FFT Calculator

Discrete Fourier transform and frequency spectrum

Real signal values x[0], x[1], … sampled at equal intervals.

Leave blank to index frequency by bin (fs = N).

X[k] = Σ x[n]·e^(−2πi·kn/N)
Samples (N)4Sample rate4 HzFrequency resolution Δf1 HzNyquist frequency2 HzDC component (mean)2.5Dominant frequency1 Hz
N is a power of two — a radix-2 FFT applies exactly.
Single-sided spectrum
kFreq (Hz)RealImag|X[k]|PhaseAmplitude
00100100°2.5
11-222.8284135°1.4142
22-202180°0.5

Bins above the Nyquist frequency mirror those below as complex conjugates, so only the single-sided spectrum is listed.

Single-sided amplitude spectrum of 4 samples across 3 frequency bins; the tallest bar marks the dominant component of amplitude 1.4142 at 1 Hz.Single-sided amplitude spectrum of 4 samples across 3 frequency bins; the tallest bar marks the dominant component of amplitude 1.4142 at 1 Hz.012