loctime

Purpose

Time localization characteristics.

Synopsis

[tm,T] = loctime(x)

Description

loctime computes the time localization characteristics of signal x. The definition used for the averaged time and the time spreading are the following:

$$\begin{eqnarray*} t_m &=& \frac{1}{E_x}\ \int_{-\infty}^{+\infty} t\ \vert x(t)\... ...E_x}\ \int_{-\infty}^{+\infty} (t-t_m)^2\ \vert x(t)\vert^2\ dt} \end{eqnarray*}$$

where $E_x$ is the energy of the signal. With this definition (and the one used in locfreq), the Heisenberg-Gabor inequality writes $B\ T\geq 1$.

Name	Description	Default value
x	signal
tm	averaged time center
T	time spreading

Examples

Here is an example of signal which corresponds to the lower bound of the Heisenberg-Gabor inequality.

         z=amgauss(160,80,50); 
         [tm,T]=loctime(z); 
         [fm,B]=locfreq(z);
         [tm,T,fm,B,T*B]
         ans = 
               80.0000   50.0000   0.0000   0.0200   1

See Also

locfreq.

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