hw1.425.09 - ECE 425 Digital Signal Processing September 4,...

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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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hw1.425.09 - ECE 425 Digital Signal Processing September 4,...

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