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

We present a matrix decomposition that can be used to derive features from processes that are described by discrete-time, time-frequency representations. These include, among others, electrocardiograms, brain wave signals, seismic signals, vibration and shock signals, speech signals for voice recognition, and acoustic transient signals. The new decomposition is based on a transformation of the basis vectors of the singular value decomposition (SVD) which we call transformed singular value decomposition or TSVD. The transformed basis vectors are obtained by forming Linear combinations of the original SVD basis vectors in a way such that the means of the transformed vectors are extrema of each other. The TSVD basis vectors are used to identify concentrations of energy density in the discrete-time, time-frequency representation by time and frequency descriptors. That is, descriptors such as the location in time, the spread in time, the location in frequency and the spread in frequency for each principal concentration of energy density can be obtained from the TSVD terms in the matrix decomposition series. Several examples are presented which illustrate the application of the new matrix decomposition far deriving principal time and frequency features from the discrete-time, time-frequency representations of nonstationary processes. Two of the examples illustrate how the derived time and frequency features can be used to classify individual short duration transient signals into respective classes, that is,: (1) automatically classify sonar signals as belonging to one of ten classes, and (2) automatically classify heartbeat signals as belonging to one of two people.