Re: zero-pad as an interpolation in frequency domain?

On Nov 19, 7:55 am, Rune Allnor <all...@xxxxxxxxxxxx> wrote:
On 19 Nov, 15:26, "A.E lover" <aelove...@xxxxxxxxx> wrote:

Hi all,

I read somewhere that we can derive mathematically the zero padding
equation to show that zero-padding is simply an interpolation in
frequency domain. I tried to derive but still could not see the
interpolation operator. Can you please tell me how to derive it from
DFT formula?

That's partially correct.

If you start with N non-zero samples and pad with q*N
zeros (q a non-zero positive integer) then you will
find that the spectrum coefficients from your original
signal are preserved in the zero-padded spectrum, and
you have q additional equidistantly spaced coefficients
between the original coefficients.

If you don't pad with q*N zeros the original spectrum
coefficients are not preserved, and the term
"interpolation" becomes, well, useless.

Rune

A.E.

If you start with N contiguous non-zero weighted samples and pad with
any positive integer number of zeros you will get perfectly valid
coefficients from your zero-padded spectrum. Just don't call them
'interpolated' where Rune can hear if they don't include the non-zero
padded coefficients.

Dale B. Dalrymple
http://dbdimages.com
http://stores.lulu.com/dbd
.

Relevant Pages

  • Re: zero-pad as an interpolation in frequency domain?
    ... equation to show that zero-padding is simply an interpolation in ... interpolation operator. ... you have q additional equidistantly spaced coefficients ... If you don't pad with q*N zeros the original spectrum ...
    (comp.dsp)
  • Re: zero-pad as an interpolation in frequency domain?
    ... equation to show that zero-padding is simply an interpolation in ... interpolation operator. ... you have q additional equidistantly spaced coefficients ... If you don't pad with q*N zeros the original spectrum ...
    (comp.dsp)
  • Re: zero-pad as an interpolation in frequency domain?
    ... equation to show that zero-padding is simply an interpolation in ... interpolation operator. ... you have q additional equidistantly spaced coefficients ... coefficients from your zero-padded spectrum. ...
    (comp.dsp)
  • Reconsideration: a false interpolation-paradigm in tetration ?
    ... For the computation of tetration to fractional heightsI employ the diagonalization ... This implements well-known manipulation of the coefficients of formal ... This interpolation follows the common idea of polynomial interpolation resp. ... the series for the logarithm, and see, whether we get the correct series. ...
    (sci.math)
  • Re: Quartic interpolation
    ... You can find a cubic satisfying these conditions. ... is called a "clamped spline". ... "nicest looking" interpolation without unnecessary extremums etc. ... I think that I can find the family of possible coefficients (with one ...
    (sci.math)
Loading