## Normalized DFT

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

*normalized DFT (NDFT)*of is

*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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