(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, XR (f), and the imaginary part, XI (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.