of other very fast processing architectures; briefly explain and sketch a not detailed Super Harvard Architecture (SHARC® DSPs). [4 Marks] d) Express the following discrete sequence: [5 Marks] as a sum of weighted impulse sequences and as a sum of minimum of scaled and shifted unit steps

Reg. No:……………………………
KIGALI INSTITUTE OF SCIENCE AND TECHNOLOGY
INSTITUT DES SCIENCES ET TECHNOLOGIE
Avenue de l'Armée, B.P. 3900 Kigali, Rwanda
INSTITUTE EXAMINATIONS – ACADEMIC YEAR 2013
END OF SEMESTER EXAMINATION: SUPPLEMENTARY EXAM
FACULTY OF ENGINEERING
COMPUTER ENGINEERING & INFORMATION TECHNOLOGY
THIRD YEAR SEMESTER II
CIT 3325 : DIGITAL SIGNAL PROCESSING
DATE: / /2013
TIME: 2 HOURS
MAXIMUM MARKS = 60
INSTRUCTIONS
1.
This paper contains Four (4 ) questions.
2.
Answer One compulsory question section A and any two (2) questions in section B
3.
Each question is 20 Marks
4.
No written materials allowed.
5.
Do not forget to write your Registration Number.
6.
Do not write any answers on this question paper.

Question 1 a) Determine the z-transforms of the following signals, the corresponding pole-zero patterns and sketch the pole-zero plot with the ROC of the following sequence. [ 5 Marks] b) State and prove the differentiation property in z-transform. [5 Marks] c) Find the circular convolution of the two sequences: x
1
(n) = {1, 2, 2, 1} and x
2
(n) = { 1, 2, 3, 1} using circle method or matrix method
Circle method [ 5 Marks]
d) Using tabular method, determine the convolution sum of two sequences: [ 5 Marks]
Question 2 a)List and briefly explain 5 advantages of digital signal processing over analog signal processing .
[5 Marks] b) Find the z-transform and the ROC of each of the following sequences: In all cases assume that n ≥ 0.
[6 Marks] c) Make a comparison between fixed-point and floating-point digital signal processors.
[9 Marks]
Question 3
a) A causal discrete-time LTI system is described by:
Where x[n] and y[n] are the input and output of the system, respectively.
i) Determine the system function H (z).

ii) Find the impulse response h[n] of the system. [6 Marks] b) Sketch and describe the working principle of the Harvard architecture processor compared with the traditional processor von Neumann machine. [6 Marks] c)
[4 Marks] d) What are the limitations of digital signal processing compared with the analog signal processing?
[4 Marks]
Question 4 a) List any five main applications of digital signal processing. [5 Marks] b) State and prove the time-shifting property in z-transform. [5 Marks] c) Sketch the butterflies diagram and compute 4-Point DFT of a sequence x[n] = {1, 2, 3, 0} using
DIT algorithm and DIF algorithm. [10 Marks]