Detection of normally-undetectable interferograms by stochastic resonance

Abstract

We utilize stochastic resonance (SR) to detect normally-undetectable interferograms by sinusoid crossing (SC)-sampling. An interferogram i(x) is represented by the locations {x_i} where it intersects with the reference r(x) = Acos(2πf_ix), where i = 0, 1,..., 2M−1 and 0 < x < T = 2MΔ = 2M/2f_i. If the bandwidth W of i(x) is such that W ≤ f_i and |i(x)| ≤ A for all x within T, then a crossing exists within each Δ = 1/2f_i, and crossing sampling satisfies the Nyquist sampling theorem with f_i as the cut-off frequency. If none of its values exceeds the detection limit Δ = Aπ/2N, where N is the number of partitions within Δ, then i(x) is normally-undetectable. Over amplitude-sampling of i(x) at equal intervals of Δ via a multi-comparator analog-to-digital converter, SC sampling has the advantage of hardware simplicity. An SC detector can be implemented with only one comparator.
A remarkable application of SR is the detection of normally-undetectable physical signals. A signal is considered normally-undetectable if none of its values exceeds the detection limit of the sampling device. Interferograms have several frequency components and the detection via SR, of signals with several sinusoid components, has not yet been demonstrated before. We consider in our numerical experiments (DEC Alpha 2000 Model 4-275), two kinds of interferograms, one representing a spectral doublet, and the other formed by superposing four different sinusoids. The occurrence of SR in SC sampling has just been reported, where it was employed to detect normally-undetectable, short-lived, high-frequency oscillations.