  Auto- and cross-spectral density functions for dynamic {random} fields and
power are derived. These are based on first- and second-order Pad\'{e}
approximants of correlation functions expanded in terms of spectral moments.
The second-order approximant permits a characterization of stir noise
observable {at high stir frequencies in the autospectral density}. A
relationship between stir imperfection and spectral kurtosis is established.
For the latter, lower bounds are established. A novel alternative measure of
correlation time for mean-square differentiable fields is introduced as the lag
at the first point of inflection in the autocorrelation function. A hierarchy
of Pad\'{e} deviation coefficients is constructed that quantify imperfections
of correlations and spectra with increasing accuracy and range of lags.
Analytical models of the spectral densities are derived and their asymptotic
behaviour is analyzed. The theoretical spectral density for the electric field
as an input quantity is compared with that for power as the measurand. For the
latter, its inverted-S shape conforms to experimentally observed stir-spectral
power densities. The effect of additive noise on the stir autocorrelation and
spectral density functions is quantified.
