# AM/FM 调制解调实验台

AM 与 FM 调制交互实验台——时域波形、频谱、I-Q 轨迹与解调器，覆盖模拟通信基础。

> 标准页面: https://elysiatools.com/zh/visualizations/am-fm-modulation

- **分类:** Signal Processing

## 概述

Interactive AM and FM modulation lab covering the two foundations of analog communications, complementing the passive spectrogram-analyzer, the abstract z-transform, and the digital-keying morse-code-oscillator (which uses OOK, the one-bit AM case). Amplitude modulation s_AM(t) = [1 + m·cos(2π f_m t)]·cos(2π f_c t) produces a carrier plus two sidebands (bandwidth 2·f_m), with the index m≤1 constraint to avoid overmodulation; frequency modulation s_FM(t) = cos(2π f_c t + β·sin(2π f_m t)) produces an infinite Bessel-function sideband family at f_c ± n·f_m with peak deviation Δf = β·f_m and Carson-rule bandwidth B ≈ 2(β+1)·f_m; double-sideband suppressed-carrier s_DSB(t) = m·cos(2π f_m t)·cos(2π f_c t) demonstrates coherent detection. The model implements all signal generators, a radix-2 Cooley–Tukey FFT for the magnitude spectrum, and three demodulators: an envelope detector (Hilbert analytic-signal magnitude, carrier DC removed) for AM, a frequency discriminator (instantaneous frequency via the phase derivative of the analytic signal) for FM, and a product/low-pass coherent detector for DSB-SC. Four visualization panels: (1) Time-domain plot of the message (cyan), carrier (amber, faint), and the live modulated signal (white) with an animated cursor. (2) Magnitude spectrum around the carrier showing AM's symmetric sideband pair or FM's Bessel sideband ladder, with the carrier line marked. (3) IQ constellation trace (I=s(t), Q=Hilbert(s)(t)) — AM draws a breathing ring whose radius tracks the message, FM draws a rotating phasor of constant radius, with a live phasor dot. (4) Demodulator output comparing the recovered message against the original (dashed). Adjustable parameters: message frequency f_m (10–2000 Hz), carrier f_c (4–20 kHz), modulation index m or β (0–5), and channel noise (0–1). Six presets: Standard AM (m=0.8), Overmodulated AM (m=1.3, envelope inversion), Narrowband FM (β=0.5), Wideband FM (β=3), DSB-SC with coherent detection, and Noisy FM (noise=0.3). Real-time diagnostics: Carson bandwidth, FM frequency deviation, output SNR, and the FM improvement factor (3/2)·β² illustrating FM's constant-envelope noise immunity. Educational content covers AM sideband structure and the overmodulation limit, FM Bessel spectra and Carson's rule, the noise-immunity trade-off and threshold effect, and the digital descendants (ASK/FSK/PSK/QAM, Wi-Fi OFDM, Bluetooth GFSK, GPS BPSK). 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