$ Insert formula here $The total energy of a continuous-time signal x(t), where x(t) is defined for −∞ < t < ∞, is 2( ) lim 2( ) T T T E x t dt x t dt ∞ ∞ −∞ →∞ − =� = � In many situations, this quantity is proportional to a physical notion of energy, for example, if x(t) is the current through, or voltage across, a resistor. If a signal has finite energy, then the signal values must approach zero as t approaches positive and negative infinity. The time-average power of a signal is lim 1 2( ) 2 T T T P x t dt ∞ T →∞ − = � For example the constant signal x(t) =1 (for all t) has time-average power of unity. With these definitions, we can place most, but not all, continuous-time signals into one of two classes: • An energy signal is a signal with finite E∞ . For example, x(t) =e−|t| , and, trivially, x(t) = 0, for all t are energy signals. For an energy signal, P∞ = 0 . • A power signal is a signal with finite, nonzero P∞ . An example is x(t) =1, for all t, though more interesting examples are not obvious and require analysis. For a
