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 $\ensuremath{L_2}$ norm is similarly xL2 = sqrt(Ex) (same result as xL2 = norm(x)). The $\ensuremath{L_1}$ 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, $\ensuremath{L_p}$ norm is computed by norm(x,p), with p=2 being the default case.