Best basis algorithm for orthonormal shift-invariant trigonometric decomposition

Adaptive signal representations in overcomplete libraries of waveforms have been widely used. The local cosine decomposition of Coifman and Wickerhauser (see IEEE Trans. Inf. Th., vol.38, no.3, p.713-18, 1992) is modified by incorporating two degrees of freedom that increase the adaptability of the best basis. These are relative shifts between resolution levels and adaptive polarity foldings. The resultant expansion is shift-invariant, and yields adaptive time-frequency distributions which are characterized by high resolution, high concentration and suppressed cross-terms associated with the Wigner distribution.