The windowed Fourier ridges are the maxima points of the spectrogram.
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.
The windows g used here are symmetric with respect to 0 and have a support within [-1/2,1/2], as in the previous table.
The windowed Fourier ridges are the maxima points of the spectrogram. If the amplitude and frequency have a small variation within the Fourier window, and if the instantaneous frequency is higher than the window's passing band, then the frequencies which maximize the spectrogram approximate the instantaneous frequencies. At these points, the complex phase of the transform is almost constant.
The windowed Fourier ridges of the sum of two analytic signals can discriminate their two instantaneous frequencies if their difference is greater than the scaled window's bandwidth:
where s is the scaling which has been applied to the Fourier window, and Dw is the bandwidth of the unscaled window g.
This is a condition on the absolute frequency difference. It is related to the structure of the time frequency tiling.
Hence, the windowed Fourier ridges can detect instantaneous frequencies provided they are not too close.