Real-world signals can be represented as suitable combinations of complex exponential signals of the type x( t) = X e ^st. In this expression, X = X _me ^{j ?} is the phasor associated with the signal and s = ? + j ? is its complex frequency.

The function Re[ x( t)] represents a decaying sinusoid if ? < 0, a growing sinusoid if ? > 0, and a steady sinusoid if ? = 0. If ? = 0, these functions reduce to a decaying exponential if ? < 0, a growing exponential if ? > 0, and a dc signal if ? = 0.

In response to a current i( t) = I e ^st, a one-port consisting of resistances, capacitances, inductances, and dependent sources responds with a voltage v( t) = V e ^st. The ratio Z( s) = v( t)/ i( t) = V/ I is called the impedance of the one-port. The impedances of the basic elements are R, sL, and 1/ sC.

Using the concept of impedance, along with the generalized Ohm's Law and Kirchhoff's laws, we can analyze a circuit using the same techniques as in ac analysis, except that we are now using s instead of j