momftfr

Purpose

Frequency moments (order 1 and 2) of a time-frequency representation.

Synopsis

[tm,T2] = momftfr(tfr)
[tm,T2] = momftfr(tfr,tmin)
[tm,T2] = momftfr(tfr,tmin,tmax)
[tm,T2] = momftfr(tfr,tmin,tmax,time)

Description

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

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

Name	Description	Default value
tfr	time-frequency representation (size (N,M)).
tmin	smallest column element of tfr taken into account	1
tmax	highest column element of tfr taken into account	M
time	true time instants	(1:M)
tm	averaged time (first order moment)
T2	squared time duration (second order moment)

Example

         sig=fmlin(200,0.1,0.4); [tfr,t,f]=tfrwv(sig); 
         [tm,T2]=momftfr(tfr); 
         subplot(211); plot(f,tm); subplot(212); plot(f,T2);

The first order moment represents an estimation of the group delay, 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.

See Also

momttfr, margtfr.

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