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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 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
  • 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
  • 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
  • wavelet - Boundary sampling for db2 DWT lifting scheme - Signal . . .
    Sweldens and Daubechies give an example polyphase matrix factorization for the db2 D4 wavelet in section 7 5 (pp 15-16) of quot;FACTORING WAVELET TRANSFORMS INTO LIFTING STEPS quot; Specifically,
  • Reading the Wavelet transform plot - Signal Processing Stack Exchange
    Magnitude plot of complex Morlet wavelet transform The real-valued Morlet wavelet only matches when the phases of the wavelet and the signal line up So as you slide it past the signal you're measuring, it goes in and out of phase, producing maxima and minima as they cancel or reinforce: Magnitude of continuous real Morlet wavelet transform
  • 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
  • Advantage of STFT over wavelet transform
    Wavelet transforms and short-term short-time Fourier transforms are broad names for classes of transformations that are not totally distinct and may overlap (pun intended) Both can be efficient for non-stationary features of data, and they both have merits or drawbacks, depending on their parameters and signal's properties STFT is typically analyzing signals on fixed-length windows with
  • Discrete wavelet transform; how to interpret approximation and detail . . .
    Discrete wavelet transform; how to interpret approximation and detail coefficients? Ask Question Asked 8 years, 5 months ago Modified 3 years, 1 month ago
  • How is wavelet time frequency resolution computed?
    An imperfect time-domain wavelet is characterized by not fitting in the frame - but what if the frequency-domain wavelet fits just fine? I've yet to meet a time-domain wavelet that doesn't decay sufficiently if the frequency-domain wavelet does; problems arise when the frequency-domain wavelet doesn't





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