Decorrelating Properties of Chromatic Derivative Signal Representations

This letter is concerned with the decorrelating properties of the recently introduced chromatic derivative signal expansions, which encode signal information by employing suitably orthogonalized differential operators. An upper bound is derived on the condition number of the autocorrelation matrix of chromatic derivative expansion coefficients, extracted at a sampling instant. It is shown that chromatic derivative signal representations may be matched to the power spectrum of the signal under analysis, in order to effect maximum signal decorrelation and in order to ensure a small condition number of the autocorrelation matrix under the chromatic derivative signal representation.