hi everyone,(adsbygoogle = window.adsbygoogle || []).push({});

i would be grateful for suggestions for the following problem:

i have a set of measurements, discrete samples from a continuous function of time. with each measurement comes a estimate of its uncertainty (standard error). by doing a discrete fourier transform, i have seen some frequency content in the amplitude spectrum that is distinctly visible above the noise. however, due to the significant noise, the amplitude of the peaks cannot be taken as the real amplitude of those oscillations. do you happen to be familiar with a method that can be used to estimate the true amplitude of the oscillations without bias? the gained precision in amplitude estimation may come with the sacrifice of frequency resolution, which is not that important to me.

i have already found some papers concerning spectrum estimation, but most of them use fairly complicated algorithms that i don't feel like implementing. i'm wondering if there is a basic solution that i have overlooked. thanks for any input! cheers

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# Spectrum estimation with noisy data, unbiased estimation of amplitudes needed

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