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Subject: Re: FFT,IFFT, and NDFT,NFFT
Date: Sun, 28 Jun 2009 06:06:00 +0000 (UTC)
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dbd <dbd@ieee.org> wrote in message <a9e25a3a-e4b4-49e4-bff1-87f869d70c97@e21g2000yqb.googlegroups.com>...
> On Jun 27, 1:25 pm, "guj " <gulatiaks...@gmail.com> wrote:
> > 1. When we have irregular sampling, we can use NDFT on it instead of FFT
> > NDFT equation
> > f_j = \sum_{k=-N/2}^{N/2-1} \hat f_k e^{(-2 *pi*i*k*x_j)}
> >
> > k= (-N/2:N/2-1)
> > x_j=time domain (j=0,1,2____M-1)
> >
> > So what my question is, whenever we have non uniform sampling in the one domain will we get uniform sampling in another domain. For ex if my time domain is irregular, will i be getting regular sampling in frequency domain
> 
> More like: In some cases of nonequispaced samples, the NFFT can
> produce equispaced Fourier coefficients.
> 
> If you want other coefficients at other spacings you could seek, for
> example, a nonequispaced discrete wavelet transform.
> >
> > 2. Inverting NDFT is not a easy task as in FFT, In ifft A inverse is equal to A conjugate, because of uniform sampling or fixed sampling in time domain that why IFFT is easy to apply. Please correct me if am wrong.
> 
> Why would you want any other function to invert the direction of the
> NFFT than an IDFT? Any finite set of the equispaced Fourier
> coefficients could represent any of an infinite number of NFFT'd
> nonequispaced sample  sets. So, how would you choose one and why?

-------------------------------------------------------------------------------------------------------
> More like: In some cases of nonequispaced samples, the NFFT can
> produce equispaced Fourier coefficients.

So you are saying, that when we have irregular sampling in one domain by application of NFFT or IDFT, we will get regular sampling in other domain, than why we cant we apply IFFT on it

>  Why would you want any other function to invert the direction of the
> NFFT than an IDFT? Any finite set of the equispaced Fourier
> coefficients could represent any of an infinite number of NFFT'd
> nonequispaced sample  sets. So, how would you choose one and why?

Actually my question was about how IFFT is easy to invert than IDFT. Is it because IFFT has equispaced sampling and which make A transpose equal to A conjugate. 

And how NFFT can be inverted. I am inverting NFFT as it will be faster than IDFT 

> > ...
> 
> Dale B. Dalrymple