**Theorem:**
Let a linear time-invariant system has an
denote the complex sinusoid
.
Then,
.

**Example:** Analog RC Lowpass Filter

The impulse response for the circuit in Fig. 1, i.e. the output measured at when , is

For a complex sinusoidal input, ,

So, , which is the transfer function of the system.

Placeholder - please ignore.

Brian L. Evans