Block transform packets - An efficient approach to time-frequency decomposition

A Block Transform Packet (BTP) is an orthonormal block transform which represents an arbitrary tiling of the time-frequency plane. This paper describes procedures for synthesizing BTP's with desirable time-frequency localization from conventional block transforms, while maintaining the computational efficiency of the progenitor transforms. Time Localizable Block Transform packets (TLBT) are constructed from the DCT while the dual Frequency Localizable Block Transform packets are synthesized starting with the time-localized Kronecker delta basis sequences. The BTP can represent a time-varying decomposition tree but requires no transition or boundary filters. This decomposition is an efficient alternative to wavelet packet decomposition. Three examples are developed to illustrate the procedure and demonstrate the enhanced compression properties of the TLBT.