Zusammenfassung
Bayesian probability theory is used to estimate the amplitude of multiple
well-separated exponentially decaying sinusoids in NMR free-induction-decay
data. Specifically the posterior probability for the amplitude is
derived independent of the phase, frequency, decay rate constant,
and variance of the noise. The estimate is shown to be accurate and
precise in the sense that as the noise approaches zero, the estimate
approaches the true value of the amplitude and the uncertainty in
the estimate approaches zero. For fixed data-acquisition time, the
uncertainty in the estimate is shown to vary inversely with the square
root of the sampling rate. Finally, the calculation is applied in
two examples. The first example demonstrates the ability of probability
theory to estimate frequencies and amplitudes in very low signal-to-noise.
The second example illustrates the use of this calculation when the
data contain multiple, well-separated sinusoids.
Nutzer