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 bt 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 bt 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.