<title>Subband video-coding algorithm and its feasibility on a transputer video coder</title>

Classification of Nonexpansive Symmetric Extension Transforms for Multirate Filter Banks

“…Eddins also observed that both the circular and symmetric extension methods work with IIR filters (linear phase IIR filters in the case of SETs) provided initial conditions are used that are consistent with the chosen extension; this technique was introduced in [26,57]. A nice example of a simple IIR approach for image coding applications using nonsymmetric extension was presented in [12]. Karlsson and Vetterli [35] proposed several extension methods as alternatives to circular convolution, but in spite of having access to [56], they were unable to obtain perfect reconstruction using symmetric extensions, and their method introduced boundary distortions in the signals being coded.…”

“…Subsequent constructions of two-channel FIR PR MFBs [45,9] and wavelets [16] with linear phase were given by dropping orthogonality. Paraunitary linear phase two-channel PR MFBs are possible using infinite impulse response (IIR) filters, and symmetric extension methods have been studied using IIR filters [57,12,3,4], but the present paper will only consider FIR filters. M-channel FIR PR MFBs have been designed in, e.g., [66,43]; of particular interest for this paper, M-channel linear phase FIR PR MFBs with M > 2 have been constructed in [68,46,58,59,44,37].…”

A theoretical framework for the analysis and design of size-limited multirate filter banks

“…Careful inspection reveals that 8 [3] and &[a can be recovered from the transmitted subband samples from the subband samples usin the LTI synthesis section of the filter bank. Recalling &at CQF filter banks satisfy the orthogonality condition Equation 9 Using LTI filtering to recover 8 [3] and 2 [4], the remaining samples can be recovered. Followmg some algebraic simplifications, it can be shown that Similar equations can be generated for recovering the samples from the right-hand boundary.…”

“…This has &ce been generalised in [3] to allow for non-uniform filter banks, M-band filter banks, and any analysin filter with generalised linear phase. The system based on boundary value replication [4] required the use of a polyphase implementation where each polyphase filter WM a first order allpass filter. Though this structure is extremely computationally efficient, the nonlinear phase nature of the synthesis filters colors the quantization noise in a fashion which yields distracting artifacts.…”