Signal Processing With The MDCT And Its Application In Stereo Coding

The Modified Discrete Cosine Transform (MDCT) can efficiently and compactlyrepresent audio signals, therefore widely used in Perceptual Audio Coding (PAC). Butas a real and critically sampled lapped transform, the MDCT does not preserve energyand has no phase information, thus unwieldy in signal analysis and processing. Dueto this limitation, when advancing to low bitrate coding, PAC uses a separate complextransform for this purpose.However, introducing a separate transform increases complexity and algorithmicdelay—both are key performance indexes in mobile communications systems. If theMDCT can be efficiently used for signal processing also, then none or less the aboveproblems. This is the primary motivation to study signal processing with the MDCT.In this dissertation, we study the relation between the MDCT and the DFT, theproperties of MDCT spectra of sinusoids, and pure MDCT domain low bitrate para-metric stereo coding. The major contributions of this work include:(1) Circulant Lapped Transform (CLT), leading to a sparse matrix representation ofMDCT-DFT conversion and a O(N) fast conversion algorithm;(2) finding and proving the linear dependency of MDCT even and odd subspectra ofsinusoids, leading to an even-odd subband partition scheme with coding gain upto 20 dB for normal music signals;(3) an exact formulation of the MDCT spectrum of a sinusoid with an arbitrary win-dow function, overcoming the limitation in the current theory, leading to a gen-eral frequency and amplitude estimation method that approaches machine preci-sion in 2 or 3 iterations averagely;(4) the Maximal Coherence Rotation (MCR) that maximizes the correlation of tworelated subband vectors, and the MCR parameters that are equivalent to the bin-aural cues.(5) an MDCT domain parametric stereo coder using the even-odd scheme and theMCR that competes MPEG-4 Parametric Stereo (PS) in quality, reduces 43.9%of complexity and cuts 20 ms in algorithmic delay.Therefore, this work not only expands the horizon of the MDCT to be an efficientaudio signal processing tool but also provides viable methods for stereo coding at lowcomplexity and low delay.