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 lockbox 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 handout.
Note that there are “practice” problems
provided directly in this assignment.
1.
An oddlength linear phase filter.
We have an oddlength linearphase 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, bandpass, or highpass.
(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.)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '05
 JOHNSON
 Digital Signal Processing, Signal Processing, Highpass filter, Lowpass filter

Click to edit the document details