Theory: Continuos FT and DFT
Hi. I can't find a place to discuss on theory. So, i decide to post it here. Hope that anyone can answer for query..
FYI, i read the Understand Digital Signal Processing.pdf
Background:
From the book, When sampling a continuos time-domain function, having a CFT, and take the DFT of those samples, the DFT results in a frequency domain sampled approximation of CFT.
Question
Why can we use the output of CFT to perform the DFT?
Reason to ask:The output of continuous fourier transform(CFT) is in frequency domain ( continuos signal ) while the input of DFT (before tranformation) have to be in discrete.
Thanks a lot
Not sure if I understood your question. I try to help anyway.
When working with digital processors can only think of discrete spaces. That is, they can move from discrete-time domain to discrete frequency domain. With a digital processor can not calculate a continuous frequency domain because it would require infinite values.
DFT is the only transform that allows you to pass discrete-time domain to discrete frequency domain.
The output of the CFT and DFT are the same, what changes are inputs. The input of the CFT is a discrete and periodic signal and the input of the DFT is a discrete signal, fixed length and must be held periodically but not.
There are other good books where you can read theory about it:
Discrete-Time Signal Processing (2nd Edition) (Prentice-Hall Signal Processing Series) by Opphenheim, Schafer and Buck
Digital Signal Processing (4th Edition) by Proakis and Manolakis.
I hope I could help.
Greetings.
Julian
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