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Advanced Digital Signalling Processes Exam for Telecommunications Engineering, Exams of Digital Signal Processing

Alliance UniversityDigital Signal Processing

A past exam paper from the master of engineering in telecommunications engineering program at cork institute of technology. The exam covers topics such as aliasing, sampling theory, spectral estimation, and filter design. Students are required to answer any four questions within the given time frame. The examiners include dr. J. Connell, mr. P. French, dr. S. Mcgrath, and mr. A. Murphy.

Typology: Exams

2012/2013

Uploaded on 03/30/2013

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Cork Institute of Technology
Master of Engineering in Telecommunications Engineering
(NFQ -Level 9)
January 2006
Advanced Digital Signalling Processes
(Time: 2 Hours)
Answer any FOUR questions.
All questions carry equal marks.
Examiners: Dr. J. Connell
Mr. P. French
Dr. S. McGrath
Mr. A. Murphy
Q1.
a) What is aliasing ? What hardware is used to avoid it and comment on its
effectiveness. Outline the rules of aliasing when it does take place. (7 marks)
b) An analogue signal is given by the expression: )
3
440cos(53)(
π
π
−−= ttx V.
It is sampled at Hzfs100=. After how many samples will the sequence
repeat itself ? Calculate )2(x.
Write out an expression for a signal, )(
1tx , lying in the spectral range
2/0 s
ff <≤ which would produce identical samples at Hzfs100
=
.
(8 marks)
c) Outline a time domain model for the sampling process and hence deduce the
spectral properties of a discrete time function. (10 marks)
Q2.
a) Discuss the spectral implications of using finite data sets to estimate the
spectrum of a signal. Include reference to concepts such as resolution, leakage
and zero-padding. (10 marks)
b) A periodic digital signal is given as {…1 -4 -2 3 1 -4 -2….}.
↑
Evaluate the spectrum using a 4-point, Radix-2 FFT. Hence indicate the
possible frequency components in the signal, their amplitude and their phase.
(8 marks)
c) Outline briefly the parametric approach to spectral estimation. Specify the
relative advantages and disadvantages over the non-parametric approach.
(7 marks)
pf2

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Cork Institute of Technology

Master of Engineering in Telecommunications Engineering

(NFQ -Level 9)

January 2006

Advanced Digital Signalling Processes

(Time: 2 Hours)

Answer any FOUR questions. All questions carry equal marks.

Examiners: Dr. J. Connell Mr. P. French Dr. S. McGrath Mr. A. Murphy

Q1.

a) What is aliasing? What hardware is used to avoid it and comment on its effectiveness. Outline the rules of aliasing when it does take place. (7 marks)

b) An analogue signal is given by the expression: ) 3

() 3 5 cos( 440

π x t = − π − t V.

It is sampled at f (^) s = 100 Hz. After how many samples will the sequence repeat itself? Calculate x ( 2 ). Write out an expression for a signal, x 1 (^) ( t ), lying in the spectral range 0 ≤ f < fs / 2 which would produce identical samples at f (^) s = 100 Hz. (8 marks)

c) Outline a time domain model for the sampling process and hence deduce the spectral properties of a discrete time function. (10 marks)

Q2.

a) Discuss the spectral implications of using finite data sets to estimate the spectrum of a signal. Include reference to concepts such as resolution, leakage and zero-padding. (10 marks)

b) A periodic digital signal is given as {…1 -4 -2 3 1 -4 -2….}.

↑ Evaluate the spectrum using a 4-point, Radix-2 FFT. Hence indicate the possible frequency components in the signal, their amplitude and their phase. (8 marks)

c) Outline briefly the parametric approach to spectral estimation. Specify the relative advantages and disadvantages over the non-parametric approach. (7 marks)

Cork Institute of Technology

Q3.

a) In relation to the design of non-recursive filters using the window method, comment on the amplitude/phase responses of even/odd order and symmetric/asymmetric impulse response filters. Hence specify their suitability, or otherwise, for LP, HP, BP, BR filtering operations. (10 marks)

b) Design an eighth order, nonrecursive filter to remove all frequencies below

1250Hz. The passband gain is to be H ( ej ω)= 1. The window function is Hamming. Assume the input signal is being sampled at 8kHz. Write out the difference equation which describes the process.

Describe precisely the effect of the filter’s phase response. (15 marks)

Q4.

An observed sequence is given by the expression (^)  

( ) 2 sin

n xn

π

. The

desired signal is (^)  

( ) 3 cos

n dn

. Using the expression for the gradient of

the error surface, ∇ = 2 RW − 2 P , calculate the weight values for a first order, optimum linear filter.

Verify the system operation for n = 2 and n = 8. (25 marks)

Q5.

a) Assuming the system in Q.4 is adaptive and employs the Least Mean Square (LMS) algorithm, calculate the weight values for the first 5 iterations starting at n = 0. Assume the initial weight values are zero and the convergence factor value is μ = 0. 1. The required sample values are:

x ( n ) = 0 1.9021 1.1756 -1.1756 -1.9021 0………….. d ( n ) = -3 -0.9271 2.4271 2.4271 -0.9271 -3………….. (12 marks)

b) Write general notes on the philosophy behind the construction of a Multilayer Perceptron and its adaptation using the Back Propagation Algorithm. (13 marks)