Re: Zero Padding in radix 2 FFT




stevenj@xxxxxxxxxxxx wrote:
>
> Um, since when was the DFT the same as the Fourier series? Let's not
> confuse approximation with definition.

well, it isn't the same as a Fourier series of a periodic
continuous-time function, but the DFT most certainly is the same as the
Fourier series of a periodic discrete-time function. the DFT maps a
discrete periodic function in one domain (call it the "time domain") of
period N, to another discrete periodic function in the reciprocal
domain (call that the "frequency domain") of the same period length, N.
both discrete periodic functions are fully defined by N complex
numbers and the DFT maps the N numbers from one to the N numbers of the
other.

do you disagree with this characterization, Steven?

r b-j

(still in FL)

.



Relevant Pages

  • Re: Zero Padding in radix 2 FFT
    ... but the DFT most certainly is the same as the ... Fourier series of a periodic discrete-time function. ... to another discrete periodic function in the reciprocal ... As I see it the DFT provides the coefficients, but this set of coefficients becomes a Fourier series only when you attach all the appropriate cos and sin functions. ...
    (comp.dsp)
  • Re: Zero Padding in radix 2 FFT
    ... whether the DFT and the Fourier Series are the same thing, ... "The discussion has been about whether the DFT is the same thing as the Fourier SERIES. ... A countinuous-time, infinite extent, periodic signal ... These are the types of signals that are considered in the literature. ...
    (comp.dsp)
  • Re: Zero Padding in radix 2 FFT
    ... > I have been saying that the product of the DFT, the coefficients, are ... > the Fourier Series as being the same thing. ... sequence numbers of the same period. ... defined from the DFT (or "DFS" if you prefer). ...
    (comp.dsp)
  • Re: Zero Padding in radix 2 FFT
    ... The Fourier Series for any periodic waveform is a set of cos and sin ... not true for DFS. ... the DFT gives us the amplitudes ... but not the Discrete Fourier Series. ...
    (comp.dsp)
  • Re: Zero Padding in radix 2 FFT
    ... but the DFT most certainly is the same as the ... >> Fourier series of a periodic discrete-time function. ... where the Xare simply the coefficients of the N sinusoids. ... but we *do* attach it to these sinusoidal functions. ...
    (comp.dsp)