Fourier Transform Power Spectrum

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Homework Help Overview

The discussion revolves around the Fourier Transform and its application to a sine wave input, specifically examining the resulting power spectrum and the relationship between amplitude and output spike amplitude in the frequency domain.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between the amplitude of the sine wave and the amplitude of the Fourier Transform output, questioning whether the observed behavior is due to power being proportional to the square of the amplitude. There is also inquiry into the averaging process involved in the transformation.

Discussion Status

Participants are actively engaging with the concepts, with some suggesting that the original poster may need to consider additional factors such as contributions from both positive and negative frequencies. There is a focus on clarifying the implications of the results obtained from the LabVIEW application.

Contextual Notes

The original poster mentions using LabVIEW for the Fourier Transform and expresses uncertainty about the handling of imaginary components in the output. There is also a reference to the averaging nature of the auto power spectrum computation, indicating a potential area of confusion.

cscott
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Input: sine wave at 10Hz, amplitude 1.

After the transform the plot has a spike at 10Hz with amplitude 0.5. If I vary the amplitude of the sine wave I get:

sine amp. - FT spike amp.
1 - 0.5
2 - 2
4 - 8

So it seems A' = A^2/2

Is this because power is proportional to A^2 and it is averaged over trough/crest so division by 2?
 
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Are you adding real and imaginary parts?

The power should be the same in both domains.
 
Sorry I think I asked my question poorly.

I'm doing this in a lab using LabVIEW and it's doing the FT. When I input a sine wave (vs time) with varied amplitude 'A', I get an output spike of amplitude (A^2)/2 centered at some fixed frequency. Is this because [itex]P \propto A^2[/itex]? Is the half for 'average'?

I'm just trying to make sense of what this VI is doing. All I know is "computes the averaged auto power spectrum of time signal".

Does my data still make no sense?

I'm not directly dealing with imaginary parts...
 
Last edited:
OK- you probably forgot to add the power in -ve and +ve frequencies.
 

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