Re: Zero Padding in radix 2 FFT

John Monro wrote: 
Jerry Avins wrote:

John Monro wrote:

Jerry Avins wrote:

Beating a dead horse into dog food:

John Monro wrote:

Jerry,
Yes, on checking back before this sub-thread you did indeed say, referring to the components of the DFT:
"All the integrals are the coefficients a_n and b_n in the series a_n*sin(nwt)f(t)dt + b_n*cos(nwt)f(t)dt. "
This doses of course infer that the DFT and the Fourier series are related but different.





My sentence that you quoted also says that the integrations also determine only the coefficients of the Fourier series. It seems to me that makes the integrations entirely equivalent to a DFT.



Jerry,
It seems to me that you are maintaining that if something is part of a whole then it is the same as the whole. Tell me this is not true! 



It is not true.

My contribution to this sub-thread was just this: if the coefficients (as obtained from the DFT output are only part of the Fourier Series then DFT is not the Fourier Series itself.



We already agreed that I didn't say it is the same, only that it (like frequency-by-frequency integration) produces the coefficients of one. Where is the difficulty?

  ...

Jerry 


Jerry, the difficulty was where you said:
"It seems to me that makes the integrations entirely equivalent to a DFT."

To my mind 'equivalent' means 'the same in all significant ways,' and the word 'entirely' strengthens this, to suggest that there are in fact no differences at all.

This did seem to be at variance to what you had written elsewhere, hence my note.

The DFT and the several integrations yield the same numbers (within roundoff errors). How do you think they differ?

Jerry
--
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Relevant Pages

  • Re: Zero Padding in radix 2 FFT
    ... Jerry Avins wrote: ... This doses of course infer that the DFT and the Fourier series are related but different. ... My sentence that you quoted also says that the integrations also determine only the coefficients of the Fourier series. ...
    (comp.dsp)
  • Re: Zero Padding in radix 2 FFT
    ... This doses of course infer that the DFT and the Fourier series are related but different. ... My sentence that you quoted also says that the integrations also determine only the coefficients of the Fourier series. ...
    (comp.dsp)
  • Re: Zero Padding in radix 2 FFT
    ... >> The DFT and the several integrations yield the same numbers ... How do you think they differ? ... The DFT and the integration for the Fourier series ... The Fourier series integral need not. ...
    (comp.dsp)
  • Re: Zero Padding in radix 2 FFT
    ... This doses of course infer that the DFT and the Fourier series are related but different. ... My sentence that you quoted also says that the integrations also determine only the coefficients of the 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)