Difference between DTFT and DFT

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david753

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difference between dtf and dtft

In DTFT, time domain sampling data is multiply by e^-j2*pi*f*n, then summation.
But, in DTF, time domain sampling data is multiply by e^-j2*pi*n*k/N, then summation.
why it divids by N in DTF, comparing to DTFT?
 

the difference is DTFT gets continuous spectrum of signals,but DFT gets discret spectrum.
 

yes , as freeinthewind written:
"DTFT gets continuous spectrum of signals,but DFT gets discret spectrum"
and in fact we use DFt , when we want to have digital data both in frequency domain and time domain.
 

FT states a integral with the product of e^(j*2*pi*f*t).
If only discrete samples of the signal can be taken, t=n*Ts, where Ts is the sampling period. The integral is also substituted with a convolution.
Now, if N samples are taken in a run, and if only discrete frquencies can be recorded, then all recordable frequencies can be represented as multiples of fs/N, where fs is the sampling frequency. So f=k*(fs/N).
Subst t and f into the FT equation and you get DFT, noting that Ts=1/fs.
 

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