Analysis of non-stationary signals is a challenging task. The purpose of this thesis is to explore an efficient and powerful technique to analyze and classify two types of non-stationary signals, that is, multimedia signals in higher frequency range (44.1 kHz) and biomedical signals in lower frequency range (2 kHz). An adaptive true non-stationary time -frequency signal analysis tool - matching pursuit, is introduced and applied to decompose the sample signals into time-frequency functions or atoms. Atom parameters are analyzed and manipulated, and discriminant features are extracted from atom parameters. Besides the parameters obtained using matching pursuit, several additional features, such as central energy and octave activeness ratio, are also derived. Linear discriminant analysis and the leave-one-out method are used to evaluate the classification accuracy rate for different feature sets. In the 6-group classification of 96 pieces of 5-second music signals, such as, christmas choir, country, greek music, jazz, rock and scottish music, the accuracy reaches 89.6%, when the feature set includes standard deviation of octave (the scale factor which controls the width of the window function), median of octave, standard deviation of innerProdI (imaginary part of the inner-product between the signal and the atom), standard deviation of realGG (real part of the inner-product between the complex atom and its conjugate), and central energy. For the database of 112 pieces of 10-second music sugnals, the 2-group classification (rock-like and classical-like) accuracy achieves 100%, having a standard deviation of octaves in the first 2,000 atoms as the discriminant feature. An accuracy of 74.2% is obtained for the 2-group knee sound signal classification, and optimum feature set comprises octave activeness ratio, central energy and standard deviation of innerProdI. From our experiments, it is evident that the matching pursuit algorithm with the Gabor dictionary decomposes non-stationary signals, including multimedia signals in higher frequency and biomedical signals in lower frequency ranges, into atoms whose parameters contain strong discriminant information sufficient for accurate and efficient signal classifications.