A nonextensive wavelet $(q,q')$-entropy for $1/f^{\alpha}$ signals

Abstract

This paper proposes a nonextensive wavelet $(q,q')$-entropy computed as a wavelet-domain generalization of the time-domain $(q,q')$ entropy of Borges and obtains a closed-form expression of this measure for the class of $1/f^{\alpha}$ signals. Theoretical wavelet $(q,q')$-entropy planes are obtained for these signals and the effect of parameters $q$ and $q'$ on the shape and behaviour of these wavelet entropies are discussed with sufficient detail. The relationship of this entropy with Shannon and Tsallis entropies is studied and some applications of the proposed two-parameter wavelet entropy for the analysis/estimation of $1/f$ signals are outlined.