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

[theneedtoknow]

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

 

[BAnders1]

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.

 

[green-fresh]

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 ).

 

[Dale]

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?

 

[theneedtoknow]

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.

 

[Dale]

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.

 

[theneedtoknow]

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)

 

[theneedtoknow]

http://img708.imageshack.us/img708/55/erroramplitude.th.jpg

So in this case it would be approximately Amplitude = 0.33 ± 0.05?

 

[Dale]

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.

 

[theneedtoknow]

Than kyou very much :)

 

[Dale]

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.