Signal Metrics

The mean of a signal stored in a matlab row- or column-vector x can be computed in matlab as

mu = sum(x)/N

or by using the built-in function mean(). If x is a 2D matrix containing N elements, then we need mu = sum(sum(x))/N or mu = mean(mean(x)), since sum computes a sum along ``dimension 1'' (which is along columns for matrices), and mean is implemented in terms of sum. For 3D matrices, mu = mean(mean(mean(x))), etc. For a higher dimensional matrices x, ``flattening'' it into a long column-vector x(:) is the more concise form:

N = prod(size(x))
mu = sum(x(:))/N

or

mu = x(:).' * ones(N,1)/N

The above constructs work whether x is a row-vector, column-vector, or matrix, because x(:) returns a concatenation of all columns of x into one long column-vector. Note the use of .' to obtain non-conjugating vector transposition in the second form. N = prod(size(x)) is the number of elements of x. If x is a row- or column-vector, then length(x) gives the number of elements. For matrices, length() returns the greater of the number of rows or columns.^I.1

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Subsections

• Signal Energy and Power

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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.