The term sinusoid means a waveform of the type
the instantaneous phase, as distinguished from the phase offset . Thus, the ``phase'' of a sinusoid typically refers to its phase offset. The instantaneous frequency of a sinusoid is defined as the derivative of the instantaneous phase with respect to time (see [84] for more):
A discrete-time sinusoid is simply obtained from a continuous-time sinusoid by replacing by in Eq.(A.1):