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DTFS, DTFT and DFT: Whats the difference

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Communications_Engineer

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difference between dtfs and dtft

Hi, I have a question about the difference between Discrete Time Fourier Series, Discrete Time Fourier Transform, and the Discrete Fourier Transform.

Please help as so many books put it differently especially the DTFS & DFT
 

fourier series dtft dtfs wiki

As i know , the DTFT and the DFT is that the first takes its input as a discrete time and its output is a continuous frequency while the DFT takes its input as discrete and its output will be discrete frequency.
 
relacion la dft con la dtft y dtfs

yeah I know about that.

But I want to know the technical difference them especially DTFS and DFT as both are used for periodic discrete sequences
 

DTFS is taken for periodic discrete signals and DFT is taken when these samples are to be fed to the computer for calculation.Actually the DTFS of a signal will be periodic discrete in nature, so this periodic signals is furthur sampled over a period so that the values can be used by computer.For this purpose DFT is taken
 

Re: difference between dtfs and dtft

Communications_Engineer said:
Hi, I have a question about the difference between Discrete Time Fourier Series, Discrete Time Fourier Transform, and the Discrete Fourier Transform.

Please help as so many books put it differently especially the DTFS & DFT
Click to expand...
i think mainly u know the difference between DTFS and DTFT.now coming to DTFS and DFS the difference is that you apply DTFS to a periodic signal and DFS to a finite discrete signal which is not periodic but made periodic by adding some values.
 

Discrete time fourier series is nothing but the fourier series of the sampled version of the analog input. Discrete time fourier transform is the fourier transform of the sampled version of the analog input. Note that DTFT will be periodic in nature and also continuous. Now if you sample DTFT then it becomes DFT and this is also periodic in nature but not continuous. Now when you take the inverse of DFT then time domain will also be periodic in nature as the frequency domain was discrete in nature (i.e. sampled).
 
in my view

(1) DTFS and DFT refer to the same thing (the spectrum of a periodic discrete-time sequence), since the properties of DFT are all the same as DTFS's. the only difference is DFT is explained in one period, and "circular" is used.

(2) DTFT and DTFS are different, since one is for aperiodic sequence, while the other is for periodic sequence. but the result of DTFT is continuous, and it's not fit computing by digital computer, therefore, the sequence is assumed to be periodic, and DTFS/DFT could be used to compute the discrete spectrum. also, the original aperiodic sequence could be recovered from IDFT, which means that this assumption does not lost any information.
 
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