Reconstruction error in transform/subband coding

We use the linear gain-plus-additive noise model for the class of PDF-optimized scalar quantizers to develop a frequency domain analysis of transform/subband coding systems. We derive a novel and explicit expression for the PSD of the reconstruction error, and show that this PSD has signal, alias and noise components. We employ this expression to compare different block transforms and subband filters with the rate-distortion optimal source coder, for a 1-D Gauss-Markov source. This paper quantifies, via the `out-of-band´ noise energy in the reconstruction error, the performance gap between DCT-based coders and coders that use subband/wavelet filters