Error in phase and magnitude results of fft

Hi everyone,

I need to analyze data from a test rig by using fft function. So I came about the question of error. If I get the amplitude of a signal form the fft, what is the error to that? Do I need to split my time signal into several parts and compare the magnitude and phase results of the fft of each to get an error or is there a simpler way?

Thanks, Tanja

Answer 1

[Walter Roberson]

http://www.mathworks.com/matlabcentral/newsreader/view_thread/256614

[Tanja]

Thanks for your answer!

Do I understand this right:

I measure a signal and want to know its amplitude at a certain frequency. If I take the amplitude given in the fft magnitude spectrum my worst case error is O(log2(N)*2*eps). Would you use this as an error bar in a result plot? This seems very low to me... And it would only be true if there is no error to the measured signal. But my signal might have somen uncertainty, as for example errors from sensor inaccuracy. How do I propagate signal error through the fft?

[Walter Roberson]

That would be relative error, not absolute error. You need to multiply it by max(abs()) of your data to estimate the absolute error.

Is the sensor inaccuracy semi-permanent (e.g., flaw in the lens) or is the inaccuracy due to noise?

If the inaccuracy is due to per-reading noise then effectively you have a high frequency additive signal that could be filtered out.

[Tanja]

I attached a picture of what the data looks like. I am interested in the ampltude and phase of the underlying low-frequency sinusoid. An I need to give an estimate of error for those results. There is noise in the signal and the pressure sensors have an error of plus/minus 0.1 psi.

I have also bee thinking: would it be useful to low-pass filter the signal or maybe window it before beforming the fft?