such as can be
imagined as a
**corkscrew**,
where the real and imaginary parts are
plotted on the *x*- and *y*-axes, and time *t* runs down the axis
of the screw.
The complex conjugate of this signal reverses the *y*-axis
and gives the screw an opposite handedness.
In *Z*-transform notation,
the **time-domain conjugate**

(45) |

(46) |

For example, given complex-valued *b*_{t} vanishing for *t*<0,
the composite filter is
a causal filter with a real time function,
whereas the filter is noncausal
and also a real-valued function of time.
(The latter filter would turn out to be symmetric in time
only if all *b*_{t} were real.)

You might be tempted to think that ,but that is true only if is real, and often it is not. Chapter is largely devoted to exploring the meaning of complex frequency.

10/21/1998