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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 2 Examinations 2012
Module Title: Digital Signal Processing
Module Code: ARTI
School: School of Mechanical, Electrical and Process Engineering
Programme Title: Bachelor of Engineering in Electronic Engineering – Year 4
Programme Code: EELES_8_Y
External Examiner(s): Dr. A. Donnellan & Mr. Ian Kennedy
Internal Examiner(s): Dr. P. O’Connor
Instructions: Answer Question 1 or Question 2 – both worth 100 marks.
Duration: 2 HOURS
Sitting: Summer 2012
Requirements for this examination: Computer Lab (B283) with MATLAB software and Microsoft Word.
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 H(z). (ii) Plot its poles & zeros in the z-plane (iii) Graph its Frequency Response (magnitude and phase) over the range 0 < ω < π. (iv) What class of filter does y(n) represent? (v) Suggest an application for this filter and determine a sampling frequency.
(30 marks)
(b) The following transfer function H(s) describes an analog filter.
Graph its frequency response (both amplitude/phase) over and comment on the results (i.e. maximum value, bandwidth, filter type, stability).
( 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 Ts = 0.025 seconds (ii) No pre-warping with Ts = 2 seconds (iii) With pre-warping with Ts = 0.025 seconds and a critical frequency of 5Hz
Specify the Difference Equation, y(n) for (c) (i) and plot it if x(n) is an impulse function.
( 50 marks)
Note:
Graphs, calculations and MATLAB code must be included in your answer.
