Because of the need to control power consumption, in many biomedical applications asynchronous processing of the data is more appropriate. In this paper, we present a scale-based decomposition algorithm for analog signals similar to the wavelet decomposition. Our procedure uses asynchronous sigma delta modulators (ASDMs) to represent the amplitude of a signal using the zero-crossing times of a binary signal. Changing the zero-crossing times into random sequences of pulse widths, it can be shown to be equivalent to an optimal level-crossing sampler using local averages as the quantization levels. Applying the generation of multi-level signals from the output of ASDMs for different scale parameters we are able to obtain a decomposer that in a few stages provides a close representation of the signal. To illustrate the performance of the proposed decomposition, we consider its application to the representation of heart sounds.