Figure 2.

Illustation of the variables entering in the computation of $\tilde{x}$^sigma_n as defined in (6). The time-frequency plane (|W|), in gray levels, is represented by the modulus of wavelet coefficients computed for frequencies between 4 and 40 Hz with 0.1 Hz resolution. The red dashed line shows the ridge computed in the 10–16 Hz band whereas the solid red line shows the d(t_j) function defined in (4). A maximum has been detected at time t^max_n and the variation of the coefficients (i.e., the instantaneous spectrum) at the time t^max_n is shown by the solid blue line. From this spectrum, we extract the average amplitude in two intervals (shown by dashed boxes comprising respectively the low and the high frequencies) to obtain $a_{\alpha }=mean\left\{{\left|W\right|}_{\left[4-10Hz;t_n^{max}\right]}\right\}$ and $a_{\beta }=mean\left\{{\left|W\right|}_{\left[20-40Hz;t_n^{max}\right]}\right\}$. We further take the maximal amplitude in the spindle band to obtain $a_{\sigma }=max\left\{{\left|W\right|}_{\left[10.5-16Hz;t_n^{max}\right]}\right\}$.