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What kind of signals are band limited?
Give examples of continuous-time signals that are band-limited. (Justify your claim that they are band-limited.)
You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!
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
