1.5 Signal power

An interesting question you could ask about a signal is its average power . A signal's instantaneous power is defined to be its square, as if it were a voltage or current passing through a 1Ωresistor. The average power is the average of the instantaneous power over some time interval. For a periodicsignal, the natural time interval is clearly its period; for nonperiodic signals, a better choice would be entire time ortime from onset. For a periodic signal, the average power is the square of the root-mean-squared (rms) value. We define therms value of a periodic signal to be

To find the average power in the frequency domain, we need to substitute the spectral representation of the signal into thisexpression.

It could well be that computing this sum is easier than integrating the signal's square. Furthermore, the contributionof each term in the Fourier series toward representing the signal can be measured by its contribution to the signal'saverage power. Thus, the power contained in a signal at its $k$ th harmonic is $\frac{a_k^2+b_k^2}{2}$ . The power spectrum $P_s(k)$ , such as shown in , plots each harmonic's contribution to the total power.