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Why is the Hanning window function best for random signal analysis?

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Wayne King
Wayne King 2012-2-21

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Hi Lisa, I don't whether I would say it's definitely "best". That is a hard thing to say, but the general rationale is that the Hanning, or Hann window is a good compromise between main lobe width, which determines frequency resolution, and side lobe level, which governs spectral leakage.
As you reduce the side lobe levels, you inevitably worsen frequency resolution by increasing the width of the main lobe.
Conversely, as you narrow the main lobe, you inevitably raise the side lobe level.
The Hann window is in a good middle ground on both measures among the commonly-used windows.

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Lisa Justin
Lisa Justin 2012-2-21
what happens when a flattop window is used instead of a hanning window. I will like to use the flattop also for both random signal s and periodic signal as it tends to compensate for the scalloping loss in fft. Why is hann window preferred to flattop for random signal?
Wayne King
Wayne King 2012-2-21
The flattop window has a broader main lobe but lower side lobes than the Hann window. The broader main lobe can smear together periodic components, but guards against spectral leakage.
The Hann window provides better frequency resolution than the flattop window.
Wayne King
Wayne King 2012-2-21
Essentially yes, the flattop window is often used in calibration, where you want to measure the amplitude of a sine wave, so your frequency resolution is not the issue, the issue is that you do not want to contaminate the measurement with sidelobe leakage from the window.
In the other situation, you generally want better frequency resolution, leakage is always an issue, but there is no free lunch. You can't have both so the Hann window is a good compromise between main lobe width and side lobe level.
Lisa Justin
Lisa Justin 2012-2-21
Thanks.
so what you mean is that when i use the flattop window on my periodic signal the magnitudes of the frequency components are not attenuated but smear together but with the hann window i get an attenuation but no smearing together.
So when i need accurate frequency magnitue i should flattop window and i need better frequency resolution i use hann window. Can't hann give me both better resolution without spectral loss?
Lisa Justin
Lisa Justin 2012-2-21
i have to choose what i need most then, whether better frequency resolution or non attenuated magnitude. hmmmm, it is had to choose cos i need both.
Thanks
Lisa Justin
Lisa Justin 2012-2-21
Do you advice that i use a hann window also for my periodic signal sinece it will give better freq. resolution with a little spectral loss.
Wayne King
Wayne King 2012-2-21
I would. I don't know if I would use the term "spectral loss", leakage results in spurious energy showing up in your spectral estimate that is not the result of signal energy. It comes from the convolution of the signal's spectrum with that of the window.
Lisa Justin
Lisa Justin 2012-3-13
what scaling do i use with hann window for my periodic signal?

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Nicolas
Nicolas 2012-3-13

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Hello! Mainly, because it filters out with 42.3 dB all the freq. after the 3dB main lobe. It is easy to compute and gets really good results

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Lisa Justin
Lisa Justin 2012-3-13
xn=signal;%%%periodic signal
w=flattopwin(length(xn));
x=xn.*w;
sc=1/sum(w);%%%%scaling
y=(fft(x)).*sc
please how would i scale if i want to usse hann window instead. what would 'sc' be?

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