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The wavelet transform can be seen as an alternative to the FFT.
Essentially it's a convolution of a small wave or 'wavelet'.
A wavelet is created from which is integral of close together cosine waves, and ends up looking like mini-version of the center freq.
- TODO: add image
Typically, the shape of the wavelet is the same for each of ranges of interest, just scaled.
With wavelet's one sees not just the intensity of frequency, but whether high or low at that point in time.
This is very interesting to monitoring and extrapolating patterns in the data.
Unlike the fft (which uses same time scale for multiple frequencies), each frequency range has very high temporal localization.
This also means different resolution between different frequencies, higher frequencies will have higher temporal resolution.
Will be better or at par with temporal resolution than the fourier frequency transform.
Under the hood, effectively, each wavelet is a FIR notch pass filter.