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Exam 2 Solution Spring 209

# Exam 2 Solution Spring 209 - EEE4001F Digital Signal...

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EEE4001F: Digital Signal Processing Class Test 2 30 April 2008 SOLUTIONS Name: Student number: Information ± The test is closed-book. ± This test has four questions, totalling 20 marks. ± Answer all the questions. ± You have 45 minutes.

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1. (5 marks) Find wŒn± D xŒn± ± yŒn± with xŒn± D . N 1/ n and yŒn± D sin .²n=3/ ²n : We can think of wŒn± as the output of a system with impulse response yŒn± to the input signal xŒn± . From the tables of Fourier transform pairs, the frequency response of the system is Y.e j! / D 8 < : 1 j ! j ² ²=3 0 ²=3 < j ! j < ²: Since x.t/ D . N 1/ n D e j±n is a complex exponential of frequency ! D ² , the output is wŒn± D /e D 0: (Alternatively find and sketch X.e / and / , and show that the product W.e / D X.e /Y.e / is zero.)
2. (5 marks) Consider the following discrete-time signal: xŒn± D 8 < : sin . 4 / when n=2 is an integer 0 otherwise : Calculate and sketch the 8-point DFT (magnitude and phase) of the first 8 samples of xŒn± , i.e. xŒ0±; xŒ1±; : : : ; xŒ7± . Show and motivate your calculations.

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Exam 2 Solution Spring 209 - EEE4001F Digital Signal...

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