LINC: a common theory of transform and subband coding

A common theory of lapped orthogonal transforms (LOTs) and critically sampled filter banks, called L into N coding (LINC), is presented. The theory includes a unified analysis of both coding methods and identity relations between the transform, inverse transform, analysis filter bank, and synthesis filter bank. A design procedure for LINC analysis/synthesis systems, which satisfy the conditions for perfect reconstruction, is developed. The common LINC theory is used to define an ideal LINC system which is used, together with the power spectral density of the input signal, to calculate theoretical bounds for the coding gain. A generalized overlapping block transform (OBT) with time domain aliasing cancellation (TDAC) is used to approximate the ideal LINC. A generalization of the OBT includes multiple block overlap and additional windowing. A recursive design procedure for windows of arbitrary lengths is presented. The coding gain of the generalized OBT is higher than that of the Karhunen-Loeve transform (KLT) and close to the theoretical bounds for LINC. In the case of image coding, the generalized OBT reduces the blocking effects when compared with the DCT