Sinusoids
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A sinusoid is a function of an angular argument, and its amplitude varies cyclically as the angle (aka phase) steadily increases or decreases. When the angle is a function of time, the concept of negative frequency is sometimes used to distinguish a decreasing angle from an increasing one. But sinusoids are not monotonic functions. Consequently, does not preserve the sign of, just as does not preserve the sign of . Note that represents a usually unknown, random phase offset. In most cases of dealing with a single, real-valued sinusoid, it is sufficient to assume that is positive. It represents the frequency, in units of radian/s.
Sometimes there are two sinusoids with the same frequency, and a known phase difference, for instance:
and
When, appears to lead by cycle ( radians). But when, the roles are reversed. So in that case it is possible to distinguish negative and positive frequencies. The diagram depicts a negative frequency. and are referred to as real and imaginary, respectively. And .
A parametric plot of imaginary vs real would trace a circular path (like the rotating wheel). The addition of a time dimension creates a corkscrew pattern. A negative frequency (decreasing phase) causes a clockwise rotation in a right hand coordinate system as time increases:
Read more about this topic: Negative Frequency