Discrete Fourier Transform Calculator

Compute X[k] = Σ x[n] · e^(−j2πkn/N) for any sequence up to 64 points. Shows DFT table, magnitude/phase spectra, and the DFT matrix for N ≤ 8.

Formula: X[k] = Σ x[n] · e^(−j2πkn/N), k = 0…N−1

N = 8 points (max 64)

kRe(X[k])Im(X[k])|X[k]|∠X[k] (°)
01.00000.00001.00000.00
11.00000.00001.00000.00
21.00000.00001.00000.00
31.00000.00001.00000.00
41.00000.00001.00000.00
51.00000.00001.00000.00
61.00000.00001.00000.00
71.00000.00001.00000.00
Magnitude Spectrum |X[k]|01234567Phase Spectrum ∠X[k] (degrees)01234567