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I need to know what is the absolute phase and the relative phase, of a signal? and why these phases are important in the signal processing?

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    $\begingroup$ if you don't have defined a moment in time that is absolutely $t=0$ then there is no "absolute phase", only relative phase. $\endgroup$ – robert bristow-johnson Apr 1 '16 at 0:01
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  • "Absolute phase" is really relative phase to a point in time at which the phase measurement is referenced (Noon GMT on Tuesday, the first sample in a time-domain window of sample data for instance, or maybe the middle sample in a vector).
  • Relative phase can also be measured with respect to another waveform of the exact same constant frequency, as the difference in phase measurement between the two waveforms at any one point will be the same at all other points, as long as the two frequencies stay identical.

Phase is important because it is one of the 3 parameters needed in an equation that completely describes a sinusoid. Without phase information, the waveform is ambiguous.

$$y(t) = a\cdot \cos\left(b\cdot t + \phi_{t_0}\right), \quad \text{ where }\phi_{t_0} \text{is the phase at time } t = t_0.$$

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    $\begingroup$ Isn't $\phi_{t_0}$ the phase at $t=0$ ?!? $\endgroup$ – Peter K. Apr 1 '16 at 11:58
  • $\begingroup$ @ alex.forencich At the big bang! :-) $\endgroup$ – Peter K. Jun 30 '16 at 12:33
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    $\begingroup$ For any isolated experiment, the observer can choose when they want to start their clock or oscillator. Any assumptions that the rest of the universe exists or did exist beforehand may or may not be needed (or even be provable). $\endgroup$ – hotpaw2 Jun 30 '16 at 13:17

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