Jul 17, 2021 · Mathematically, once the mother wavelet is parameterized, change in scale is a uniform shift of the wavelet in log-frequency - hence, peak center frequency is exactly inversely related to scale. This is fundamental to CWT (CQT formulation) and enables tight frames .

The Gabor wavelet is basically the same thing. It's apparently another name for the Modified Morlet wavelet. Quoting from Wavelets and Signal Processing: [The Modified Morlet wavelet] does not satisfy the admissibility condition but is nonetheless commonly used.

Wavelet transforms can be more difficult to interpret than FFT at face value due to the various representations, nomenclature and output formats. I had to study more than 15 resources to get a good sense of the variety and which one is used by Pywavelets (which does not provide much theory or explanation in its documentation).

Nov 19, 2020 · In the wavelet transform case, you apply a filter bank on the overall signal at once. In this way, you obtain a coarse-to fine resolution pattern on the time/frequency representation. Both methods result in similar time/frequency representations which can be derived from each other. The major differences: (1) STFT is uniform yet CWT is not.

Oct 2, 2021 · Wavelet Scattering is an equivalent deep convolutional network, formed by cascade of wavelets, modulus nonlinearities, and lowpass filters. It yields representations that are time-shift invariant, robust to noise, and stable against time-warping deformations - proving useful in many classification tasks and attaining SOTA on limited datasets.

The wavelet method is imposed. I do not really know how to do it. First I tried to understand the mathematical formula to transcribe it into a python algorithm: it's clearly beyond my abilities and my knowledge (and filling this gap would take me months, even years)

May 5, 2015 · The wavelet function is in effect a band-pass filter and scaling it for each level halves its bandwidth. The scaling and detail basically divide the signal into two applying a high-pass filter resulting into the detail coefficients - (which is the highest level of the transform) and a low-pass filter which results in the scaling coefficients ...

When doing feature extraction, it might be useful to first identify, or learn, what coefficients/bands of your wavelet transform are indeed useful to you. Two proposed steps: with proper coefficient normalization (if needed), verify if picking the highest coefficients is efficient for your purpose

Sep 28, 2020 · Wavelet length is fixed at 1024, so if the input is any shorter, then higher scale wavelets can never fully multiply the signal. The greater the disparity, the more the wavelet is "seen" similar to "Naive higher" by the signal; this can be seen in the question's heatmaps differing by vertical shifts.

A Constant Q transform is a variation on the DFT. In other words, it is a type of wavelet transform. I only have a casual understanding of both types of transforms myself, so take what I'm saying with a grain of salt. A standard DFT uses a constant window size throughout all frequencies.