HW2_FA08 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN...

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Department of Electrical and Computer Engineering ECE 410 Digital Signal Processing Homework 2 Due Wednesday, September 10, 2008 Prof. Bresler / Prof. Jones 1. Find a closed-form expression (no sums) for the DTFT of the following sequences: (a) (b) (c) (d) (e) 8 , where | | 1 5 , where | | 1 10 4 , where | | 1 0.6 cos 2. The DTFT of x[n] is as given in the following figure. Determine x[n] for each case. (a) Xd(ω) 2 1 ‐π − 3π − 4 π 2 ω 0 π 2 3π 4 π (b) Xd(ω) 2 1 ω ‐π 0 π 3. Find a closed-form expression for the inverse DTFT of the following sequence: 4 2 sin 2 10cos 6 . Determine in terms 4. Let [n] be an arbitrary signal, not necessarily real-valued, with DTFT of for the following : (a) (b) (c) 5. Let , where * denotes complex conjugate 3 be a signal with DTFT as shown in the following figure. Determine and sketch the DTFT of cos . 6. Consider the complex sequence . | for the case of large N. and sketch | (a) Find a closed-form expression (no sums) for Explain how does the plot change as N decreases. (b) Find a closed-form expression (no sums) for the N-point DFT of the finite length sequence , 0,1, … , 1. Sketch | | for the case of large N. (c) Find the DFT of for the case of , where is an integer. Sketch | |. 7. Find a closed-form expression (no sums) for the DFT of the following finite-length sequence of length : 0, 1, You can assume that is even. ,0 ,0 1 1 ...
View Full Document

Ask a homework question - tutors are online