# Inverse windowing

Started by September 22, 2005
```Hi All,

I am taking FFT of incoming signal and then windowing (convolving H(f)
with the signal) it in frequency domain. After that I perform filtering
of the signal. Now before taking the the IFFT, I want to do inverse
windowing. What should be my H(f) for this?

```
```You generally don't do that.. Windowing allows you to better resolve
some components when you're doing a block based transform.  For windows
that taper to zero near the ends, you really can't go backwards (and
the noise you'll introduce into the signal by attempting to do so
doesn't really make sense).

```
```"Duane" <duanestorey@excite.com> wrote in message
> You generally don't do that.. Windowing allows you to better resolve
> some components when you're doing a block based transform.  For windows
> that taper to zero near the ends, you really can't go backwards (and
> the noise you'll introduce into the signal by attempting to do so
> doesn't really make sense).
>

I agree.  But, to answer the question just in case:

You multiply in time by w(t) <> convolve in frequency by W(f), right?

To undo the multiply in time, divide in time by the same function.
This is equivalent to:
Multiply in time by 1/w(t) = r(t) <> convolve in frequency by R(f).

If w(t) has any zeros in it (like at the ends) then look out! (as above)

Consider this: if w(t) has zeros at the ends as many popular windows do
(although it's not necessary) then r(t) will have very large values at the
ends.  These very large values represent a high "quefrency" cosine in
frequency - sort of a very fine "comb filter".  Perhaps not what you
want....

Fred

```
```Fred Marshall wrote:
> "Duane" <duanestorey@excite.com> wrote in message
>
>>You generally don't do that..

Normally you use overlapping (and energy-preserving) windows if you want
to use the data for further processing and presumably inverse FFT.
```
```Lars L. Hansen wrote:
> Fred Marshall wrote:
> > "Duane" <duanestorey@excite.com> wrote in message
> >
> >>You generally don't do that..
>
> Normally you use overlapping (and energy-preserving) windows if you want
> to use the data for further processing and presumably inverse FFT.

Nope.

There are mainly two reasons for using windows like the von Hann,
Hamming, Blackman, Kaiser etc, windows:

- In filtering one wants to supress sidelobes (at the expence of
main lobe width).
- In non-paramateric spectrum estimation one wants to reduce the
variance of the periodogram (at the expense of feature smearing).

While the question of energy preservating windows pops up from
time to time here on comp.dsp, it seldom is very significant in
practical applications.

Rune

```