The term sinusoid is used here to designate a waveform of the
type

Thus, a sinusoid is defined as a cosine at amplitude ,
frequency , and phase . (See [83] for a fuller
development and discussion.) We could also have defined a sinusoid
based on the sine function as
, in
which case would be different by
(
radians). A sinusoid's phase is typically denoted by either
or , and is in radian units. We may call

the instantaneous phase, as distinguished from the
phase offset . The instantaneous frequency
of a sinusoid is defined as the derivative of the instantaneous
phase with respect to time (see [83] for more):

A discrete-time sinusoid is simply obtained from a continuous-time
sinusoid by replacing by :