Comparative study of shift-invariant symmetric wavelets and cosine local discriminant basis in noisy transients classification

Linear transforms in the time-frequency domain have proven very effective for non-stationary signal analysis. As such, wavelets and local trigonometric transforms have attracted substantial attention during the last decade and both methods have undergone extensive refinement. One recent development is the availability of algorithms for wavelet design and shift-invariant (SI) algorithms for both the wavelet and cosine transforms. Discriminant analysis of features extracted from a projection into a transformed space can be sensitive to shifts in the time-domain. The application of a shift-invariant transform is therefore attractive. Here, a comparative study is performed between two SI-wavelet transforms, the conventional transforms and the local cosine transform, on four classes of signals corrupted with underwater background noise. Training sets are reduced to 50 samples per class, and SNR is low in order to reflect real applications where samples are rare and noisy. Features are extracted from local discriminant bases to maximise the class separability. A Fischer discriminant analysis is performed on bases components to sort the coefficients according to their discriminant power. In our application, a maximum of 99% classification success rate is achieved and results show that performance differences between transforms can reach more than 20%.