Summary: In recent years, wavelet packets have proven their capabilities for dimensionality reduction in waveform recognition. A well-accepted scheme is the local discriminant bases (LDB) algorithm which relies on the best-basis paradigm. In this paper, we combine the LDB algorithm with signal-adapted filter banks based on the lattice structure to construct more powerful LDBs. Here, in addition to the conventional tree adjustment, we adapt the shape of the analyzing atoms to extract discriminatory information among signal classes. We apply our shape-adapted LDBs, which we also call morphological LDBs, for current tasks of biosignal processing, namely feature extraction in waveforms from audiology and electrocardiology. With respect to these applications, we show that our morphological LDBs outperform LDBs based on a fixed dictionary. We also present results which seem to open new research perspectives in audiology.