V2EX wavelet transform

Wavelet Transform

Definition|释义

小波变换:一种把信号表示为不同尺度(scale)位置(time/space shift)上的“小波(wavelet)”组合的数学方法,用于时频(或时尺度)分析。它特别适合处理非平稳信号(特征随时间变化的信号),常用于去噪、压缩、特征提取与多分辨率分析。(注:相关概念还包括连续小波变换 CWT 与离散小波变换 DWT。)

Pronunciation|发音(IPA)

/wevlt trnsfrm/

Examples|例句

We used a wavelet transform to remove noise from the audio.
我们用小波变换去除了音频中的噪声。

Unlike the Fourier transform, the wavelet transform can localize brief transients in both time and frequency, making it useful for analyzing spikes in biomedical signals.
不同于傅里叶变换,小波变换能在时间与频率两方面定位短暂瞬变,因此适合分析生物医学信号中的尖峰事件。

Etymology|词源

wavelet 来自 wave(波) + 指小词后缀 -let,字面意思是“小波”;transform 源自拉丁语 transformare(“改变形状、变换”)。合起来,“wavelet transform”直译为“小波的变换”,强调用一族可伸缩、可平移的小波函数对信号进行分解与表示。

Related Words|相关词汇

Literary Works|文学与经典著作中的出现

  • Stéphane Mallat, A Wavelet Tour of Signal Processing(系统介绍小波理论与信号处理应用)
  • Ingrid Daubechies, Ten Lectures on Wavelets(小波数学基础的经典著作)
  • Martin Vetterli & Jelena Kovaevi, Wavelets and Subband Coding(小波与子带编码/滤波器组的权威教材)
  • David L. Donoho & Iain M. Johnstone 等关于“小波去噪(wavelet denoising)”的论文(统计与信号处理领域广泛引用)
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