How the Fast Fourier Transform (FFT) Operates
The Fast Fourier Transform is an algorithmic implementation of the Discrete Fourier Transform (DFT) that converts continuous time-domain audio samples into discrete frequency bins. In audio analysis, FFT reveals the harmonic composition, pitch overtones, and spectral power distribution of sound waves as standardized by the W3C Web Audio API AnalyserNode specification ↗.
Frequency Bin Resolution Formula
The frequency resolution (Δf) describes the width of each spectral bin in Hertz:
Δf = Sample Rate / FFT SizeFor example, at a standard studio sample rate of 48,000 Hz:
- 2,048 FFT Size: Δf = 23.4 Hz (Fast response, coarser bass separation)
- 4,096 FFT Size: Δf = 11.7 Hz (Balanced general analysis)
- 8,192 FFT Size: Δf = 5.86 Hz (Fine musical note pitch separation)
- 16,384 FFT Size: Δf = 2.93 Hz (Ultra-high precision for low-frequency modal resonance)
Windowing Functions & Spectral Leakage
Because real-world audio is finite, cutting sample buffers introduces spectral leakage. Windowing tapers the edges of the buffer to zero to minimize side-lobe artifacts (Harris, IEEE Proceedings 1978 ↗):
- Hann / Hamming: Standard general-purpose window with good frequency resolution and low leakage.
- Blackman-Harris: Superior dynamic range (side-lobe suppression >92 dB) ideal for identifying quiet harmonics beside loud fundamentals.
- Flat-Top: Calibrated specifically for exact amplitude/voltage measurement at peak frequencies.