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Re: Sonograms

Subject: Re: Sonograms
From: Walter Knapp <>
Date: Tue, 08 Jul 2003 09:03:13 -0400
Gianni Pavan wrote:
> A weighting function must be applied to a signal segment before being 
> analyzed by FFT; the FFT sees the signal as a circular series of sample and 
> the weighting avoids sharp transitions at the edges of the segment.
> The most used ones are (there are others to be used in very specific 
> situations):
> Hanning
> Hamming
> K-Bessel
> Gaussian
> 
> The weighting has two main effects: one is to reduce the amplitude and thus 
> the "importance" of the edges: this slightly increases time selectivity. 
> The other is a decrease of frequency selectivity: this produces a larger 
> peak in the frequency spectrum. These two effects are clearly related with 
> the inverse relation among time and frequency selectivity. Longer the 
> signal, better the frequency selectivity.
> 
> The shape of the weighting function is very important: other than affecting 
> time selectivity and thus  the frequency peak width, it also affects the 
> shape of the frequency peak. Some produce sidelobes, that are secondary 
> peaks on both sides of the main peak. Weighting functions producing the 
> narrowest peaks also produce the highest sidelobes. Those with larger peaks 
> has lower sidelobes...
> Sidelobes become very evident when you set a window length shorter than the 
> FFT size (in some programs this is called zero padding).
> The presence of sidelobes is particularly evident when the signals are very 
> clear, the signal to noise ratio is high, and when you plot the sonogram 
> with a very high dynamic range. I like to show 96 dB of dynamic range on my 
> sonograms to see all components of the signal and of the background. Thus I 
> prefer to use windows with no sidelobes at all. This means to have larger 
> peaks I normally compensate by increasing the window length. Unfortunately 
> few programs allows a complete control on all analysis parameters.
> 
> The Hanning function is the typical window used in most signal analysis 
> procedures; its shape is a cosinusoid.
> Try to use the K-bessel and Gaussian ones to increase time selectivity and 
> to avoid the sidelobes typical of the Hanning window. Linear (no weighting 
> at all) and Hamming windows are not reccomended becouse of their sidelobes. 
> Hamming has the best frequency selectivity but you have to pay this with 
> sidelobes spreading on the whole spectrogram.
> 
> To make some experiments I suggest to record or synthetize a constant 
> frequency and a frequency modulated tone and then to analyze them with the 
> different windows you can set by changing size and shape.
> 
> Gianni

I would only add that this amplifies something I've tried to make clear. 
A sonogram is a compromise dictated by the math involved. A good one is 
a darned good representation of the sound, but it's not exact. Use care 
in making decisions based on the fine details of a sonogram.

Thanks for the discussion Gianni, it's surprisingly hard to find good 
explanations of this stuff.

Walt




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