Signal Energy and Power

In a similar way, we can compute the signal energy (sum of squared moduli) using any of the following constructs:

Ex = x(:)' * x(:)
Ex = sum(conj(x(:)) .* x(:))
Ex = sum(abs(x(:)).^2)

The average power (energy per sample) is similarly Px = Ex/N. The norm is similarly xL2 = sqrt(Ex) (same result as xL2 = norm(x)). The norm is given by xL1 = sum(abs(x)) or by xL1 = norm(x,1). The infinity-norm (Chebyshev norm) is computed as xLInf = max(abs(x)) or xLInf = norm(x,Inf). In general, norm is computed by norm(x,p), with p=2 being the default case.

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Order a Hardcopy of Mathematics of the DFT

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written by Julius Orion Smith III
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.