How get amplitude and phase as a function of time?

In summary, the conversation discusses the relationship between a function of time and its Fourier transform, which is represented by amplitude and phase as functions of frequency. The question is then raised if it makes sense to speak of amplitude and phase as functions of time. It is concluded that for a function like f(t) = cos(t), the amplitude as a function of time would be 1 and the phase would be 0. However, this is different from the modulus and argument of the function. The argument is shown to be 0 due to the function only having a real part.
  • #1
Jhenrique
685
4
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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  • #2
[itex]\text{abs}(f(t))[/itex] and [itex]\text{arg}(f(t))[/itex] of course
 
  • #3
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.
 
  • #5

FAQ: How get amplitude and phase as a function of time?

1. What is amplitude and phase as a function of time?

Amplitude and phase as a function of time refer to the changing values of amplitude and phase over a period of time. Amplitude is the measure of the strength or intensity of a wave, while phase is the measure of the position of a wave in its cycle.

2. How can I get amplitude and phase as a function of time?

To get amplitude and phase as a function of time, you will need to measure the amplitude and phase of a wave at different points in time. This can be done using specialized equipment such as an oscilloscope or by analyzing data from experiments or simulations.

3. What factors affect the amplitude and phase of a wave?

The amplitude and phase of a wave can be affected by a variety of factors, including the properties of the medium the wave is traveling in, the frequency of the wave, and any external forces or sources that may be acting on the wave.

4. How does the amplitude and phase of a wave change over time?

The amplitude and phase of a wave can change over time due to factors such as interference, damping, and resonance. These changes can be observed by measuring the amplitude and phase of the wave at different points in time.

5. Why is it important to understand the amplitude and phase as a function of time?

Understanding the amplitude and phase as a function of time is crucial in many fields of science, including physics, engineering, and telecommunications. This knowledge allows us to accurately predict and manipulate the behavior of waves, which is essential in the development of technologies such as wireless communication, medical imaging, and earthquake detection.

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