TO BE ANSWERED IN BOOKLETS
DURATION:
50 minutes
INSTRUCTOR: Dr. P. F. Driessen
THIS EXAMINATION CONSISTS OF:
COVER SHEET
THREE PAGES OF QUESTIONS
STUDENTS MUST COUNT THE NUMBER OF PAGES IN THIS EXAMINATION PAPER BEFORE BEGINNING TO WRITE, AND REPORT ANY DISCREPANCY IMMEDIATELY TO THE INVIGILATOR
CANDIDATES ARE NOT PERMITTED ANY REFERENCE MATERIAL
AT THE END OF THE EXAMINATION, PLEASE SUBMIT:
TOTAL MARKS 30.
Question 1 (10 marks)
1.1. For a transfer function with one pole and one zero, where (approximately) in the complex z-plane would you place the pole and zero z_{1} to obtain a high pass filter characteristic with zero response at f=0 and maximum response at f=f_{s}/2? 1.2. Draw a sketch to show the pole and zero locations.
1.3. Draw a sketch of the approximate frequency (magnitude) response.
1.4. Derive the difference equation to implement this high pass filter in terms of .
1.5. Draw a diagram of an implementation of the filter.
Question 2 (10 marks)
2.1. Find the (causal) inverse z- transform of
(1) |
2.2. Write numerical values for the coefficients of the first two terms.
Question 3 (10 marks)
Design a simple digital filter whose transfer function
corresponds to a delay of two sample times, i.e.
y(k) = x(k-2) | (2) |
3.1. Specify H(z).
3.2. Find the frequency response (amplitude and phase) of this filter.
3.3. Find the impulse response h(k) of this filter by taking the inverse z-transform of H(z).
3.4. Show by convolution that the output of the filter y(k)is x(k-2) as expected.