Exam1_2012.pdf - ECE 513 DIGITAL SIGNAL PROCESSING Cranos M Williams EXAM 1 NAME STUDENT ID 1 System Transfer Functions(20 Pts Given below are the

Exam1_2012.pdf - ECE 513 DIGITAL SIGNAL PROCESSING Cranos M...

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ECE 513 - DIGITAL SIGNAL PROCESSING Cranos M. Williams EXAM 1: September 25, 2012 NAME: STUDENT ID: 1. System Transfer Functions: (20 Pts) Given below are the difference equations for several linear time-invariant systems. As- sume that all of the systems are causal and right sided. Perform the following for each system: Find the Z-transform, H ( z ), of the impulse response of the system. Give the region of convergence of the system. Is the system stable? If the system is unstable, write (ONLY) the zeros and/or poles of a stablized system that would result in the same magnitude response. (a) y ( n ) = x ( n ) - 2 . 5 x ( n - 1) + x ( n - 2) + 2 2 y ( n - 1) - 1 4 y ( n - 2) (b) y ( n ) = x ( n ) - 2 · 2 x ( n - 1) + 2 x ( n - 2) (c) y ( n ) = x ( n ) + 2 x ( n - 1) + x ( n - 2) + 2 · 2 y ( n - 1) - 4 y ( n - 2) NOTE: The roots of a general polynomial ax 2 + bx + c is given as ¯ x 1 , 2 = - b ± b 2 - 4 ac 2 a . 1
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ECE 513 - Exam 1: Name: Student ID: 2 1. (cont’d)
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ECE 513 - Exam 1: Name: Student ID: 3 2. Filtering Long Sequences: (20 Pts) We obtain 6 . 8 seconds of a real sampled speech signal that was sampled at a sampling rate of 8000 samples per second. We wish to use the overlap-save filtering procedure with an FIR digital filter with 120 real coefficients.
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