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) Numbered Display Equation

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

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For such signals, we examine instead the average power.

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

(8.62) Numbered Display Equation

For the cosine function, the average power is finite:

(8.63) Numbered Display Equation

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 inline for an energy signal and for a power signal.

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

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