# 小波变换与多分辨率分析

连续和离散小波变换、尺度图和多分辨率分析的交互式可视化

> 标准页面: https://elysiatools.com/zh/visualizations/wavelet-transform

- **分类:** Math

## 概述

Comprehensive interactive visualization of continuous and discrete wavelet transform demonstrating time-frequency localization, multi-resolution analysis, and comparison with FFT. Features four mother wavelets: Haar (piecewise constant), Daubechies 4 (compact support orthogonal), Morlet (complex exponential modulated Gaussian), and Mexican Hat (second derivative of Gaussian). CWT module with formula W(a,b) = (1/sqrt(|a|))*integral(x(t)*psi*((t-b)/a)dt), scale parameter a (1-128), translation parameter b, and real-time wavelet shape preview. DWT decomposition tree showing multi-level structure: approximation coefficients A (low-pass) and detail coefficients D (high-pass) with adjustable decomposition levels (1-5). Scalogram visualization displaying time-frequency heatmap with logarithmic Y-axis (scale/1/frequency) and color-coded coefficient magnitude. Six test signals: sine wave (pure frequency), step function (edge detection), impulse (time localization), chirp (frequency sweep), noisy signal (denoising demo), and custom drawable signal. Interactive features: animate wavelet scan across signal, step-by-step decomposition visualization, coefficient thresholding for compression/denoising, and reconstruction quality metrics (MSE, SNR, compression ratio). FFT vs Wavelet comparison mode showing STFT spectrogram side-by-side with CWT scalogram to demonstrate adaptive multi-resolution vs fixed window trade-offs. Educational content covers Heisenberg uncertainty principle in time-frequency localization, multi-resolution analysis theory, orthogonality and energy preservation, compact support properties, JPEG2000 image compression, signal denoising applications, edge detection, ECG biomedical analysis, and when to use FFT vs wavelets. Uses KaTeX for formula rendering. Multi-language support (zh, en, es, fr, de, ru, pt).

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