Spectrum analyzer: windowing

Hello,

i want to do measurements with a FFT-spectrum-analyzer.
Assume, the displayed frequenzy range is 25.6kHz. I use 400 lines of
resolution. Thus, i have frequency points ever 64Hz (the frequency
bins are 64Hz sperated from each other). I use Hanning windowing.
Now, i change the frequency range from 25.6kHz to 6.4kHz. The
resolustion is still 400 lines. So the frequency bins are
6400/400=16Hz sperated from each other. The window is still a Hanning
one. But what is with the width of the window? Is ist constant in both
measurements? Or does it adapt to the frequency range? Is main peak
(from 0dB to 3dB) wider when the frequency bins are more far away from
each other?

Thank you in advance,

Jens

 

[Fred Bartoli]

JensGraf@gmx.de a écrit :

Hello,

i want to do measurements with a FFT-spectrum-analyzer.
Assume, the displayed frequenzy range is 25.6kHz. I use 400 lines of
resolution. Thus, i have frequency points ever 64Hz (the frequency
bins are 64Hz sperated from each other). I use Hanning windowing.
Now, i change the frequency range from 25.6kHz to 6.4kHz. The
resolustion is still 400 lines. So the frequency bins are
6400/400=16Hz sperated from each other. The window is still a Hanning
one. But what is with the width of the window? Is ist constant in both
measurements? Or does it adapt to the frequency range? Is main peak
(from 0dB to 3dB) wider when the frequency bins are more far away from
each other?

Windowing is done in time domain, by multiplying the time series with a
weighting function which spans all the acquired time length.
Now, the acquired time length is related to the intended frequency span.
The less span, the more frequency resolution, the longer the time
series. As the weighting function weights the time series in the same
manner in terms of samples, whatever its time lenght, its effects in the
frequency domain are the same WRT to the total freq span. IOW the shape
of the windowing effects in frequency domain are constant in terms of
frequency bins, whatever the frequency span.

You can easily verify this by injecting a single frequency into your
analyser, say 640Hz, starting at 6.4kHz span. Being a single ray and
neglecting frequency leakage, it should be within only one bin (you'll
have to precisely adjust frequency so as to visualy reduce frequency
leakage as much as possible). Now switch the window in, and observe how
it modifies (widening) the visualized spectrum. Then switch the
frequency span to 12.8kHz or 25.6kHz and notice that the spectrum lines
shape and (percentage span) width has not changed.

I remember having seen a very good appnote on the subject, but I can't
find it ATM.

--
Thanks,
Fred.