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

  • Thread starter theneedtoknow
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In summary, the conversation discussed using a Fast Fourier Transform program to extract the frequency with maximum amplitude from experimental data. The program directly outputs the frequency and amplitude but provides no errors. To get the frequency error, the speaker graphs the output and takes the half-width at half amplitude. They are wondering if there is a similar way to provide an error for the amplitude. The conversation also mentions using FFT to measure the speed of sound and the difficulty of calculating errors with only one set of data. The speaker suggests using Gaussian white noise to estimate the amplitude error and provides a rough estimate for the error. However, they also mention that there may be a more rigorous and elegant way to obtain the estimate.
  • #1
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 [Broken]
 
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  • #2
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.
 
  • #3
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 ).
 
  • #4
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 [Broken]
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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  • #5
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.
 
  • #6
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.
 
  • #7
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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  • #9
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.
 

1. How do you assign error to a scientific experiment?

Assigning error to a scientific experiment involves evaluating and quantifying the potential sources of uncertainty in the data and results. This can include factors such as measurement error, experimental design, and variability in data collection. Different methods, such as statistical analysis or expert judgment, can be used to assign error to different aspects of the experiment.

2. Why is it important to assign error in scientific research?

Assigning error is crucial in scientific research because it helps to accurately interpret and communicate the results of an experiment. By understanding the potential sources of uncertainty, researchers can better assess the reliability and validity of their findings. This is important for building upon previous research and making informed decisions based on scientific evidence.

3. What are the different types of error that can be assigned in a scientific experiment?

There are several types of error that can be assigned in a scientific experiment, including random error, systematic error, and human error. Random error is caused by chance and can be reduced through repetition and statistical analysis. Systematic error is consistent and can be caused by equipment or procedural flaws. Human error is introduced by mistakes or biases in data collection or analysis.

4. How can you minimize error in a scientific experiment?

To minimize error in a scientific experiment, researchers can carefully design their experiments, use reliable and calibrated equipment, and follow established protocols for data collection and analysis. It is also important to identify and account for potential sources of error and to repeat experiments to ensure consistency and accuracy in the results.

5. Can error be completely eliminated in a scientific experiment?

While it is not possible to completely eliminate error in a scientific experiment, it can be reduced and controlled through careful planning, proper techniques, and multiple trials. However, some level of error is inherent in all experiments and it is important for researchers to acknowledge and account for it in their results and conclusions.

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