Does anyone have any recommendations as to how to assign error to this?

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Discussion Overview

The discussion revolves around methods for estimating errors in frequency and amplitude derived from Fast Fourier Transform (FFT) analysis of experimental data, particularly in the context of astronomical observations. Participants explore various approaches to quantify uncertainty when direct error measurements are unavailable.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes using the half-width at half-maximum of the peak in frequency space to estimate error in frequency.
  • Another participant shares a similar experience from a lab assignment, suggesting the same method for frequency error estimation.
  • A question is raised about the nature of the frequency being analyzed, prompting a discussion on different experimental contexts.
  • A participant suggests that without the ability to repeat measurements, estimating errors becomes more complex and may depend on noise characteristics.
  • One participant mentions the challenge of analyzing historical brightness data of a star, emphasizing the need to derive error estimates from a single dataset.
  • Concerns are expressed regarding the assumption of uniform standard deviation among measurements, with a suggestion that the data may exhibit Gaussian white noise characteristics.
  • A proposed method for estimating amplitude error is discussed, with a participant suggesting a rough estimate based on visual analysis of the data.
  • Another participant agrees with the rough estimate for amplitude error, linking it to the characteristics of Gaussian white noise.
  • A cautionary note is provided about the potential lack of rigor in the proposed methods, indicating that more sophisticated approaches may exist.

Areas of Agreement / Disagreement

Participants express a range of views on how to estimate errors, with some agreeing on the use of half-width at half-maximum for frequency but differing on methods for amplitude error estimation. The discussion remains unresolved regarding the most rigorous approach to error estimation.

Contextual Notes

Participants acknowledge limitations in their methods, particularly the reliance on assumptions about noise characteristics and the inability to repeat measurements for statistical analysis.

theneedtoknow
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I am using a Fast Fourier Transform program to extract the frequency with max amplitude from a set of experimental data. Now, the program directly spits out the frequency along with the max amplitude. However, it provides no errors for either. So, to get the error in the frequency, i graph the output in the general viscinity of the frequency the program provided, and i see how wide the peak is at that frequency, and i take the error in frequency as the half-width of that peak at half the amplitude of the peak. Is there any similar way to provide an error for the amplitude of that peak?

Here is an example of the graph of the output near the highest peak of one of the sets of data
http://img709.imageshack.us/img709/9784/example.th.jpg
 
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I once had a lab assignment in which we used FFT's to measure the speed of sound. We took the full width at half maximum (in frequency space) as the error estimate in our measurement for the frequency.
 
frequency of what ? of light wave or sound wave ?
and about what is this experiment?
because i now another way to calculate errors in experiments (with out drawing but in need equation or something like that ).
 
theneedtoknow said:
I am using a Fast Fourier Transform program to extract the frequency with max amplitude from a set of experimental data. Now, the program directly spits out the frequency along with the max amplitude. However, it provides no errors for either. So, to get the error in the frequency, i graph the output in the general viscinity of the frequency the program provided, and i see how wide the peak is at that frequency, and i take the error in frequency as the half-width of that peak at half the amplitude of the peak. Is there any similar way to provide an error for the amplitude of that peak?

Here is an example of the graph of the output near the highest peak of one of the sets of data
http://img709.imageshack.us/img709/9784/example.th.jpg
The real way to get the error in both is to perform your measurement multiple times on the same subject and get the mean and standard deviation of the frequency and the max amplitude. If you cannot do that, but only have one set of data then it is more difficult in general. In that case, I would say that it depends pretty strongly on your noise characteristics. Do you know if you have Gaussian white noise?
 
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Sadly, there is no way for me to repeat the measurements - I'm analyzing the differences in brightness of a star as recorded by observers all over the world over the course of the last 120 years. The FFT gives me the period of rotation of the star( 1 / the frequency with highest amplitude), and the amplitude of variation in brightness. So , any error I quote must somehow come from a single set of observations, which is why I use the half-width at half-amplitude as the error in frequency. Unfortunately there doesn't seem to be any kind of similar way of getting the error in the amplitude.
 
Hmm, this is a non-trivial problem. The individual source data measurements can probably safely be assumed to be uncorrelated, and you can probably even assume that the errors for each source measurement are normally distributed with zero mean, but the assumption that they would all have the same standard deviation is suspicious. However, I don't see a way of characterizing the noise without that assumption. If you make that assumption then you simply have Gaussian white noise which you should be able to estimate from your signal.
 
DaleSpam said:
Hmm, this is a non-trivial problem. The individual source data measurements can probably safely be assumed to be uncorrelated, and you can probably even assume that the errors for each source measurement are normally distributed with zero mean, but the assumption that they would all have the same standard deviation is suspicious. However, I don't see a way of characterizing the noise without that assumption. If you make that assumption then you simply have Gaussian white noise which you should be able to estimate from your signal.

Ok I think I get what you mean, So i just do something like this: (following post)
 
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Yeah, that seems like a good rough estimate. So since Gaussian white noise before the FFT becomes Gaussian white noise after the FFT you can probably use that 0.33 (in the appropriate units) as an estimate for your amplitude error.
 
  • #10
Than kyou very much :)
 
  • #11
You are welcome, but I should caution you that there is a lot of hand waving in this and there is probably a more rigorous and elegant way to get your estimate.
 

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