Difference between revisions of "HW1.5 Ananya Panja ECE301Fall2008mboutin" - Rhea

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-Energy and Power Classifications
-The total energy of a continuous-time signal x(t), where x(t) is defined for −∞ < t < ∞,
-is
-( ) lim 2( )
-T
-T T
-E x t dt x t dt
-∞
-∞
-<math>−∞ →∞ −
-=� = �</math>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
-<math>lim 1 2( )
-T
-T T
-P x t dt
-∞ T
-→∞ −
-= �</math>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 power
-signal, E∞ = ∞.
-Example Most would suspect that x(t) = sin(t) is not an energy signal, but in any case we<math>Insert formula here</math>

Latest revision as of 19:07, 5 September 2008