by

Ciro Santilli (@cirosantilli, 37)

Normalized DFT

There are actually two possible definitions for the DFT:

1/N, given as "the default" in many sources:
$x_{n} = \frac{1}{N} \sum_{k = 0}^{N - 1} X_{k} e^{i 2 π \frac{kn}{N}}$
(1)
$1/ N$ , known as the "normalized DFT" by some sources: www.dsprelated.com/freebooks/mdft/Normalized_DFT.html, definition which we adopt:
$x_{n} = \frac{1}{N} \sum_{k = 0}^{N - 1} X_{k} e^{i 2 π \frac{kn}{N}}$
(2)

The

1/ N

is nicer mathematically as the inverse becomse more symmetric, and power is conserved between time and frequency domains.

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