Practice Question on "Digital Signal Processing"
Topic: Nyquist Theorem and Sampling
Question
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
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?
