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In the case of the pure tone a useful quantity to determine is the mean square value, i.e. the time average of the signal squared 〈x²(t)〉_t [8]

(1.7)

where 〈〉_t denotes a time average.

For the pure tone in Figure 1.2a then we obtain

(1.8)

where A is the signal amplitude.

The root mean square value is given by the square root of 〈x²(t)〉_t or

(1.9)

For the general case of the complex pure tone in Eq. (1.1) or (1.2) we obtain:

(1.10)

or

(1.11)

since . The mean square value then is the sum of the squares of all the harmonic components of the wave weighted by a constant of 1/2.