This inverse DFT calculator reconstructs a time-domain signal from its frequency-domain samples using the inverse discrete Fourier transform. Enter the frequency bins above.
Formula
x[n] = (1 ÷ N) × Σk=0..N−1 X[k] × e(j2πkn/N)
How it works
Each output sample x[n] sums the N complex frequency components, each rotated by its phase, then scaled by 1/N. It is the exact inverse of the forward DFT.
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Frequently Asked Questions
What is the inverse DFT?
It reconstructs a time-domain signal from its frequency samples, the exact inverse of the discrete Fourier transform.
What is the IDFT formula?
x[n] equals one over N times the sum of X[k] times e to the j2pi k n over N, over all k.
Why divide by N?
The 1/N factor normalizes the transform so the inverse exactly recovers the original samples.