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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 2 Examinations 2010
Module Title: Digital Signal Processing
Module Code: ARTI
School: School of Electrical & Electronic Engineering
Programme Title: Bachelor of Engineering in Electronic Engineering – Year 4
Programme Code: EELES_8_Y
External Examiner(s): Dr. A. Donnellan & Dr. P. O’Sullivan
Internal Examiner(s): Dr. P. O’Connor
Instructions: Answer Question 1 or Question 2 – both worth 100 marks.
Duration: 2 HOURS
Sitting: Autumn 2010
Requirements for this examination: Computer Labs (B283 & B180) with MATLAB software.
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the correct examination paper. If in doubt please contact an Invigilator.
- (a) The following difference equation describes a digital filter
(i) Find an expression for its frequency response H(ω). (ii) Graph its magnitude and phase over the range 0 < ω < π. (iii) What class of filter does y(n) represent? (iv) Comment on the contribution, if any, of the input term x(n-2) to the filter’s frequency response.
(30 marks)
(b) The following transfer function H(s) describes an analog filter.
Graph its frequency response and comment on the results (i.e. maximum value, bandwidth, filter type).
(20 marks)
(c) Using the Bilinear Transform technique design a digital filter to have similar properties to the continuous time filter H(s) in (b) above with
(i) No pre-warping with a sample time of 0.04 seconds (ii) With pre-warping with a sample time of 0.04 seconds (iii) No pre-warping with a sample time of 0.02 seconds
Comment on your observations.
(40 marks)
(d) Using H(z) from part (c)(iii), specify its Difference Equation, y(n) and plot it if x(n) is an impulse function.
(10 marks)
Note:
Graphs, calculations and MATLAB code must be included in your answer.
