FFT Bin Resolution

Formula

Description

The frequency resolution of an FFT is determined by the sampling rate divided by the number of points in the transform. Each FFT bin spans Δf hertz, and the total number of usable bins is N/2 (due to the Nyquist limit). To resolve two closely spaced frequencies, Δf must be smaller than their separation. Increasing N improves resolution but requires a longer time-domain record (T = N/Fs) and more computation. Zero-padding increases the number of bins but does not improve true spectral resolution.

Variables

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

Practical Notes

For audio analysis at Fs = 48 kHz with N = 4096: Δf = 11.7 Hz. For finer resolution, increase N to 16384 giving Δf = 2.9 Hz but requiring 341 ms of data. Windowing functions (Hann, Hamming, Blackman) reduce spectral leakage but slightly widen the effective bin width. Real-time spectrum analyzers use overlapping FFT blocks for continuous coverage.