Re: zero-pad as an interpolation in frequency domain?
- From: dbd <dbd@xxxxxxxx>
- Date: Mon, 19 Nov 2007 11:59:22 -0800 (PST)
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
.
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