# 希尔伯特–黄变换（EMD）实验室

交互式希尔伯特–黄变换实验室：经验模态分解筛选过程、固有模态函数、瞬时频率，以及 HHT 与短时傅里叶变换的时频分辨率对比。

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

- **分类:** Signal Processing

## 概述

Interactive Hilbert-Huang Transform (HHT) and Empirical Mode Decomposition (EMD) laboratory, distinct from the existing wavelet-transform/wavelet-synthesizer (preset mother-wavelet bases) and spectrogram-analyzer (fixed-window STFT): here the basis is fully data-driven. Full sifting pipeline from Huang et al. (Proc. R. Soc. Lond. A 454, 903, 1998): interior extrema detection, mirror-extended cubic-spline upper/lower envelopes (Burden-Faires natural spline with endpoint mirroring, the classic endpoint-effect treatment), envelope-mean subtraction, and IMF conditions (#extrema vs #zero-crossings differ by at most one, zero envelope mean); sifting stops with the scale-free Rilling-Flandrin-Goncalves criterion (sigma(t) = |m|/a < theta1 on (1-alpha) of samples, IEEE SPL 10, 134, 2003) with Huang's SD recorded for display, over/under-sifting explored via the theta1 slider, and negligible-energy edge-artifact modes rejected. Decomposition: x(t) = sum of IMFs + monotone residual, exact reconstruction (verified < 1e-9), orthogonality index, up to 8 IMFs. Hilbert spectral analysis: radix-2 FFT analytic signal (positive frequencies doubled, negative zeroed), amplitude and phase separation, instantaneous frequency dtheta/dt via branch-unwrap-safe centered differences valid up to Nyquist, amplitude-gated and median-smoothed; Hilbert amplitude spectrum H(t, omega) = sum a_j(t) delta(omega - omega_j(t)) on a 160x80 time-frequency grid plus marginal spectrum h(omega). STFT comparison panel (Hann window, adjustable 32-256 samples, log-color spectrogram) sharing the time axis to show the fixed-window trade-off against window-free HHT instantaneous frequency. Six physics-anchored signal presets, each with its own sampling rate and time unit: linear chirp 2-28 Hz with AM (IMF1 instantaneous frequency tracks the ramp with R^2 = 0.997), switched 32->8 Hz tones (a single adaptive IMF whose IF switches within one time bin while STFT arrival error is about half a window), synthetic ECG with PQRST timing, 20 Hz QRS ringing and baseline wander (QRS lands in IMF1 at ~23 Hz, wander recovered as the last IMF with correlation 0.98), seismogram with P/S/surface-wave packets (IF median 13.0/5.5/2.8 Hz in the respective arrival windows), tide record (M2/S2/N2 semidiurnal + K1/O1 diurnal constituents + storm surge, hourly-scale separation), and a vowel-like glottal source with 6 Hz vibrato (formant-weighted harmonics, vibrato visible in the IF spread). Adjustable added noise (0-0.5 x RMS, seeded) demonstrates extra high-frequency IMFs appearing. Panels: input waveform with playhead, animated sifting lab showing successive iterates with envelopes and mean for IMF1, stacked IMF lanes with per-IMF frequency/iterations/energy, HHT heatmap with overlaid instantaneous-frequency traces and marginal spectrum, and the side-by-side STFT spectrogram. Diagnostics chips: IMF count, total sifting iterations, IMF1 mean frequency, valid IF fraction, orthogonality index, HHT peak frequency, residual energy, reconstruction exactness. Educational content: EMD and sifting with IMF conditions and endpoint effects, Hilbert transform/analytic signal/instantaneous frequency and why monocomponentity matters, HHT vs Fourier vs wavelet uncertainty trade-offs, applications (ECG, seismology, tides, speech, machinery) and honest caveats (mode mixing, noise sensitivity, EEMD/CEEMDAN variants). Multi-language support (zh, en, es, fr, de, ru, pt).

## 相关内容

- [零级反应 - Zero-Order Reaction](https://elysiatools.com/zh/visualizations/zero-order-reaction): 零级反应动力学和浓度随时间变化的交互式可视化
- [一级反应 - First-Order Reaction](https://elysiatools.com/zh/visualizations/first-order-reaction): 一级反应动力学和指数浓度衰减的交互式可视化
- [二级反应 - Second-Order Reaction](https://elysiatools.com/zh/visualizations/second-order-reaction): 二级反应动力学和双分子碰撞动力学的交互式可视化
- [阿伦尼乌斯方程 - Arrhenius Equation](https://elysiatools.com/zh/visualizations/arrhenius-equation): 温度对反应速率影响的交互式可视化 - 探索活化能、指数因子和速率常数的关系
- [可逆反应 - Reversible Reaction](https://elysiatools.com/zh/visualizations/reversible-reaction): A ⇌ B 可逆反应动力学的交互式可视化 - 探索正逆反应速率、平衡常数和浓度随时间的变化
- [连续反应 - Consecutive Reaction](https://elysiatools.com/zh/visualizations/consecutive-reaction): A → B → C 连续反应动力学的交互式可视化 - 探索中间物浓度峰值、决速步和所有物种的完整演化
- [链式反应 - Chain Reaction](https://elysiatools.com/zh/visualizations/chain-reaction): 自由基链式反应聚合的交互式可视化 - 探索引发、增长、终止步骤，链增长动画和分子量分布
- [勒夏特列原理 - Le Chatelier's Principle](https://elysiatools.com/zh/visualizations/le-chateliers-principle): 勒夏特列原理的交互式可视化 - 探索浓度、压强和温度变化如何影响化学平衡，配合分子动力学动画展示平衡移动过程