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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