Orthogonality of the DFT Sinusoids

We now show mathematically that the DFT sinusoids are exactly orthogonal. Let

where the last step made use of the closed-form expression for the sum of a geometric series (§6.1). If , the denominator is nonzero while the numerator is zero. This proves

[How to cite this work] [Order a printed hardcopy]

Copyright ©

Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

[Automatic-links disclaimer]