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For a periodic signal, we use Hertz, or the number of cycles per second, to quantify how fast its values are changing.

However, how can we quantify how fast the phase of a periodic signal is changing? Given that phase of a periodic signal is expressed in degree, can we use degree per second as a measurement of how fast the phase is changing?

Thanks.

Edit: Here are the illustrations of fast and slow changing phase.

enter image description here

Source: RF Microelectronics (Razavi) Fig. 9.15

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  • \$\begingroup\$ In what sense is the phase angle changing? \$\endgroup\$
    – Chu
    Commented Jul 9, 2021 at 0:22
  • \$\begingroup\$ As mentioned in the answer, for \$\sin(\theta) = \sin(\omega t)\$, \$\omega\$ is the speed with which the phase \$\theta\$ is changing. \$\endgroup\$
    – AJN
    Commented Jul 9, 2021 at 0:52
  • \$\begingroup\$ @Chu Please refer to the edit as illustration of phase change. \$\endgroup\$
    – Underdog
    Commented Jul 9, 2021 at 1:26
  • \$\begingroup\$ @AJN So you mean frequency is a measurement of phase change because the derivative of phase is frequency? \$\endgroup\$
    – Underdog
    Commented Jul 9, 2021 at 1:28
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    \$\begingroup\$ Yes. More details in the existing posted answer. \$\endgroup\$
    – AJN
    Commented Jul 9, 2021 at 1:46

2 Answers 2

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Generally, harmonic signals have a phase: the derivative of phase over time is the frequency of such a signal, I.e. a sine or cosine.

Now, not all periodic signals are harmonic signals. But we can decompose any periodic signal into a sum of harmonic signals (that's the Fourier series of the periodic signal).

It's easy to see that every harmonic component of that sum can have its own phase. There isn't such a thing as "the phase" for a non-harmonic signal.

However, it can be useful to think in terms of the phase of the fundamental frequency, I.e. the harmonic component of the same frequency as your periodic signal, and call that the phase of the non-harmonic periodic signal. However, that fundamental can, when the periodic signal is composed of two periodic signals whose periods are rationally related but not multiples of each other, be of zero amplitude and then you can't really define the phase of it.

So: long story short: strictly speaking, only harmonic signals have phase. Some periodic non-harmonic signals can be assigned a property analog to that concept, but not all of them.

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  • \$\begingroup\$ Then suppose there is a harmonic periodic signal, how can we quantify the speed that its phase change? \$\endgroup\$
    – Underdog
    Commented Jul 9, 2021 at 2:57
  • \$\begingroup\$ I answered that: find the Fourier series, find the frequency of the fundamental frequency component. \$\endgroup\$
    – mmmm
    Commented Jul 9, 2021 at 3:08
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\$d \phi/dt \$ can be measured in any units and extrapolated to cycles per second or 1 cycle/__us or Hz or as a % deviation from the initial frequency. Your choice.

80% of the phase change or 10 to 90% of the full scale also converts to T=0.35/f-3dB

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