Zero padding the frequency spectrum

Hi NG,

As far as I have understood the FFT, it is sometimes beneficial to pad
the time-signal with zeros to achieve an increased "resolution" (I know
well that it is not an actual increase of resolution, rather an
interpolation that takes place).

So my question is: Is it not possible to do the same thing the other
way around? Say you have a 512-point frequencyspectrum and you pad it
with zeros to make it 1024 samples long. Then you compute the IFFT,
would you not expect to see the time-signal "spread" out over 1024
samples, i.e. interpolated?

Thanks!

Best,

M.L.

"M.L." <morten.langer@gmail.com> wrote in message
news:1140106217.632279.209110@f14g2000cwb.googlegroups.com...
> Hi NG,
>
> As far as I have understood the FFT, it is sometimes beneficial to pad
> the time-signal with zeros to achieve an increased "resolution" (I know
> well that it is not an actual increase of resolution, rather an
> interpolation that takes place).
>
> So my question is: Is it not possible to do the same thing the other
> way around? Say you have a 512-point frequencyspectrum and you pad it
> with zeros to make it 1024 samples long. Then you compute the IFFT,
> would you not expect to see the time-signal "spread" out over 1024
> samples, i.e. interpolated?

Yes. It works both ways.
For a nice tutorial on this (first hit on google BTW) is here
http://www.dspguru.com/howto/tech/zeropad.htm

Cheers
Bhaskar

Hi,

First hit on Google, eh? *blush*

Thanks! That was really helpful. Turned out I inserted the padding in
the wrong place.. 

Best,

M.L.

Bhaskar Thiagarajan wrote:

> "M.L." <morten.langer@gmail.com> wrote in message
> news:1140106217.632279.209110@f14g2000cwb.googlegroups.com...
> 
>>Hi NG,
>>
>>As far as I have understood the FFT, it is sometimes beneficial to pad
>>the time-signal with zeros to achieve an increased "resolution" (I know
>>well that it is not an actual increase of resolution, rather an
>>interpolation that takes place).
>>
>>So my question is: Is it not possible to do the same thing the other
>>way around? Say you have a 512-point frequencyspectrum and you pad it
>>with zeros to make it 1024 samples long. Then you compute the IFFT,
>>would you not expect to see the time-signal "spread" out over 1024
>>samples, i.e. interpolated?
> 
> 
> Yes. It works both ways.
> For a nice tutorial on this (first hit on google BTW)

How did you form your search query?
I've noticed value of search depends in a (to me) non-intuitive manner 
on choice of search terms.
I assume "searching" is an art rather than a science.



> is here
> http://www.dspguru.com/howto/tech/zeropad.htm
> 
> Cheers
> Bhaskar
> 
> 

Bhaskar Thiagarajan wrote:
> "M.L." <morten.langer@gmail.com> wrote in message
> news:1140106217.632279.209110@f14g2000cwb.googlegroups.com...
> > Hi NG,
> >
> > As far as I have understood the FFT, it is sometimes beneficial to pad
> > the time-signal with zeros to achieve an increased "resolution" (I know
> > well that it is not an actual increase of resolution, rather an
> > interpolation that takes place).
> >
> > So my question is: Is it not possible to do the same thing the other
> > way around? Say you have a 512-point frequencyspectrum and you pad it
> > with zeros to make it 1024 samples long. Then you compute the IFFT,
> > would you not expect to see the time-signal "spread" out over 1024
> > samples, i.e. interpolated?
>
> Yes. It works both ways.
> For a nice tutorial on this (first hit on google BTW) is here
> http://www.dspguru.com/howto/tech/zeropad.htm
>
> Cheers
> Bhaskar

BTW, this technique can be used to interpolate by a non integer > 1 as
well, provided that the IFFT size is supported.

John

"Richard Owlett" <rowlett@atlascomm.net> wrote in message
news:11v9om2f8isj0e5@corp.supernews.com...
> Bhaskar Thiagarajan wrote:
>
> > "M.L." <morten.langer@gmail.com> wrote in message
> > news:1140106217.632279.209110@f14g2000cwb.googlegroups.com...
> >
> >>Hi NG,
> >>
> >>As far as I have understood the FFT, it is sometimes beneficial to pad
> >>the time-signal with zeros to achieve an increased "resolution" (I know
> >>well that it is not an actual increase of resolution, rather an
> >>interpolation that takes place).
> >>
> >>So my question is: Is it not possible to do the same thing the other
> >>way around? Say you have a 512-point frequencyspectrum and you pad it
> >>with zeros to make it 1024 samples long. Then you compute the IFFT,
> >>would you not expect to see the time-signal "spread" out over 1024
> >>samples, i.e. interpolated?
> >
> >
> > Yes. It works both ways.
> > For a nice tutorial on this (first hit on google BTW)
>
> How did you form your search query?
> I've noticed value of search depends in a (to me) non-intuitive manner
> on choice of search terms.
> I assume "searching" is an art rather than a science.

I used
zero padding in frequency domain
as my query (pretty much the subject line).
My search terms are usually intuition based...and it helps to know the extra
advanced options available in google when the first simple searches return
too many (or too few) hits.

Cheers
Bhaskar

> > is here
> > http://www.dspguru.com/howto/tech/zeropad.htm
> >
> > Cheers
> > Bhaskar
> >
> >

Thank you.

Bhaskar Thiagarajan wrote:

 > "Richard Owlett" <rowlett@atlascomm.net> wrote in message
 > news:11v9om2f8isj0e5@corp.supernews.com...
 > [MASSIVE *SNIP*]
 >
 >>> For a nice tutorial on this (first hit on google BTW)
 >>
 >>
 >> How did you form your search query?
 >> I've noticed value of search depends in a (to me) non-intuitive manner
 >> on choice of search terms.
 >> I assume "searching" is an art rather than a science.
 >
 >
 >
 > I used
 > zero padding in frequency domain
 > as my query (pretty much the subject line).
 > My search terms are usually intuition based...and it helps to know 
the extra
 > advanced options available in google when the first simple searches 
return
 > too many (or too few) hits.
 > [minor snip]


Love intuition. Glad I'm not alone ;)

M.L. wrote:
> Hi NG,
>
> As far as I have understood the FFT, it is sometimes beneficial to pad
> the time-signal with zeros to achieve an increased "resolution" (I know
> well that it is not an actual increase of resolution, rather an
> interpolation that takes place).
>
> So my question is: Is it not possible to do the same thing the other
> way around? Say you have a 512-point frequencyspectrum and you pad it
> with zeros to make it 1024 samples long. Then you compute the IFFT,
> would you not expect to see the time-signal "spread" out over 1024
> samples, i.e. interpolated?

I do that all the time to interpolate or decimate (instead of zero
padding i cut of the higher frequency bins and IFFT). Probably not the
fastest interpolation, but undoubtfully (correct me if i'm wrong) the
most accurate. Plus it lets you interpolate by any size you want.

Bhaskar Thiagarajan wrote:
...
> For a nice tutorial on this (first hit on google BTW) is here
> http://www.dspguru.com/howto/tech/zeropad.htm
...

Thanks, Bhaskar--I agree. :-)

In honor of your kind mention of that page, I've fixed its link to Rick 
Lyons' course "Digital Signal Processing Made Simple For Engineers".

=g2
-- 
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Hi,

Thanks all of you for your input and answers. I appreciate it!

Best,

M.L.