Exam 2 Solution Spring 209

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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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.)
Background image of page 2
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.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 6

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online