PyWavelets CWT implementation - Signal Processing Stack Exchange 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
time frequency - Wavelet Scattering explanation? - Signal Processing . . . 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
Discrete wavelet transform; how to interpret approximation and detail . . . 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)
wavelet - CWT at low scales: PyWavelets vs Scipy - Signal Processing . . . Wavelet amplitudes comparison Instead of looking at max amplitude, I define a measure of "mean amplitude": mean of absolute value of tail-trimmed wavelet, where "tail" = any absval 1e7 times less than peak amplitude (instead of strictly zero which is rarer) This is to unbias the mean for wavelets with long tails: (-- code2)
wavelet - Boundary sampling for db2 DWT lifting scheme - Signal . . . In section 6 (page 10) of Sweldens's "The Lifting Scheme: A New Philosophy in Biorthogonal Wavelet Constructions", the following is written about boundary values over discrete signals: Let us first consider the case of wavelets on an interval
wavelet - What do computed CWT frequencies and color values correspond . . . It's exactly the same here in time, and similar in frequency: per convolution theorem, "convolution in time <=> multiplication in frequency", and we're multiplying by the wavelets' frequency responses in frequency, for every row of CWT, which measures the alignment of input signal's frequency with the wavelet's - and each wavelet is narrowly
wavelet - Other time-frequency-plane tiling than STFT, DWT, ConstantQ . . . b) the Wavelet transform gives a non-linear tiling (better frequency resolution for low-frequencies, and better time-domain resolution for higher-frequencies) c) Constant-Q transform (such as NonStationaryGaborTransform) have a logarithmic scale for frequency bins (instead of linear with STFT) and have a time-frequency tiling like this (y-axis