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ECE 425
Digital Signal Processing
September 4, 2009
Fall 2009
Homework 1
Assigned:
September 4, 2009
Due:
September 11, by 4:00pm in the 425 lock-box on the 2nd floor of Phillips
Goals & concepts:
Review CTFT properties; understand the time/frequency trade-off for
rectangles/sincs; timelimited/bandlimited signals; convolution with delta
functions is easy.
1.
A timelimited signal cannot be bandlimited.
Recall the CTFT pair
The definitions of timelimited and bandlimited will be given in class. Consider a non-
causal, infinite duration signal
.
(a) Sketch the CTFT
of
Carefully label both the frequency axis and the height
of the delta functions. Is this signal bandlimited? Is it timelimited?
Now we’ll take a “window” of the signal, and to keep things simple we’ll window it from
to
. We can define this as multiplying the signal by a continuous-time
rectangle function: we will define the
continuous time
“rectangle” (or “rect”) function in
EE 302 as follows:
(b) Note that the rectangle function is timelimited. Using the definition of the forward
CTFT as
,
find the CTFT of
. Sketch it, carefully labelling both zero-crossings and the
main-lobe height. Is the rectangle function bandlimited?

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