Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications

8.5 POWER SPECTRAL DENSITY

We begin with a brief review of power and energy for nonrandom signals.

Definition: Energy The energy of deterministic waveform x(t) is defined as

(8.61)

If x(t) is periodic on , then E is infinite. For example, for x(t) = cos(ω t):

For such signals, we examine instead the average power.

Definition: Average Power The average power of deterministic X(t) is defined as

(8.62)

For the cosine function, the average power is finite:

(8.63)

Unlike an infinite-length periodic signal, the energy E of a finite-duration nonrandom signal is finite and thus has zero average power P.

Definition: Energy and Power Signals An energy signal has finite energy and zero power. A power signal has infinite energy and finite power. They are characterized concisely as for an energy signal and for a power signal.

The rectangle function rect(t) is an example of an energy signal whereas ...