# How much do Windowing procedures harm the signal?

Started by December 23, 2006
```Hello experts,

I was cruising on Internet for faily long time and I could not get the
answer to my questions regarding windowgin procedure.

1. Everybody are writing how good windowing is for supressing leakage
(amplitudes at frequencies higher and lower than the signal frequency).
However nobody says how much it supresses amplitude at signal
frequency itself.  It surely must suppress it a bit, after all if you
multiply signal with something LESS than 1 it must be smaller.  But how
much? (if possible, make an estimate at least for Hann window)

2. Windowing is designed for getting rid of edge effects, that is,
voltage is changing between -1 and 1 V, you can start with signal of -1
V and end with signal + 0.5 V, hence edge.  However, I have a different
problem, my signal is positioned ON carrier, which changes without any
order between say -10 V and 10 V.  So what happens is that I can start
with - 5V and end with + 7 V, despite my signal is only 1 V large.  Is
windowing good for this situation too?  Or should I try something else?

Marko.

```
```Pygmalion skrev:
> Hello experts,
>
> I was cruising on Internet for faily long time and I could not get the
> answer to my questions regarding windowgin procedure.
>
> 1. Everybody are writing how good windowing is for supressing leakage
> (amplitudes at frequencies higher and lower than the signal frequency).
>  However nobody says how much it supresses amplitude at signal
> frequency itself.  It surely must suppress it a bit, after all if you
> multiply signal with something LESS than 1 it must be smaller.  But how
> much? (if possible, make an estimate at least for Hann window)

The question can not be answered. Multiplication in time domain
corresponds to convolution in frequency domain. So each frequency
component in the "true" periodogram is modified according to the
sidelobes of the window function and the rest of the "true"
periodogram.

Do note that the truncated data set corresponds to convolving the
"true" periodogram of a random process of infinite duration with the
spectrum of the rectangular window function. This repesents a
certain amount of spectral leakage. Window functions are used
because they trade some of this spectrum leakage for a smoother
spectrum.

> 2. Windowing is designed for getting rid of edge effects, that is,
> voltage is changing between -1 and 1 V, you can start with signal of -1
> V and end with signal + 0.5 V, hence edge.

Wrong. Windowing is used to reduce sidelobes in the spectrum.

Rune

```
```There is a definitive paper written on this very subject - "On Use of
Windows for Harmonic Analysis with the Discrete Fourier Transform," by
Frederick Harris, Proceedings of the IEEE Vol 66 No.1 (c. 1978).

He discusses and tabulates many facets of over 20 window functions,
including the one you mention.

Jeff
```
```Pygmalion wrote:
> Hello experts,
>
> I was cruising on Internet for faily long time and I could not get the
> answer to my questions regarding windowgin procedure.
>
> 1. Everybody are writing how good windowing is for supressing leakage
> (amplitudes at frequencies higher and lower than the signal frequency).
>  However nobody says how much it supresses amplitude at signal
> frequency itself.  It surely must suppress it a bit, after all if you
> multiply signal with something LESS than 1 it must be smaller.  But how
> much? (if possible, make an estimate at least for Hann window)

It's only the relative amplitudes of the signal and the leakage that
matters. If the signal is reduces to half it's unwindowsd magnitude and
leakage is reduced to 1 tenth. multiplying by 2 makes that unchanged and
one fifth.

> 2. Windowing is designed for getting rid of edge effects, that is,
> voltage is changing between -1 and 1 V, you can start with signal of -1
> V and end with signal + 0.5 V, hence edge.  However, I have a different
> problem, my signal is positioned ON carrier, which changes without any
> order between say -10 V and 10 V.  So what happens is that I can start
> with - 5V and end with + 7 V, despite my signal is only 1 V large.  Is
> windowing good for this situation too?  Or should I try something else?

Bringing both ends of your sequence smoothly to zero eliminates the
effect you describe. That's why windowing works.

Jerry
--
Engineering is the art of making what you want from things you can get.
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```
```"Rune Allnor" <allnor@tele.ntnu.no> wrote in message
>
>> 2. Windowing is designed for getting rid of edge effects, that is,
>> voltage is changing between -1 and 1 V, you can start with signal of -1
>> V and end with signal + 0.5 V, hence edge.
>
> Wrong. Windowing is used to reduce sidelobes in the spectrum.

Hmmm... I should think that the edges are what cause the sidelobes.  Witness
the FT of a rectangular window and compare it to a triangular window or a
raised cosine.  Attenuating the edges cause the sidelobes to go down - in
general at least - and generally at the expense of the main lobe width.

To the OP's question about how much the signal is changed.  The window
applies to all the signal components equally.  The corresponding correlation
in frequency that matches the multiplication in time should help make that
more evident.

Fred

```
```Pygmalion
Harris' paper is one of the best explainations of how and why to
window. Be careful of some of the table entries for Blackman and 4-term
minimum sidelobe windows. Google on Nuttall and windows to look for
references to Albert Nuttall's 1980 paper in the Transactions on ASSP
with some corrections.

Look for the original paper here:
http://www.eng.vt.edu/me5714/textbook/windows.pdf

Rune
The 'sidelobes' are visible because of signals with discontinuity at
the data ends which the FFT treats as circularly connected. Sine or
cosine components that are continuous when wrapped have the zeros of
their sidelobe patterns at frequency samples so the appearance of the
sidelobes is reduced, but I expect you know that ,so Pygmalion's
statement was correct.

Dale B. Dalrymple
http://dbdimages.com

```
```Jerry Avins wrote:
> > 1. Everybody are writing how good windowing is for supressing leakage
> > (amplitudes at frequencies higher and lower than the signal frequency).
> >  However nobody says how much it supresses amplitude at signal
> > frequency itself.  It surely must suppress it a bit, after all if you
> > multiply signal with something LESS than 1 it must be smaller.  But how
> > much? (if possible, make an estimate at least for Hann window)
>
> It's only the relative amplitudes of the signal and the leakage that
> matters. If the signal is reduces to half it's unwindowsd magnitude and
> leakage is reduced to 1 tenth. multiplying by 2 makes that unchanged and
> one fifth.
>
Right.  But how do you know how much is the signal's magnitude reduced?
And what is the factor to multiply the obtained spectrum to obtain
signal's exact amplitude?  I really wish to obtain exact amplitude and
not so much to get rid of sidelobes.

Marko

```
```>
>Jerry Avins wrote:
>> > 1. Everybody are writing how good windowing is for supressing
leakage
>> > (amplitudes at frequencies higher and lower than the signal
frequency).
>> >  However nobody says how much it supresses amplitude at signal
>> > frequency itself.  It surely must suppress it a bit, after all if
you
>> > multiply signal with something LESS than 1 it must be smaller.  But
how
>> > much? (if possible, make an estimate at least for Hann window)
>>
>> It's only the relative amplitudes of the signal and the leakage that
>> matters. If the signal is reduces to half it's unwindowsd magnitude
and
>> leakage is reduced to 1 tenth. multiplying by 2 makes that unchanged
and
>> one fifth.
>>
>Right.  But how do you know how much is the signal's magnitude reduced?
> And what is the factor to multiply the obtained spectrum to obtain
>signal's exact amplitude?  I really wish to obtain exact amplitude and
>not so much to get rid of sidelobes.

In the table in Harris's paper, look at the column entitled 'Coherent
Gain'.

I'm glad someone provided a link to this paper - I have used it for many
years as a source of reference, but it was at work, so I couldn't remember
exactly where to find the figure you wanted when I made my earlier post.

Jeff
>
>Marko
>
>

```
```OK, so it is a usual practice to use windowing, and then divide it with
coherent gain in order to obtain real magnitude for oscillation?

Regards, Marko

Jeff Caunter wrote:
> >
> >Jerry Avins wrote:
> >> > 1. Everybody are writing how good windowing is for supressing
> leakage
> >> > (amplitudes at frequencies higher and lower than the signal
> frequency).
> >> >  However nobody says how much it supresses amplitude at signal
> >> > frequency itself.  It surely must suppress it a bit, after all if
> you
> >> > multiply signal with something LESS than 1 it must be smaller.  But
> how
> >> > much? (if possible, make an estimate at least for Hann window)
> >>
> >> It's only the relative amplitudes of the signal and the leakage that
> >> matters. If the signal is reduces to half it's unwindowsd magnitude
> and
> >> leakage is reduced to 1 tenth. multiplying by 2 makes that unchanged
> and
> >> one fifth.
> >>
> >Right.  But how do you know how much is the signal's magnitude reduced?
> > And what is the factor to multiply the obtained spectrum to obtain
> >signal's exact amplitude?  I really wish to obtain exact amplitude and
> >not so much to get rid of sidelobes.
>
> In the table in Harris's paper, look at the column entitled 'Coherent
> Gain'.
>
> I'm glad someone provided a link to this paper - I have used it for many
> years as a source of reference, but it was at work, so I couldn't remember
> exactly where to find the figure you wanted when I made my earlier post.
>
> Jeff
> >
> >Marko
> >
> >

```
```>
>OK, so it is a usual practice to use windowing, and then divide it with
>coherent gain in order to obtain real magnitude for oscillation?
>

Yes, I would say so. Sometimes, however, this 'comes out in the wash' if
you are applying other processes too, and employ some kind of overall
calibration factor.

Jeff
```