Fourier Spectroscopy: A Bayesian Way

Figure 4

Examination of Gaussian prior for even and odd spectra modelled by Brownian bridge process. The spectral discretisation = 5.68 GHz is used, and the lower and upper spectral limits are set to = 0 GHz and = 3747.4 GHz (Nyquist assumptions), respectively. The scalings of the processes are chosen by  V². (a) Prior samples and for even and odd spectra. The spectra vanish towards the spectral limits. (b) Prior samples mapped to data domain to give even (odd) data-like quantity for optical path difference obtained for  mm and = 0. With increasing distance to the origin, the amplitude drops which is well bounded by the signal envelopes for the chosen bandwidth . Fourier coefficients up to order = 64 and 330 settle in the double-sided domain and single-sided domain , respectively.

(a)

(b)