Biorthogonality in lapped transforms: a study in high-quality audio compression

The demand for high-quality audio in transmission systems such as Digital Audio Broadcast (DAB) and High-Definition TeleVision (HDTV), as well as commercial products such as the MiniDisc (MD) and the Digital Compact Cassette (DCC), has generated considerable interest in audio compression schemes. The common objective is to achieve high quality at a rate significantly smaller than the 16 bits/sample used in current Compact Disc (CD) and Digital Audio Tape (DAT) systems. This thesis explores the current state of audio compression research, placing special emphasis on one important aspect: the short-time spectral decomposition. In conventional audio coders, the short-time spectral decomposition serves to recast the audio signal in a representation that is not only amenable to perceptual modeling but also conducive to deriving transform coding gain. This decomposition is commonly achieved by a multirate filter bank, or equivalently, a lapped transform. Towards the goal of improving the performance of audio compression schemes, this thesis contains the formulation of a biorthogonal cosine-modulated filter bank which is a generalization of Malvar's extended lapped transform (ELT). The ELT, a popular implementation of cosinemodulated filter banks, is of particular interest because it forms the major building block of signal decomposition schemes in many audio coders. Conventional lapped transforms are designed to be orthogonal filter banks in which the analysis and synthesis filters are identical. Allowing the analysis and synthesis filters to differ leads to a biorthogonal transform which has more degrees of design freedom than its orthogonal counterpart. The thesis contains proofs for three special cases and for the general case that the incorporation of biorthogonality into an M-channel ELT yields an increase of M/2 degrees of freedom. This additional flexibility allows the design of synthesis filter banks with improved sidelobe behavior which should be beneficial to audio coder performance. Thesis Supervisor: Jae S. Lim Title: Professor of Electrical Engineering