An N-sample DFT yields exactly N discrete frequency values.

Evidence

0, 1, 2, … N − 1. This means that the transform values only exist at a finite number of discrete frequencies. This is a bit like the harmonics in a Fourier series, except that there is a finite number of them. ■ N discrete input time samples are transformed into N discrete frequency samples whose spacing is proportional to the sampling frequency divided by the number of samples. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2794

Categorization

• XREF: Extends the Fourier-series intuition introduced earlier in the book to the finite discrete case.