A system and method for encoding and/or decoding a signal, such as an
audio signal, employing a reversible transform obtained via matrix
lifting. This reversible transform not only converts integer input to
integer output, but also reconstructs the exact input from the output. It
is one of the key modules for lossless and progressive to lossless audio
codecs. The system and method of the invention produces smaller
quantization noise and better compression performance of lossless and
progressive to lossless codecs previously known. A number of embodiments
employing RMDCT solutions are described. Matrix lifting is used to
implement a reversible fast Fourier transform (FFT) and a reversible
fractional-shifted FFT, respectively, which are further combined with
reversible rotations to form a RMDCT. A progressive-to-lossless embedded
audio codec (PLEAC) employing RMDCT is implemented with superior results
for both lossless and lossy audio compression.