Building a signal from complex exponentials

x[n] = Σu ( X[u] / M ) · exp( j 2π u n / M ),  M = 8

Each panel is one term of the inverse DFT: the complex exponential for frequency u, already scaled and rotated by its coefficient X[u]/M. Panels with the same colour are conjugate pairs. Tick panels on and off to see which terms the reconstruction is using.

Signal x[n]

Presets

Power spectrum |X[u]/M|²

Bars come in mirrored pairs because x[n] is real: |X[M−u]| = |X[u]|. Faded bars are terms left out of the sum. Click a bar to toggle it.

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Terms

Sum of the ticked complex exponentials

Terms used
8 of 8
Largest error |x[n] − sum|
0.000
Largest imaginary part
0.000
original x[n] sum of ticked terms