Difference between revisions of "Practice problem finding band limited signals ECE438F11" - Rhea

Latest revision as of 11:38, 26 November 2013

Question

Give examples of continuous-time signals that are band-limited. (Justify your claim that they are band-limited.)

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Answer 1

(From an email written by a student.)

I am not sure what else could be band-limited other than the sinc function and pure-frequencies. Can you please give us some more examples?

Instructor's comment: One way to come up with new band-limited signals is to transform a known band-limited signal. For example, do you know a transformation that will simply change the amplitude of the Fourier transform? Or how about a transformation that would simply shift the frequencies of the Fourier transform? Another way to obtain new band-limited signal is to combine band-limited signals into a well chosen function. For example, what happens if you take a linear combination of band-limited signals? Or what if you multiply two band-limited signals? -pm

Answer 2

$ x(t) = sin(t) $.

$ x(t) = cos(t) $.

Instructor's comment: Yes, pure frequencies signals such as sine and cosine are band-limited. Can you justify your answer? -pm

Answer 3

By nature of the Fourier Transform, band limited signals

(those whose frequency response = 0 outside of an arbitrary window, signals which are not one or two sided in the frequency domain)

can only be constructed from signals which may have a nonzero component at ANY point in time (-inf,inf).

Examples of such signals:

Pure frequencies $ sin(t) , cos(t) $

Constants $ x(t) = 1 $

Sincs

Trains?

Back to ECE438 Fall 2011 Prof. Boutin