A new matrix decomposition based on optimum transformation of the singular value decomposition basis sets yields principal features of time-frequency distributions

The classification of objects or quantities in all fields of science depends on the quality of the features used for classifying them. This includes, for example, classification of phenomenon described by nonstationary processes such as electrocardiograms, seismic geophysics signals, submarine transient acoustic signals, and speech signals for recognition. This paper presents a new matrix decomposition that is used to obtain a set of principal features from time-frequency representations for classifying nonstationary time series processes. This new matrix decomposition is based a transformation of the orthonormal basis from singular value decomposition (SVD). The new basis set yields extrema of the first moment for each vector in the new basis set. These basis sets for time and frequency can then be used to construct features relating to the location and spread of each energy density highlight in the time-frequency plane. This new matrix decomposition is presented in this paper along with a simple example to illustrate its application.