  We develop the tools necessary to assess the statistical significance of
resonant features in the CMB correlation functions, combining power spectrum
and bispectrum measurements. This significance is typically addressed by
running a large number of simulations to derive the probability density
function (PDF) of the feature-amplitude in the Gaussian case. Although these
simulations are tractable for the power spectrum, for the bispectrum they
require significant computational resources. We show that, by assuming that the
PDF is given by a multi-variate Gaussian where the covariance is determined by
the Fisher matrix of the sine and cosine terms, we can efficiently produce
spectra that are statistically close to those derived from full simulations. By
drawing a large number of spectra from this PDF, both for the power spectrum
and the bispectrum, we can quickly determine the statistical significance of
candidate signatures in the CMB, considering both single frequency and
multi-frequency estimators. We show that for resonance models, cosmology and
foreground parameters have little influence on the estimated amplitude, which
allows to simplify the analysis considerably. A more precise likelihood
treatment can then be applied to candidate signatures only. We also discuss a
modal expansion approach for the power spectrum, aimed at quickly scanning
through large families of oscillating models.
