Lapped Nonuniform Orthogonal Transforms with Compact Support

Filterbanks are an integral part of most perceptual coder systems, tasked with shaping the noise produced by the quantizer in the en- coder. Because of this shaping, the quantizer noise can then be con- trolled to stay below the masking threshold of the human ear, and become inaudible. In most current perceptual coders, an unmodified MDCT is used as the filterbank, as the MDCT has many properties that make it a good choice for this scenario. One disadvantage, however, is the uniform time-frequency reso- lution of the MDCT. This stands in contrast to the human auditory system, which has a non-uniform time-frequency resolution. This mis- match results in an unexploited gap that, if closed, could lead to a more efficient perceptual audio coder. Previous work has attempted to design non-uniform filterbanks us- ing MDCTs and subband merging, but with system design parameters that have lead to less-than-ideal filterbank properties. In this work, we will build upon the idea of subband merging, but with revised system design parameters, and novel post-processing steps: One contribution is to use an overlapping subband merging transform over a Hadamard transform. This transform sacrifices spec- tral resolution and has a non-flat frequency response, but improves temporal resolution of the filterbank. Since the main objective of sub- band merging is to improve temporal resolution of the filterbank, this is a reasonable choice. The second contribution is to reduce time domain aliasing, produced by the MDCT, in the subband domain. This operation is derived from the aliasing cancellation operation in the IMDCT and again greatly improves temporal resolution of the filterbank. This aliasing reduction concept is subsequently extended to improve the performance of time- varying filterbanks. This is achieved by introducing a third subband transform that matches the time-frequency resolution of one transform frame to its neighbor. First, all methods are investigated and compared using their time- frequency resolution measures. In a second step, a listening test is conducted to confirm the improved coding efficiency of this novel non- uniform filterbank. To that end, an experimental coder is designed that supports both this filterbank, and the state-of-the-art uniform MDCT. The improved coding efficiency is confirmed statistically.