Amplitude Estimation in Nuclear Magnetic Resonance Data

Probability theory is applied to the problem of estimating the amplitudes of the sinusoids in nuclear magnetic resonance data containing two exponentially decaying sinusoids. The posterior probability-density of one of the amplitudes is derived independent of the phases, frequencies, decay-rate constants, variance of the noise, and the amplitude of the other sinusoid. This probability-density function is then applied in an illustrative example and the results are contrasted with those obtained by traditional analysis techniques.