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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 - Wikipedia
    A wavelet is a wave -like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times Wavelets are termed a "brief oscillation" A taxonomy of wavelets has been established, based on the number and direction of its pulses
  • 一文讲懂小波变换（wavelet transform） - 知乎
    比较一下这些公式不难发现，小波变换和傅里叶变换最主要区别就是基函数的不同，傅里叶用的是正弦函数，而小波变换用的是其他的函数，这里的小波函数有非常多种形式可以去选择。 那么在离散信号处理处理时， D [a,b]=\frac {1} {\sqrt {b}}\sum^ {p-1}_ {m=0}=f [t_m]\psi [\frac {t_m-a} {b}],a=\tau,b=s , a=k2^ {-j},b=2^ {-j} 会多层次的分解信号。 小波变换有啥用呢？ 最突出的作用就是，用他来存储数据只需要很少的空间。 比如说，我们常见的JPG2000格式，他就是把像素点经过小波变换之后，取出其中幅值大小前百分之多少的数值，进行储存，因此极大的减少了存储量。
  • 小波变换（Wavelet Transform）-CSDN博客
    小波变换 （wavelet transform，WT）是一种新的变换分析方法，它继承和发展了短时傅立叶变换局部化的思想，同时又克服了窗口大小不随频率变化等缺点，能够提供一个随频率改变的“时间-频率”窗口，是进行信号时频分析和处理的理想工具。
  • What Is a Wavelet? - MATLAB Simulink - MathWorks
    What Is a Wavelet? A wavelet is a waveform of effectively limited duration that has an average value of zero and nonzero norm Many signals and images of interest exhibit piecewise smooth behavior punctuated by transients
  • 1 Introduction to Wavelet Analysis - Stanford University
    Given a mother wavelet, an orthogonal family of wavelets can be obtained by properly choosing a = af and b = nbo, where m and n are integers, a0 > 1 is a dilation parameter, and b0 > 0 is a translation parameter
  • wavelet_百度百科
    Fischer prefers to use a less common mathematical process known as the wavelet transformation, which represents the sound in terms of short, discrete components known as wavelets 菲舍尔更喜欢一种比较不常用的数学方法——小波变换，这种方法可以将声音分解成比较短的离散的小波成分。
  • A Really Friendly Guide to Wavelets - Columbia University
    The wavelet transform or wavelet analysis is probably the most recent solution to overcome the shortcomings of the Fourier transform In wavelet analysis the use of a fully scalable modulated window solves the signal-cutting problem
  • A Review of Wavelet Analysis and Its Applications: Challenges and . . .
    This article reviews the development history of wavelet theory, from the construction method to the discussion of wavelet properties Then it focuses on the design and expansion of wavelet transform
  • Wavelet - from Wolfram MathWorld
    Wavelets are especially useful for compressing image data, since a wavelet transform has properties which are in some ways superior to a conventional Fourier transform





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