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Signal Energy and Power

In a similar way, we can compute the signal energy $ {\cal E}_x$ (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 $ L2$ norm is similarly xL2 = sqrt(Ex) (same result as xL2 = norm(x)). The $ L1$ 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, $ Lp$ norm is computed by norm(x,p), with p=2 being the default case.


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``Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition'', by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8.
Copyright © 2014-04-06 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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