Firstly, we give a review and a definition of linear transformations that can be employed for the analysis, parameterisations or compression of biomedical data. We are particularly considering the wavelet transform, the wavelet packet transformation and the Gabor expansion under the aspect of data defined on a finite interval. For this, we introduce a novel matrix notation for each transformation method. Also, appropriate signal extension methods are described for data on finite intervals. Secondly, methods for the feature selection are studied and developed. A simple energy reduction approach is stated to start with. Then, statistical tests are explained that can be used to increase the significance when only few data points are available. These methods select certain time-frequency coefficients and the separability performance of each selected coefficient can be evaluated by a receiver operating characteristic (ROC) analysis. The ROC analysis is used to develop a signal-to-noise-like criterion, that selects and combines significant time-frequency coefficients to a coefficient set for which a separability can be stated. Also, the found coefficient set can be again evaluated by ROC analysis. Thirdly, the classification method is introduced by support vector machines (SVM) starting with an introduction to learning theory, followed by the SVM theory. Then, we show how SVM can be used for detection of biomedical signals by introducing a connection to a diagnostic test. Also, multi-class SVM classifiers are stated with the novelty of introducing a neutral class. Moreover, it is shown that the non-linear decision boundary found by the SVM can also be evaluated by a ROC analysis. The first application of some of the introduced signal processing tools comprises data from subjects that suffer from panic disorder. The feature selection is shown for statistical tests based on time-frequency transformed data. This approach is confirmed by the use of SVM where better separability results are obtained for the parameterised data than for the unparameterised data. The second application is the development of a differential diagnosis method for determining cochlear hearing loss based on time-frequency transformed otoacoustic emissions. By our feature selection method a set of distinctive coefficients are determined which generalises and enhances previous studies. Then, SVM are applied for the classification which are again evaluated by a ROC analysis.