Discrete-time Energy and Power signals The energy E of a discrete-time signal x(n) is given by

where x* is the complex conjugate of x. If x(n) is the real sequence then x(n) x*(n) = x²(n).  The above definition can also be written follows

 (there are 2N+1 terms here)

The average power P of the signal is

If E is finite but non zero (that is 0 < E < ∞) the signal is an energy signal. This is a power signal if E is infinite but P is finite and nonzero (that is 0 < P < ∞). Obviously, when E is finite, P = 0. If E is infinite P can be or cannot be finite.

If both E and P are finite, then the signal is no energy or a power signal.

The terms "energy" and "power" are used independently of whether the quantity , in continuous time case) in fact is related to physical energy. Even if this type a relationship exists, these quantities, ∑ (.) and ∫ (.), can have the wrong dimensions and scaling. Still it is handy to use these terms in a regular fashion. It is helpful to imagine that x(t) or x(n) is voltage across, or, current through, the 1-ohm resistor.

Example 1.2.1 For signal x(n) = 1 for all n,

Therefore x(n) is a power signal.

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