hw8.220.06 - ECE 220 Multimedia Signal Processing Fall 2006...

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ECE 220 Multimedia Signal Processing October 17, 2006 Fall 2006 Mini-Homework 8 Assigned: Thursday, October 17, 2006 Due: Wednesday, October 25, by 4:30 pm in the 220 lock-box on the 2nd floor of Phillips. Office hours: See the web page for everyone’s office hours: Goals & concepts: Computing linear convolutions using the DFT; understanding the DCT basis functions and applying them in an image viewing example. Relevant text sections: Oppenheim & Schafer hand-out on the DFT and DCT (from Chapter 8 of “Discrete-Time Signal Processing,” Oppenheim, Schafer, and Buck), class notes. 1. Linear convolution & DFT manipulation. We have two finite-duration sequences, given by We wish to compute the linear convolution using the DFT. Both sequences must be zero- padded to a length N to allow use of the DFT to compute the linear convolution. What is the minimum N ? 2. Computing spatial frequency in and thereby relative sensitivity to simple images. A image (120 pixels wide, 80 pixels tall) is represented by its DCT coeffi- cients. (The DCT used is DCT-2, and the unitary definition is used; this is the definition given in class and in equations 8.158 and 8.159 in the O & S handout.) Therefore, there are
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