FFT Frequency Bin

Formula

Description

Each FFT output bin represents a frequency range of width Fs/N hertz. The k-th bin corresponds to the frequency k × Δf. The total number of unique frequency bins is N/2 + 1 (from DC to Nyquist). Choosing the FFT size involves a tradeoff between frequency resolution (finer with larger N), time resolution (faster update with smaller N), and computational cost. Power-of-two FFT sizes (256, 512, 1024, 2048, 4096) are most efficient for radix-2 FFT algorithms.

Variables

• Δf — Frequency width per bin (Hz)
• Fs — Sampling frequency (Hz)
• N — Number of FFT points

Practical Notes

For real-time spectrum analysis: N = 256 gives fast updates but coarse resolution, N = 4096 gives fine resolution but slower updates. Overlap processing (50-75% overlap between consecutive FFT frames) improves time resolution without sacrificing frequency resolution. The spectrogram (waterfall display) shows how the spectrum evolves over time using successive FFT frames.