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Statistical significance of spectral peaks
Natalia
post Aug 21 2012, 02:34
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Hello forum folks!

I have results of FFT for a number of signals, and I need to check the significance of a certain peak at a certain frequency in each of them.
I am sorry for asking so bluntly, but how can this be done?
I'm a total dummy to FFT, so I would really appreciate any simple and easy-to-follow directions smile.gif
Thank you all so much!

Natalia
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saratoga
post Aug 21 2012, 04:10
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QUOTE (Natalia @ Aug 20 2012, 21:34) *
I have results of FFT for a number of signals, and I need to check the significance of a certain peak at a certain frequency in each of them.


What do you mean by "significance"?
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Natalia
post Aug 21 2012, 07:28
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It means rejecting the null hypothesis, which is that the time series is simply white noise at the given frequency. In other words, proving that the peak at a given frequency is not by chance (noise) by due to periodicity.
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Arnold B. Kruege...
post Aug 21 2012, 08:50
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QUOTE (Natalia @ Aug 20 2012, 21:34) *
Hello forum folks!

I have results of FFT for a number of signals, and I need to check the significance of a certain peak at a certain frequency in each of them.
I am sorry for asking so bluntly, but how can this be done?
I'm a total dummy to FFT, so I would really appreciate any simple and easy-to-follow directions smile.gif
Thank you all so much!


You may find this reference helpful:

Frequency response matching criteria from JAES

The way that you use this chart is that you first characterize your peak or dip's bandwidth, in terms of a fraction of an octave and center frequency. Then you follow the line that is closest to the bandwidth to your center frequency. Then you see if your peak or dip's height or depth is greater or less than the bandwidth line at that frequency. If it is above the line then it is a sizable fraction of what it takes to be audible.
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Natalia
post Aug 22 2012, 01:43
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QUOTE (Arnold B. Krueger @ Aug 21 2012, 16:50) *
QUOTE (Natalia @ Aug 20 2012, 21:34) *
Hello forum folks!

I have results of FFT for a number of signals, and I need to check the significance of a certain peak at a certain frequency in each of them.
I am sorry for asking so bluntly, but how can this be done?
I'm a total dummy to FFT, so I would really appreciate any simple and easy-to-follow directions smile.gif
Thank you all so much!


You may find this reference helpful:

Frequency response matching criteria from JAES

The way that you use this chart is that you first characterize your peak or dip's bandwidth, in terms of a fraction of an octave and center frequency. Then you follow the line that is closest to the bandwidth to your center frequency. Then you see if your peak or dip's height or depth is greater or less than the bandwidth line at that frequency. If it is above the line then it is a sizable fraction of what it takes to be audible.


Thank you Arnold! But I need some statistical test to prove it, because I need to add this result to the paper.

Here's the theory and guidelines as to how to do it in R package:

http://stats.stackexchange.com/questions/1...pectral-density

I was wondering if anyone knows any other solution.

Thank you!
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