Method Of Splitting Signals By The Paired Transform

The mathematical structure of the discrete Fourier transform (DFT) contains a unitary transform, that defines the splitting of the DFT by a certain set of short and separable transforms. This unitary transform is called the paired transform, a wavelet-like transform, which defines the representation (or decomposition) of a discrete signal in the form of a set of independent short signals. Properties of such paired representation are considered and the basis paired functions are described. The paired transform is fast, and many operations over signals can be reduced to processing their short splitting-signals. Examples of decomposition and filtration of signals by splitting-signals are given