ELEC309 Second Semester Exam Paper 2016-17.pdf - PAPER CODE NO EXAMINER Dr A Al-Ataby ELEC 309 DEPARTMENT EE&E TEL NO 48045 Second Semester Examinations

ELEC309 Second Semester Exam Paper 2016-17.pdf - PAPER CODE...

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PAPER CODE .................... ELEC309 ............... PAGE .... 1 ........ OF .............. 6 .......................... CONTINUED PAPER CODE NO. EXAMINER: Dr A. Al-Ataby ELEC 309 DEPARTMENT: EE&E TEL. NO: 48045 Second Semester Examinations 2016-17 SIGNAL PROCESSING AND DIGITAL FILTERING TIME ALLOWED: THREE HOURS INSTRUCTIONS TO CANDIDATES The numbers in the right hand margin represent an approximate guide to the marks available for that question (or part of a question). Total marks available are 100. Answer ALL Questions Additional Information: z-Transform Table
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PAPER CODE .................... ELEC309 ............... PAGE .... 2 ........ OF .............. 6 .......................... CONTINUED 1. a) For the type 3 finite impulse response (FIR) filter: i) Prove that the z-domain transfer function in this case satisfies: ) ( ) ( 1 z H z z H N 5 ii) Explain why it must have a zero at z = -1 and a zero at z = 1. 3 iii) Can it be used as a high-pass filer? Explain why. 2 b) Compare (with numerical values) the cost of computing the 256-point DFT of a length-2048 signal, using a direct DFT, a pre-wrapped DFT and a pre- wrapped FFT. 6 c) For the following FIR filter transfer function: 3 2 1 064 . 0 48 . 0 2 . 1 1 ) ( z z z z H i) Provide two realisations of the filter in standard direct and transposed direct forms. 4 ii) Provide a cascade realisation of the filter using three first-order parts (Hint: the above transfer function can be re-written as: 3 1 ) 4 . 0 1 ( ) ( z z H ) 2 iii)
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