The empirical pdf of wavelet or MDCT coefficients of audio signal generally feature a sharp peak at the origin, together with heavy tails. We show that such features may be reproduced if audio signals are modelled as sparse series of waveforms, randomly taken from a union of two significantly different orthonormal bases. In this context we obtain estimates for the behavior of “observed” coefficients, and numerical results on audio signals. Unlike more classical approaches involving optimization algorithms, our approach approaches thus relies on an explicit model. These allow us to analyze mathematical properties of such signals and corresponding estimators, and derive simple estimation algorithms.