How get amplitude and phase as a function of time?

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Discussion Overview

The discussion revolves around the concepts of amplitude and phase as functions of time, particularly in relation to the Fourier transform of a time-dependent function. Participants explore whether it is meaningful to express amplitude and phase in the time domain and how to derive them from a given function.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that while amplitude and phase can be defined in the frequency domain using the Fourier transform, it is unclear how to express them meaningfully in the time domain.
  • Another participant proposes using the absolute value and argument of the function directly, implying that these could serve as amplitude and phase in the time domain.
  • A further contribution points out that for a specific function like cos(t), the amplitude is constant (A(t) = 1) and the phase is zero (φ(t) = 0), raising questions about the distinction between these values and the absolute and argument functions.
  • Some participants argue that since the function has only a real part, the modulus is defined differently, leading to a conclusion that the argument and phase are not equivalent concepts.

Areas of Agreement / Disagreement

Participants express differing views on whether amplitude and phase can be meaningfully defined in the time domain, with some asserting that they can be derived directly from the function, while others challenge this notion and emphasize the distinction between argument and phase.

Contextual Notes

There are unresolved assumptions regarding the definitions of amplitude and phase in the context of real-valued functions, as well as the implications of using the Fourier transform for these definitions.

Jhenrique
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Given a function of the time like ##f(t)##, its Fourier transform is ##F(\nu)## and by definition, ##Abs(F(\nu))=A(\nu)## and ##Arg(F(\nu)) = \varphi(\nu)##, so I have amplitude and phase as function of the frequency, but make sense speak in amplitude and phase as function of the time? If yes? How get them?
 
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[itex]\text{abs}(f(t))[/itex] and [itex]\text{arg}(f(t))[/itex] of course
 
MisterX said:
[itex]\text{abs}(f(t))[/itex] and [itex]\text{arg}(f(t))[/itex] of course

But if f(t) = cos(t) thus the amplitude as function of the time is A(t) = 1 and the phase is φ(t) = 0 what is different of Abs(f(t)) and Arg(f(t)), respectively.
 

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