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| − | = | + | <center><font size= 4> |
| + | '''[[Digital_signal_processing_practice_problems_list|Practice Question on "Digital Signal Processing"]]''' | ||
| + | </font size> | ||
| + | |||
| + | Topic: Nyquist Theorem and Sampling | ||
| + | |||
| + | </center> | ||
| + | ---- | ||
| + | ==Question== | ||
Give examples of continuous-time signals that are band-limited. (Justify your claim that they are band-limited.) | Give examples of continuous-time signals that are band-limited. (Justify your claim that they are band-limited.) | ||
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===Answer 2=== | ===Answer 2=== | ||
| − | + | <math>x(t) = sin(t) </math>. | |
| + | |||
| + | <math>x(t) = cos(t) </math>. | ||
| + | |||
| + | :<span style="color:purple"> Instructor's comment: Yes, pure frequencies signals such as sine and cosine are band-limited. Can you justify your answer? -pm </span> | ||
| + | |||
| + | ---- | ||
| + | ==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 <math>sin(t) , cos(t) </math> | ||
| + | |||
| + | Constants <math> x(t) = 1 </math> | ||
| + | |||
| + | Sincs | ||
| + | |||
| + | Trains? | ||
| + | |||
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[[2011_Fall_ECE_438_Boutin|Back to ECE438 Fall 2011 Prof. Boutin]] | [[2011_Fall_ECE_438_Boutin|Back to ECE438 Fall 2011 Prof. Boutin]] | ||
Latest revision as of 11:38, 26 November 2013
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?
