Theoretical signal-to-noise ratio and resolution for the stochastic excitation technique in radio frequency spectroscopy

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Abstract
Analytical expressions are derived for the signal-to-noise ratio and resolution in the stochastic excitation technique applied to radio frequency spectroscopy such as ion cyclotron resonance and nuclear-magnetic resonance. The expressions reduce to particularly simple forms under two limiting cases. Under intermediate cases, numerical calculations have been performed for them. Their results and the inspection of the limiting forms confirm the following properties: (1) noise on the spectrum is mainly due to that employed for the excitation; (2) the signal-to-noise ratio is independent of the observation period and it is always unity; (3) resolution is given by the observation period and, in consequence, it increases linearly with the observation period. Finally, a comparison is made of some features for the present technique with three other techniques, namely, the pulsed Fourier transform, the rapid scan, and the conventional continuous-wave techniques.