  We describe a new method for estimating the degree of "transientness" and
"tonality" of a class of compound signals involving simultaneously transient
and harmonic features. The key assumption is that both transient and tonal
layers admit sparse expansions, respectively in wavelet and local cosine bases.
The estimation is performed using particular form of entropy (or theoretical
dimension) functions. We provide theoretical estimates on the behavior of the
proposed estimators, as well as numerical simulations. Audio signal coding
provides a natural field of application.
