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:

I hope I could help.

Greetings.

Julian