frequency (in units of radians per sample) is simply the advancement of phase for that sample Complex representation In some applications, such as averaging the values of phase at several moments of time, it may be useful to convert each value to a complex number, or vector representation: This representation is similar to the wrapped phase representation in that it does not distinguish between multiples of 2 in the phase, but similar to the unwrapped phase representation since it is continuous. A vector-average phase can be obtained as the arg of the sum of the complex numbers without concern about wrap-around. See also Analytic signal Frequency modulation Group delay Instantaneous amplitude Negative frequency References Further reading Signal processing Digital signal processing Time–frequency analysis Fourier analysis Electrical engineering Audio engineering