Fourier Spectroscopy: A Bayesian Way

Figure 9

(a) Posterior means and with associated 2- uncertainty bands evaluated at maximum of settings posterior for = 1/2 GHz (see Table 1). Most likely, the spectral quantities and are finite only for the domain between = 32.425 GHz and = 913.425 GHz. This upper limit is approximately 4 smaller than the Nyquist frequency = 3747.4 GHz. The dips in at 557 and 752 GHz are caused by absorption due to atmospheric water vapour. (b) , , and obtained by mapping posterior means , ,  nV, = 5.997 μV/m, and  μV/m² to data domain. (c) Cosine transform of dependent on optical path difference and order (bandwidth ) of Fourier coefficients. The envelope , incorporating the scaling = 1.1299 × 10⁻¹² V², bounds best. (d) Zoom of (b) dependent on and . Globally, the sine transform of is best summarised by the envelope with the scaling  V². Since holds, the single-sided domain is determined mainly by . (e) Histogram of residuals, that is, difference between measured data and posterior mean prediction scaled by noise level . The data is well described, because the mean and the variance of the residuals are almost vanishing and close to unity, respectively. (f) Residuals versus optical path difference.

(a)

(b)

(c)

(d)

(e)

(f)