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Cork Institute of Technology
Bachelor of Engineering (Honours) in Electronic Engineering- Award
(NFQ Level 8)
Autumn 2006
Applied Digital Signal Processing
(Time: 2 Hours)
Answer any four questions [each 25 marks] Maximum available mark is 100.
Examiners: Dr. J.Connell Prof. G. Hurley Dr. S. Foley
Q1. (a) A Dual-Tone, Multi-Frequency signal consisting of a 770Hz and a 1336Hz component is sampled at 8kHz. Discuss an analysis procedure for accurately determining the spectral content of the digital signal. Assume that 40ms maximum of data is available. [10 marks]
(b) A 30Hz, unity amplitude sinwave is sampled at 80Hz. Use a Goertzel cell to evaluate the DFT at the frequency of interest. [15 marks]
Q2. (a) Describe the Blackman-Tukey method of spectral analysis and comment on its performance in comparison to a straight DFT on the N samples. [10 marks]
(b) The causal impulse response of an LTI system is given as h ( n )={2 -4 3}. The causal input is given as x ( n )={6 -1}. Show that r (^) yx ( l )= h ( l )* rxx ( l ). Indicate how this expression might be used in system identification. [15 marks]
Q3. (a) File1 contains digital data sampled at f (^) s Hz. Describe in detail using
amplitude plots the spectral implications of creating a new file2 using every 3 rd^ sample from file1. [10 marks]
(b) A signal of bandwidth 0 ≤ f ≤ 7. 5 kHz is sampled at 15kHz. It is required to generate a second sequence of samples corresponding to a sampling frequency of 5kHz. Discuss a strategy for producing the second sequence. Write efficient software to perform the task. Assume any filter used is 4 th^ order. [15 marks]
Q4. (a) Draw the block diagram for an adaptive processor being used for noise cancellation. Explain how it works. [7 marks]
(b) A first order adaptive linear combiner has input 7
x cos 2 k k
= −^ π and a desired
input (^)
d 4 sin^2 k k
π (^). Calculate the optimum tapweight values and the
minimum MSE value. [18 marks]
Q5. (a) Draw the block diagram of an adaptive processor being used for system identification or modelling. Explain how it works. [7 marks]
(b) A system identifier consists of a processor with ADConverters on Port 0 and Port 2. The plant output is connected to Port 0 and the plant input is connected to Port 2. Assuming a first order, nonrecursive filter is used, write pseudo- assembler software to implement the system. The weights are adapted using the LMS algorithm. The adaptation gain constant is μ = 0. 01. [18 marks]
