Technical Report Number
This paper describes the Psi-decomposition of a signal, in which the signal is written as a weighted sum of certain elementary synthesizing functions. The set S of synthesizing functions consists of dilated and translated versions of two parent functions, which are concentrated in both the time and frequency domains. The weighting constant in the Psi-decomposition define a transform called the Phi-transform. The Phi-Transform of a signal captures both the frequency content and the temporal evolution of a non stationary signal. The Phil-transform is linear, continuous, and continuously invertible. The set S of synthesizing functions used in the Psi-decomposition is non-orthogonal, hence considerable flexibility is permitted in its construction. We will show with the help of two examples that the set S is easy to construct.
Kumar, Arun; Fuhrmann, Daniel R.; Frazier, Michael; and Jawerth, Bjorn, "A New Transform For Time-Frequency Analysis" Report Number: WUCS-90-26 (1990). All Computer Science and Engineering Research.