Multidimensional Filter Banks Research Articles

On constructing regular filter banks from domain bounded polynomials

The design of regular two-channel bi-orthogonal filter banks is shown to be reducible to the design of pairs of real polynomials with domain bounded to the interval /spl lsqb//spl minus/1,1/spl rsqb/. Techniques for designing polynomials satisfying various constraints are outlined. Transformation of polynomials to multidimensional bi-orthogonal filter banks is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Multidimensional multirate filters and filter banks derived from one-dimensional filters

A method by which every multidimensional (M-D) filter with an arbitrary parallelepiped-shaped passband support can be designed and implemented efficiently is presented. It is shown that all such filters can be designed starting from an appropriate one-dimensional prototype filter and performing a simple transformation. With D denoting the number of dimensions, the complexity of design and implementation of the M-D filter are reduced from O(N/sup D/) to O(N). Using the polyphase technique, an implementation with complexity of only 2N is obtained in the two-dimensional. Even though the filters designed are in general nonseparable, they have separable polyphase components. One special application of this method is in M-D multirate signal processing, where filters with parallelepiped-shaped passbands are used in decimation, interpolation, and filter banks. Some generalizations and other applications of this approach, including M-D uniform discrete Fourier transform (DFT) quadrature mirror filter banks that achieve perfect reconstruction, are studied. Several design example are given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for R/sup n/

New results on multidimensional filter banks and their connection to multidimensional nonseparable wavelets are presented. Among the topics discussed are sampling in multiple dimensions, multidimensional perfect reconstruction filter banks, the two-channel case in multiple dimensions, the synthesis of multidimensional filter banks, and the design of compactly supported wavelets. >

The analysis and design of multidimensional FIR perfect reconstruction filter banks for arbitrary sampling lattices

A general analysis of multidimensional multirate filter banks is presented. The approach is applicable to discrete signal spaces of any dimension, to multirate systems based on arbitrary downsampling and upsampling lattices, and for filter banks with any number of channels. A new numerical design procedure is also presented for multidimensional multirate perfect reconstruction filter banks, which is based on methods of nonlinearly constrained numerical optimization. An error function that depends only on the analysis filter impulse response coefficients is minimized, subject to a set of quadratic equality constraints that involve both the analysis and synthesis filter coefficients. With this design framework, it is possible to design a wide variety of filter banks that have a number of desirable properties. The analysis and synthesis filters that result are finite impulse response (FIR) and of equal size. In addition, both paraunitary and nonparaunitary filter banks can be designed with this method. Unlike paraunitary filter banks, nonparaunitary filter banks are capable of performing analysis bank functions more general than band-splitting with flat passband filters. >

Nearest matched filter classification of spatiotemporal patterns

Recent advances in massively parallel optical and electronic neural network processing technology have made it plausible to consider the use of matched filter banks containing large numbers of individual filters as pattern classifiers for complex spatiotemporal pattern environments such as speech, sonar, radar, and advanced communications. This paper begins with an overview of how neural networks can be used to approximately implement such multidimensional matched filter banks. The nearest matched filter classifier is then formally defined. This definition is then reformulated to show that the classifier is equivalent to a nearest neighbor classifier in a separable infinite-dimensional metric space that specifies the local-in-time behavior of spatiotemporal patterns. The result of Cover and Hart is then applied to show that, given a statistically comprehensive set of filter templates, the nearest matched filter classifier will have near-Bayesian performance for spatiotemporal patterns. The combination of near-Bayesian classifier performance with the excellent performance of matched filtering in noise yields a powerful new classification technique. This result adds additional interest to Grossberg's hypothesis that the mammalian cerebral cortex carries out local-in-time nearest matched filter classification of both auditory and visual sensory inputs as an initial step in sensory pattern recognition-which may help explain the almost instantaneous pattern recognition capabilities of animals.