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wavelet    
n. 小浪,微波

小浪,微波

wavelet
子波; 小波

wavelet
n 1: a small wave on the surface of a liquid [synonym: {ripple},
{rippling}, {riffle}, {wavelet}]

Wavelet \Wave"let\, n.
A little wave; a ripple.
[1913 Webster]

A waveform that is bounded in both {frequency}
and duration. Wavelet tranforms provide an alternative to
more traditional {Fourier transforms} used for analysing
waveforms, e.g. sound.

The {Fourier transform} converts a signal into a continuous
series of {sine waves}, each of which is of constant frequency
and {amplitude} and of infinite duration. In contrast, most
real-world signals (such as music or images) have a finite
duration and abrupt changes in frequency.

Wavelet transforms convert a signal into a series of wavelets.
In theory, signals processed by the wavelet transform can be
stored more efficiently than ones processed by Fourier
transform. Wavelets can also be constructed with rough edges,
to better approximate real-world signals.

For example, the United States Federal Bureau of Investigation
found that Fourier transforms proved inefficient for
approximating the whorls of fingerprints but a wavelet
transform resulted in crisper reconstructed images.

{SBG Austria (http://mat.sbg.ac.at/~uhl/wav.html)}.

["Ten Lectures on Wavelets", Ingrid Daubechies].

(1994-11-09)


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  • 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
  • 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
  • What does the intensity values on wavelet transform mean? Amplitude or . . .
    A standard continuous wavelet transformation (the one that produce a 2D scale shift map) is a linear operator It produces real or complex coefficients that are related to the amplitude on "how a given wavelet at specific shift and scale matches the signal" These coefficients are (most generally) homogeneous with the signal's amplitude
  • 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)
  • Power Energy from Continuous Wavelet Transform
    use wavelet transform to extract frequencies from given signal 3 Normalized Wavelet power spectrum 0
  • Wavelet thresholding - Signal Processing Stack Exchange
    The soft thresholding is also called wavelet shrinkage, as values for both positive and negative coefficients are being "shrinked" towards zero, in contrary to hard thresholding which either keeps or removes values of coefficients In case of image de-noising, you are not working strictly on "intensity values", but wavelet coefficients
  • 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 - 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





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