Seeing Sound in Frequency Space
Every complex signal — a musical chord, a radio transmission, or an earthquake rumble — is actually a sum of simple sine waves at different frequencies. The Fast Fourier Transform is the mathematical microscope that lets us peer into this hidden frequency world. Developed by Cooley and Tukey in 1965, the FFT is one of the most important algorithms in the history of computing.
How the Spectrum Analyzer Works
This simulator builds a composite signal from up to three sine wave components, each with adjustable frequency and amplitude. The FFT then decomposes this signal back into its constituent frequencies, displaying the power spectrum as a bar chart. Watch how peaks appear at exactly the input frequencies — the FFT is invertible and lossless.
From Time Domain to Frequency Domain
In the time domain (top waveform), overlapping sinusoids create a complex-looking wave. In the frequency domain (bottom spectrum), the same information appears as clean, separated peaks. This dual representation is the foundation of modern signal processing — some operations are trivial in one domain but nearly impossible in the other.
Applications Everywhere
The FFT powers audio equalizers, MRI scanners, radar systems, speech recognition, and data compression. Every time you stream music, make a phone call, or use Wi-Fi, the FFT is working behind the scenes to analyze and manipulate the frequency content of signals traveling at the speed of light.