2D AM / FM Modulation

Real amplitude and frequency modulation with a live FFT spectrum — genuine sidebands, not hand-drawn

Message Signal m(t) = cos(2π·f_m·t)

Carrier Signal c(t) = A_c·cos(2π·f_c·t)

AM Output s(t) = A_c(1+m·msg)·cos(ω_ct)

FFT Spectrum (live) |S(f)| — real DFT of s(t), Hann window, N=1024

Mode

Message

Carrier

Modulated

Parameters

Carrier freq f_c200 Hz

Message freq f_m20 Hz

Mod. index m0.80

Live Metrics

200

f_c (Hz)

f_m (Hz)

—

Bandwidth

0.80

Mod. index

Formula

AM: s(t) = A_c[1 + m·cos(ω_mt)] · cos(ω_ct)
Sidebands measured at f_c±f_m by a real 1024-point DFT.
Bandwidth ≈ 2·f_m

About the 2D AM/FM Modulation Simulator

What It Demonstrates

This companion to the 3D AM/FM simulator runs the exact same modulation mathematics on a flat 2D canvas, but computes its spectrum with a genuine Cooley-Tukey FFT run on the real modulated sample buffer — the AM sidebands and FM sideband spreading you see are measured, not drawn from a formula.

How to Use

Switch between AM and FM with the mode buttons. Drag the carrier and message frequency sliders, then raise the modulation index — in FM watch extra sideband pairs appear in the live FFT output exactly where the Bessel-function theory predicts them, because the spectrum comes from the same numerically phase-integrated signal that draws the waveform above it.

Did You Know?

A Hann window is applied to the sample buffer before the FFT runs. Without it, the abrupt edges of a finite sample block would smear energy across many extra bins (spectral leakage) — windowing is exactly what real spectrum analyzers do before computing a DFT on any finite chunk of real-world signal.