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From: dbd <dbd@ieee.org>
Newsgroups: comp.soft-sys.matlab
Subject: Re: FFT,IFFT, and NDFT,NFFT
Date: Sat, 27 Jun 2009 19:40:31 -0700 (PDT)
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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?
> ...

Dale B. Dalrymple