V2EX discrete wavelet transform

Discrete Wavelet Transform

定义 Definition

离散小波变换(DWT)是一种把离散信号分解到不同尺度(频率/分辨率)位置(时间/空间)上的方法,常用于信号压缩、去噪、特征提取等。它通常通过一组滤波器组(低通/高通)下采样实现多层分解。(该术语也常与连续小波变换 CWT 相对。)

发音 Pronunciation

/ dskrit welt trnzfrm /

例句 Examples

The discrete wavelet transform helps remove noise from audio signals.
离散小波变换有助于去除音频信号中的噪声。

Using a discrete wavelet transform, the image was decomposed into multiple scales so that edges could be enhanced without amplifying high-frequency noise.
通过离散小波变换,图像被分解为多个尺度,从而在不放大高频噪声的情况下增强边缘细节。

词源 Etymology

Discrete 源自拉丁语 discretus(“分开的、区分开的”),强调在数学或计算中以离散取样点/序列处理;wavelet 是 “wave”(波)+ 指小后缀 “-lt”,意为“小波”,指具有局部性、可伸缩平移的波形;transform 来自拉丁语 transformare(“改变形状/转换”)。合起来表示“对离散信号进行小波域转换的变换方法”。

相关词 Related Words

文学与著作中的用例 Works

  • Stéphane Mallat, A Wavelet Tour of Signal Processing(系统介绍 DWT 与多分辨率分析)
  • Ingrid Daubechies, Ten Lectures on Wavelets(小波理论经典著作,涵盖离散情形与构造)
  • Gilbert Strang & Truong Nguyen, Wavelets and Filter Banks(以滤波器组视角讲解 DWT 的实现)
  • David L. Donoho, “De-Noising by Soft-Thresholding”(相关去噪方法常与小波/离散小波变换并用)
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