FFT Calculator

Discrete Fourier transform and frequency spectrum

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

k	Freq (Hz)	Real	Imag	\|X[k]\|	Phase	Amplitude
0	0	10	0	10	0°	2.5
1	1	-2	2	2.8284	135°	1.4142
2	2	-2	0	2	180°	0.5

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