Wavelet Scattering explanation? - Signal Processing Stack Exchange 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 Core results and intuition are provided in this
PyWavelets CWT implementation - Signal Processing Stack Exchange PyWavelets Breakdown: Wavelet, prior to integration, matches exactly with the shown code blob, which is an approximation of the complete real Morlet (used by Naive) assuming $\sigma > 5$ in the Wiki pywt integrates real Morlet via np cumsum(psi) * step, accounting for the differential step size The integrated wavelet, int_psi, is reused for all scales For each scale, the same int_psi is
Power Energy from Continuous Wavelet Transform How can power or energy be computed from Continuous Wavelet Transform? Is it just $\sum |\text {CWT} (x)|^2$, or are there other considerations, particularly if interested in a subset of frequencies?
cwt - Continuous Wavelet Transform vs Discrete Wavelet Transform . . . The discrete wavelet transform is applied in many areas, such as signal compression, since it is easy to compute I notice that, However, the continuous wavelet transform (CWT) is also applied to different subjects
Wavelet thresholding - Signal Processing Stack Exchange What is the difference between soft thresholding and hard thresholding Where we use soft and hard thresholding in image for denoising I understand that in hard thresholding, the coefficients below
Wavelet basis orthonormality - Signal Processing Stack Exchange I recently started learning about wavelet transforms, and there's something that is confusing me My understanding was that most wavelet decompositions are simply a decomposition of a given signal in an orthonormal basis
Wavelet center frequency explanation? Relation to CWT scales? 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 I don't know how other measures are affected
fft - Which time-frequency coefficients does the Wavelet transform . . . The Fast Wavelet Transform recursively subdivides your signal and computes the sum and difference of the two halves each time The difference is the magnitude of the transform for the current wavelet and the sum is returned for the caller to compute the magnitude of the transform for a dilated wavelet with half the frequency
interpret wavelet scalogram - Signal Processing Stack Exchange My knowledge of wavelets is less than epsilon Bear with me If I have a signal of two well separated sinusoids (15 and 48 Hz) plus some random noise, I can clearly make out the two in a spectrogra