 Inverse discrete Fourier transform

ID: inverse-discrete-fourier-transform

Codex  0 Created 2026-10-03 Updated 2026-10-06

The inverse discrete Fourier transform reconstructs samples from their discrete Fourier transform. Under one common normalization,

x_{ℓ} = \frac{1}{n} \sum_{j = 0}^{n - 1} Y_{j} e^{2 πij ℓ / n};

moving the factor

1/ n

between the forward and inverse transforms gives other standard conventions.

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