## Normalized DFT

A more ``theoretically clean'' DFT is obtained by projecting onto the
*normalized DFT sinusoids* (§6.5)

*normalized DFT (NDFT)*of is

It can be said that only the NDFT provides a proper *change of
coordinates* from the time-domain (shifted impulse basis signals) to
the frequency-domain (DFT sinusoid basis signals). That is, only the
NDFT is a pure
*rotation* in , preserving both orthogonality and the unit-norm
property of the basis functions. The DFT, in contrast, preserves
orthogonality, but the norms of the basis functions grow to
. Therefore, in the present context, the DFT coefficients can be
considered ``denormalized'' frequency-domain coordinates.

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