Moments The first and second order moments, in time and in frequency, of a time-frequency energy distribution tfr are defined as $$\begin{eqnarray*} f_m(t) &=& \frac{\int_{-\infty}^{+\infty} f\ \mbox{tfr}(t,f)\ ... ...df} {\int_{-\infty}^{+\infty} \mbox{tfr}(t,f)\ df}\ - f_m(t)^2; \end{eqnarray*}$$ for the time moments, and as $$\begin{eqnarray*} t_m(f) &=& \frac{\int_{-\infty}^{+\infty} t\ \mbox{tfr}(t,f)\ ... ...dt} {\int_{-\infty}^{+\infty} \mbox{tfr}(t,f)\ dt}\ - t_m(f)^2; \end{eqnarray*}$$ for the frequency moments. They describe the averaged positions and spreads in time and in frequency of the signal. For some particular distributions, if the signal is considered in its analytic form, the first order moment in time also corresponds to the instantaneous frequency, and the first order moment in frequency to the group delay of the signal. These moments can be obtained numerically thanks to the functions momttfr.m and momftfr.m.
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