hw6.220.06 - ECE 220 Multimedia Signal Processing September...

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ECE 220 Multimedia Signal Processing September 26, 2006 Fall 2006 Homework 6 Assigned: September 26, 2006 Due: Wednesday, October 4, 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: http://people.ece.cornell.edu/~hemami/ece220 Goals & concepts: General use of the DTFT to evaluate systems and linear phase filters. Linear phase filters and the meaning and manifestation of “delay,” using the convolution and modulation properties of the DTFT, practice with the DTFT equations. Relevant text sections: Oppenheim & Schafer hand-out. Note that there are “practice” problems provided directly in this assignment. 1. An odd-length linear phase filter. We have an odd-length linear-phase filter with impulse response . Notice that this impulse response can be written as the convolution of with itself: . (a) Find the frequency response directly by evaluating the DTFT sum and writing it in the form . What is M ? (HINT — factor out from each of the 5 terms in the sum, and then merge two of them into a cosine.) (b) Now use the convolution property of the DTFT to find the frequency response; write it as . (HINT — M should be the same, but A and B will have different forms). (c) Sketch the both the magnitude and phase responses and characterize this filter as low- pass, band-pass, or high-pass. (d) The input to this filter is . Find the output. (HINT — find the magnitude response at and them appropriately deal with the delays of both the input and the filter.) (e) Now the input to the filter is . What delay will this signal experience? (You should be able to answer this without actually computing the output.)
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hw6.220.06 - ECE 220 Multimedia Signal Processing September...

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