Wavelet Ridges

The wavelet ridges are the maxima points of the normalized scalogram.

They indicate the instantaneous frequencies within the limits of the transform's resolution.

The latter is determined by the Heisenberg boxes which tile the time frequency plane.


Wavelets used

Approximatively analytic wavelets are used:

like Gabor wavelets. The atoms are similar to a windowed Fourier transform's, but, after rescaling, the window width is proportional to the "frequency" x=h/s.

Hence, similar windows are used, but with a different time frequency tiling.

The wavelet ridges are the maxima points of the normalized scalogram. Under conditions which are similar to the spectrogram's, the frequencies which maximize the normalized scalogram approximate the instantaneous frequencies. The difference is that the time frequency resolution structure is different.

Time frequency resolution

The wavelet ridges of the sum of two analytic signals can discriminate their two instantaneous frequencies if their relative differences are greater than the relative wavelet bandwidth:

and

where Dw is the wavelet bandwidth and h its frequency center.

These conditions bear on the relative frequency differences. They are related to the structure of the time frequency tiling.

Hence, the wavelet ridges can detect instantaneous frequencies provided their relative distances are not too small.


Examples of Wavelet Ridges