M-channel Perfect Reconstruction Filter Bank Research Articles

Design of M-Channel Perfect Reconstruction Filter Banks with IIR-FIR Hybrid Building Blocks

This paper discusses a new structure of M-channel IIR perfect reconstruction filter banks. A novel building block defined as a cascade connection of some IIR building blocks and FIR building blocks is presented. An IIR building block is written by state space representation, where we easily obtain a stable filter bank by setting eigenvalues of the state transition matrix into the unit circle. Due to cascade connection of building blocks, we are able to design a system with a larger number of free parameters while keeping the stability. We introduce the condition which obtains the new building block without increasing of the filter order in spite of cascade connection. Additionally, by showing the simulation results, we show that this implementation has a better stopband attenuation than conventional methods.

$M$-Channel Nonlinear Phase Filter Banks in Image Compression: Structure, Design, and Signal Extension

This paper describes a transform coding technique based on M-channel perfect reconstruction filter banks with a nonlinear phase. In contrast with linear-phase filter banks, the nonlinearity provides an extra degree of freedom that can be used to design a more efficient transform. We present new lattice structures of paraunitary and perfect reconstruction (biorthogonal) filter banks, which can be implemented with a lower computational complexity and/or represented by a few free parameters, through the decomposition of the lattice blocks and the displacement across the delay block. We further discuss a smooth extension method for nonlinear-phase filter banks to obtain a nonexpansive transform. The promise of our proposed approaches is demonstrated through several design examples, extended signals and compression results

M-channel compactly supported biorthogonal cosine-modulated wavelet bases

We generalize the theory of compactly supported biorthogonal two-channel wavelet bases to M-channel. A sufficient condition for the M-channel perfect reconstruction filter banks to construct M-channel biorthogonal bases of compactly supported wavelets is derived. It is shown that the construction of biorthogonal M-channel wavelet bases is equivalent to the design of a M-channel perfect reconstruction filter bank with some added regularity conditions. A family of M-channel biorthogonal wavelet bases based on the cosine-modulated filter bank (CMFB) is proposed. It has the advantages of simple design procedure, efficient implementation, and good filter quality. A new method fur imposing the regularity on the CMFBs is also introduced, and several design examples are given.

Classification of Nonexpansive Symmetric Extension Transforms for Multirate Filter Banks

This paper describes and classifies a family of invertible discrete-time signal transforms, referred to as symmetric extension transforms(SET's), for finite-length signals. SET's are algorithms for applying perfect reconstruction multirate filter banks to symmetric extensions of finite-length signals, thereby avoiding the boundary artifacts introduced by simple periodic extension. A key point is when such symmetric decompositions can be formed with no increase in data storage requirements (“nonexpansive decompositions”). Transforms based on three types of symmetric extension and four classes of linear phase filters are analyzed in terms of their memory requirements for general M-channel perfect reconstruction filter banks. The classification is shown to be complete in the sense that it contains all possible nonexpansive SET's. Completeness is then used to deduce design constraints on the construction of nonexpansive M-channel SET's, including new obstructions to the existence of certain classes of filter banks. This paper also forms the principal technical reference on the SET algorithms incorporated in the Federal Bureau of Investigation's digital fingerprint image coding standard.

Exact interpolation and iterative subdivision schemes

We examine the circumstances under which a discrete-time signal can be exactly interpolated given only every Mth sample. After pointing out the connection between designing an M-fold interpolator and the construction of an M-channel perfect reconstruction filter bank, we derive necessary and sufficient conditions on the signal under which exact interpolation is possible. Bandlimited signals are one obvious example, but numerous others exist. We examine these and show how the interpolators may be constructed. A main application is to iterative interpolation schemes, used for the efficient generation of smooth curves. We show that conventional bandlimited interpolators are not suitable in this context. A better criterion is to use interpolators that are exact for polynomial functions. We demonstrate that these interpolators converge when iterated, and show how these may be designed for any polynomial degree N and any interpolation factor M. This makes it possible to design interpolators for iterative schemes to make best use of the resolution available in a given display medium.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>