momttfr

Purpose

Time moments of a time-frequency representation.

Synopsis

[fm,B2] = momttfr(tfr,method)
[fm,B2] = momttfr(tfr,method,fbmin)
[fm,B2] = momttfr(tfr,method,fbmin,fbmax)
[fm,B2] = momttfr(tfr,method,fbmin,fbmax,freqs)

Description

momttfr computes the time moments of order 1 and 2 of a time-frequency representation:

$$f_m(t) = \frac{1}{E}\ \int_{-\infty}^{+\infty} f\ \mbox{tfr}(... ...\ \int_{-\infty}^{+\infty} f^2\ \mbox{tfr}(t,f)\ df - f_m(t)^2.$$

Name	Description	Default value
tfr	time-frequency representation (size (N,M))
method	chosen representation (name of the corresponding M-file).
fbmin	smallest frequency bin	1
fbmax	highest frequency bin	M
freqs	true frequency of each frequency bin. freqs must be of length fbmax-fbmin+1	auto1
fm	averaged frequency (first order moment)
B2	squared frequency bandwidth (second order moment)

¹ freqs goes from 0 to 0.5 or from -0.5 to 0.5 depending on method.

Examples

         sig=fmlin(200,0.1,0.4); tfr=tfrwv(sig);
         [fm,B2]=momttfr(tfr,'tfrwv'); 
         subplot(211); plot(fm); subplot(212); plot(B2);
         freqs=linspace(0,99/200,100); tfr=tfrsp(sig); 
         [fm,B2]=momttfr(tfr,'tfrsp',1,100,freqs); 
         subplot(211); plot(fm); subplot(212); plot(B2);

The first order moment represents an estimation of the instantaneous frequency, and the second order moment the variance of this estimator. We can see that the estimation is better around the time center position than at the edges of the observation interval. Besides, the second estimator (using the spectrogram) has a lower variance than the first one (using the Wigner-Ville distribution), but presents an important bias.

See Also

momftfr, margtfr.

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