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## Time-domain conjugate

A complex-valued signal

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

is written
 (45)
Now consider the complex conjugate of a frequency function. In Z-transform notation this is written
 (46)
To see that it makes a difference in which domain we take a conjugate, contrast the two equations (45) and (46). The function is a spectrum, whereas the function is called an envelope function.''

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.

Next: Spectral transfer function Up: CORRELATION AND SPECTRA Previous: Spectra of complex-valued signals
Stanford Exploration Project
10/21/1998