Fast statistical evaluation of multichannel spectra using the Walsh transform

Any counting spectrum of 2sup(n) channels can be decomposed unequivocally into n+1 independent contributions of progressively decreasing resolution scales. This decomposition is most simply performed on the Walsh transform of the spectrum. The ratio of the normative integral of each contribution to the level of the fluctuations is used to quantify the statistical relevance in terms of the resolution. An optimisation criterion allows to reduce the spectrum to a relevant number of broader channels covering the same range. Test analyses are presented