**(1) Phase spectrum of one channel**

The Fourier transform of time function x (t) is given by

X (f) in expression (1) is especially referred to as the
(complex) Fourier spectrum. Since X (f) is a complex function,
it can be represented as amplitude |X (f)| and phase θ (f) using
the real part, X_{R }(f), and the imaginary part, X_{I }(f).

Therefore,

Expression (2) is the amplitude of the Fourier spectrum (MAG
display). With this analyzer, expression (3) is referred to as
the phase spectrum.

With this analyzer, the starting point of a frame is the origin
and the phase of the cosine wave is assumed to be 0 degrees.
Even if X (f) in expression (2) is the same, the waveform of
time signal x (t) differs largely if phase spectrum θ (f) is
different.

When measuring the phase spectrum, the trigger function is
usually used to measure the phase spectrum with respect to a
certain time. As an application, the phase spectrum is used for
field balancing of a body of rotation.

**(2) Phase difference between two channels**

The phase difference between two channels is obtained as a phase
spectrum of the transfer function or cross spectrum which is a
complex function. If the transfer function of the system
(frequency response function) is H (f), it is represented by

|H (f)| represents the amplitude spectrum of the system and θ
(f) indicates the phase characteristic of the waveform.