Fourier Theorems for the DFT

Fourier Theorems

Rayleigh Energy Theorem (Parseval's Theorem)

**Search Mathematics of the DFT**

**Would you like to be notified by email when Julius Orion Smith III publishes a new entry into his blog?**

**Theorem: **
For any
,

*Proof: *This is a special case of the power theorem.

Note that again the relationship would be cleaner (
)
if we were using the *normalized DFT*.

Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.

Comments

No comments yet for this page