Filter Bank Structure Research Articles

A Lattice Structure of Biorthogonal Linear-Phase Filter Banks With Higher Order Feasible Building Blocks

This paper proposes a lattice structure of biorthogonal linear-phase filter banks (BOLPFBs) using new building blocks which can obtain long filters with fewer number of building blocks than conventional ones. The structure is derived from a generalization of the building blocks of first-order LPFBs. Furthermore, the proposed building blocks are applicable for both even and odd number of channels. The resulting FBs have good performance in stopband attenuation and low implementation costs.

Analysis and synthesis of speech using least Pth norm filter design

In this paper we analyze the combination of speech and FIR filter design aspect to achieve good results in speech quality. A new approach in the time domain based on the least Pth norm is presented to extract maximum information that represents speech. The aim of this paper is to improve the perceived quality of speech through the introduction of least Pth norm algorithm that attenuates speech contaminated with noise. This approach relates to a filter bank structure and a method for filtering and separating an information signal into different bands, particularly for filtering and separation of speech signals. Then the desired signal is reconstructed from the independent components representing every band. This approach differs from the traditional approaches since no priori knowledge of the noise statistics is required, instead the noise signals are only assumed to have finite energy. Since the estimation criterion for the filter design is to minimize the worst possible amplification of the estimation error signal in terms of modeling errors and additive noise, this approach is highly robust and appropriate in practical speech analysis and synthesis. This paper presents a least Pth approach to the optimal design of FIR digital filter banks in the minimax sense for speech analysis and synthesis. The signal to noise ratio (SNR) of around 50–60 dB is achieved with various speech samples.

MIIND (Multiple Interacting Instantiations of Neural Dynamics) - bridging neural dynamics and cognitive modelling

Event Abstract Back to Event MIIND (Multiple Interacting Instantiations of Neural Dynamics) - bridging neural dynamics and cognitive modelling Marc De Kamps1* and Frank Van Der Velde2 1 University of Leeds, United Kingdom 2 University of Leiden, Netherlands MIIND is a C++ framework with a PYTHON interface which facilitates modelling in cognitive neuroscience. In MIIND one can create networks in terms of spatial configurations. The node of such networks can be endowed with algorithms that evolve the state of the nodes. In this way network processes can be modelled in a very generic way. In principle any coupled system of equations which can be represented by a sparse irregular network can be modelled. Users can provide their own algorithms in a transparent way. MIIND also has some predefined algorithms: Wilson-Cowan dynamics and population density techniques for leaky-integrate-and-fire (LIF) neurons. Wilson-Cowan dynamics is widely used in models of high level cognition. Population density techniques describe large populations of spiking neurons in terms of a density function which captures the characteristics of the population in a way that is often more efficient than a straightforward simulation of the population. Networks of such equations are closely linked to coupled systems of Fokker-Planck equations. Since MIIND can create complex spatial structures and provides algorithms for modelling neural dynamics, it is suitable for modelling high level cognition. One example of its application is modelling object-based attention in vision in terms of interacting hierarchical neural networks, the so-called neural blackboard architecture. Another application is the investigation of the behaviour of the dynamics of cortical circuits. MIIND does not provide simulations of spiking neurons, such as NEST, NEURON, GENESIS or MOOSE, although it could encapsulate algorithms which drive such simulations. MIIND does not provide a monolithic interface, but offers modelling support at various levels. Modellers may decide, for example, to use only the representation of sparse networks, or to use the simulation loop for other than neural processes. Developers can easily borrow parts of MIIND while disregarding the parts that are not of interest. MIIND also comes with a library that can implement filter operations between layers of nodes. In this way it is easy to implement large filter bank structures, which are used in biologically inspired models of object recognition, such as HMAX and successors. This opens the possibility to model biological vision on the one hand, and to apply the principles to biologically inspired artificial vision on the other hand. MIIND uses ROOT for visualisation and data management. ROOT is a powerful Open Source package, developed by CERN. It relies on the GNU Scientific Library (GSL) for scientific computing. MIIND is still in its infancy. Important future challenges are: the development of parallelisation of the simulation loop, extending the visualisation capabilities and the development of population density techniques which go beyond LIF neurons. Conference: Neuroinformatics 2008, Stockholm, Sweden, 7 Sep - 9 Sep, 2008. Presentation Type: Poster Presentation Topic: Large Scale Modeling Citation: De Kamps M and Van Der Velde F (2008). MIIND (Multiple Interacting Instantiations of Neural Dynamics) - bridging neural dynamics and cognitive modelling. Front. Neuroinform. Conference Abstract: Neuroinformatics 2008. doi: 10.3389/conf.neuro.11.2008.01.090 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 28 Jul 2008; Published Online: 28 Jul 2008. * Correspondence: Marc De Kamps, University of Leeds, Leeds, United Kingdom, dekamps@comp.leeds.ac.uk Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Marc De Kamps Frank Van Der Velde Google Marc De Kamps Frank Van Der Velde Google Scholar Marc De Kamps Frank Van Der Velde PubMed Marc De Kamps Frank Van Der Velde Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Generalized Discrete Multiwavelet Transform With Embedded Orthogonal Symmetric Prefilter Bank

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Prefilters are generally applied to the discrete multiwavelet transform (DMWT) for processing scalar signals. To fully utilize the benefit offered by DMWT, it is important to have the prefilter designed appropriately so as to preserve the important properties of multiwavelets. To this end, we have recently shown that it is possible to have the prefilter designed to be maximally decimated, yet preserve the linear phase and orthogonal properties as well as the approximation power of multiwavelets. However, such design requires the point of symmetry of each channel of the prefilter to match with the scaling functions of the target multiwavelet system. It can be very difficult to find a compatible filter bank structure; and in some cases, such filter structure simply does not exist, e.g., for multiwavelets of multiplicity 2. In this paper, we suggest a new DMWT structure in which the prefilter is combined with the first stage of DMWT. The advantage of the new structure is twofold. First, since the prefiltering stage is embedded into DMWT, the computational complexity can be greatly reduced. Experimental results show that an over 20% saving in arithmetic operations can be achieved comparing with the traditional DMWT realizations. Second, the new structure provides additional design freedom that allows the resulting prefilters to be maximally decimated, orthogonal and symmetric even for multiwavelets of low multiplicity. We evaluated the new DMWT structure in terms of computational complexity, energy compaction ratio as well as the compression performance when applying to a VQ based image coding system. Satisfactory results are obtained in all cases comparing with the traditional approaches. </para>

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.

Theoretical Complex Cepstrum of DCT and Warped DCT Filters

In this letter, we derive the theoretical complex cepstrum (TCC) of the discrete cosine transform (DCT) and warped DCT (WDCT) filters. Using these derivations, we intend to develop an analytic model of the warped discrete cosine transform cepstrum (WDCTC), which was recently introduced as a speech processing feature. In our derivation, we start with the filter bank structure for the DCT, where each basis is represented by a finite impulse response (FIR) filter. The WDCT filter bank is obtained by substituting z <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> in the DCT filter bank with a first-order all-pass filter. Using the filter bank structures, we first derive the transfer functions for the DCT and WDCT, and subsequently, the TCC for each filter is computed. We analyze the DCT and WDCT filter transfer functions and the TCC by illustrating the corresponding pole-zero maps and cepstral sequences. Moreover, we also use the derived TCC expressions to compute the cepstral sequence for a synthetic vowel /aa/ where the observations on the theoretical cepstrum corroborate well with our practical findings

Generalized adaptive IFIR filter bank structures

Adaptive filters based on filter bank (FB) techniques have attracted attention recently due to their ability to improve convergence rate and reduce the computational complexity. This paper investigates a generalized adaptive interpolated finite impulse response (IFIR) FB structure. The IFIR model is a set of cascade of an interpolator and a sparse filter connected in parallel. The IFIR FB models the system impulse response as a linear combination of double indexed set of functions. The modeling capabilities and delay properties of the structure are investigated. Realizations of adaptive IFIR FB structures with delaying and delayless properties are presented. The delaying structure is obtained by employing orthogonal set of the basis functions for the interpolating FB. It is shown that delayless adaptive IFIR FB structure, as a special case of general adaptive IFIR FB, can be obtained by relaxing the orthogonality condition on the basis functions. This allows flexibility to choose the interpolators. The interpolators could be chosen to improve convergence rate of the adaptive algorithm. In general, optimal design of interpolator FB requires a priori knowledge of the input process and the system. One method of choosing the interpolators is by a non-linear optimization procedure based only on a priori knowledge of input process. We present a new method to adapt the interpolators themselves based on a common cost function and hence require no a priori knowledge of the input statistics. The convergence rate and steady state error performance of these structures are compared with the classical fullband filter in system identification scenario. Its application in acoustic echo cancellation (AEC) is presented.

Design of nonuniform cosine-modulated filter-banks with the perfect-reconstruction property and arbitrary filter lengths

Abstract In this paper' a method is proposed to construct recombination nonuniform cosine-modulated filter banks (CMFBs) with a perfect-reconstruction property and with arbitrary filter lengths. In this filter bank (FB) structure, certain channels of an original M-channel uniform FB are merged by a set of transmultiplexers (TMUXs), yielding nonuniform outputs, and the length restrictions on the original CMPB and the recombination TMUKs are avoided, allong them to have arbifrary filter lengths. By imposing certain improved matching conditions on the protote filters, nonuniform FBs with arbitrary filter lengths and with good properties can be obtained. As a result, the flexibility of selecting modulation types and filter lengths is greatly increased in the design of recombination nonuniform CMFBs. Another benefit due to the flexibility is that the system delay can be reduced. *Supported by National Natural Science FoLndation of China (Grant Nos. 60672125 and 60372047)

Multi-Plet Two-Channel Perfect Reconstruction FIR and Causal Stable IIR Filter Banks

This paper proposes a new class of two-channel structural perfect reconstruction (PR) finite-impulse response / infinite-impulse response (FIR/IIR) filter banks (FBs) called the multi-plet FBs. It generalizes the structural PR FBs proposed by Phoong and the conventional triplet FB in that it employs multiple lifting steps similar to the conventional lifting structure. Apart from the important structural PR property, the multi-plet FB can be systematically designed to meet a given specification on the passband/stopband ripples and transition bandwidth: a low-order prototype PR FB with a much wider transition band is first designed using nonlinear optimization in order to obtain a symmetric frequency response and prescribed passband and stopband ripples. As only a few variables are required, its performances can easily be controlled. A subfilter is then designed using second-order cone programming (SOCP) so that the prototype FB can be warped by means of frequency transformation to meet the desired transition bandwidth, while preserving the PR condition, passband/stopband ripples and lifting structure of the prototype FB. The design procedure is very general and it applies to both linear-phase/low-delay FIR and IIR multi-plet FBs. By formulating the K-regularity conditions as a set of linear equality constraints on the subfilter coefficients, multi-plet-based wavelet bases can easily be designed under the SOCP framework. Design examples show that the proposed approach offers more flexibility in controlling the frequency characteristics of the PR FBs and lower design complexity than conventional methods

Comments on “Multi-dimensional filter banks and wavelets—A system theoretic perspective”

In [S. Basu, Multi-dimensional filter banks and wavelets—a system theoretic perspective, J. Franklin Inst. 335B(8) (1998) 1367–1409], the problems of constructing and parameterizing multi-dimensional (MD) filter banks (FB) and wavelets were studied extensively, especially in the situation of two-dimensional (2D) and quincunx-downsampled systems. Finding the other filter complementary to a given 2D filter for quincunx sampling and linear phase perfect reconstruction (LPPR) system is based on the fact that the construction is possible if and only if the polyphase components of the given filter do not share any common zero. The construction is elaborated in another book chapter [S. Basu, Multidimensional signals, circuits and systems, in: K. Galkowski, J. Wood (Eds.), On the Structure of Linear Phase Perfect Reconstruction Quincunx Filter Banks, Taylor & Francis, London, 2001, pp. 193–208 (Chapter 10)] by the same author. This approach further relies on the fact that the resultant of the polyphase components is monomial. In this comment, we show that both above mentioned facts are not necessarily true for the quincunx FB as well as for general MD FB.

M-band filtering and nonredundant directional wavelets

This article introduces families of nonadaptive directional wavelets. Unlike curvelets and contourlets, they are nonredundant and form orthonormal bases for L 2 ( R 2 ) . Their implementation derives from a single nonseparable filter bank structure with nonuniform sampling. We give several examples of frequency partitioning, including constructions based on separable multiresolution analyses. We show how to obtain orthonormal bases of wavelets with fast decay and compactly supported, biorthogonal wavelet bases. Some aliasing phenomena that can occur in these constructions are discussed.

Multiplierless filter Bank design: structures that improve both hardware and image compression performance

Design techniques for high-performance, fixed-point, multiplierless filter banks are presented. Image compression using the biorthogonal 9/7 discrete wavelet transform provides a motivating example. Image compression and hardware performance of two commonly used filter structures, direct and cascade, and two known filter bank structures, nonpolyphase and polyphase, are compared. A technique is shown for designing a fixed-point polyphase filter structure, which is highly efficient from a hardware standpoint, such that image-compression quality is not significantly deteriorated by the use of fixed-point mathematics. The result is a polyphase structure with about twice the throughput rate of nonpolyphase structures, and peak signal-to-noise ratio values for lossy compression within 0.2 decibels of those achieved using floating-point filters.

A new framework for characterization of halftone textures

Characterization of halftone texture is important for quantitative assessment of halftone quality. In this paper, we develop a new framework based on directional local sequency analysis and a filter bank structure. We decompose a halftone image into subband images, from which we can easily reconstruct the original halftone. Based on these subband images, we define the directional sequency spectrum which is analogous to the two-dimensional Fourier spectrum, and formulate several texture measures. Two test image sets are used to justify these measures.

A Generalized Oversampled Structure for Cosine-Modulated Transmultiplexers and Filter Banks

In this paper, a new structure, called the channel split-and-add method, for designing oversampled transmultiplexers and filter banks is presented. The proposed method is based on an initial design with an additional number of bands. The band number is then reduced to the desired value by the proper combination of adjacent and/or nonadjacent bands (subchannels). With the proposed approach it is always possible to perform the filtering tasks at the lowest data rate of the system. An example illustrates the design flexibility achieved with the proposed structure.

A delayless adaptive IFIR filterbank structure for wideband and narrowband active noise control

Active noise control (ANC) applications involve adaptive filters with hundreds of taps. These filters are associated with high computational burden depending on the number of taps in the filter and may suffer from slow convergence if the reference signal spectrum has a large dynamic range. Subband and filterbank techniques have been proposed to address these problems. It is known that linear systems can be modeled exactly using a set of filter bank basis functions. Filter bank adaptive filter (FBAF) is one such model in adaptive filterbank techniques. The FBAF model is a parallel bank of filters with each bank (channel) comprising of cascade of a set of short length filter called interpolator followed by adaptive sparse filter also called the model filter. The interpolator-sparse model filter cascade in each channel is identical to the classical interpolated finite impulse response (IFIR) filter. Hence, the structure is called IFIR filterbank structure. The filterbank basis functions are orthonormal, which introduces delay in the signal path, thereby, degrading the performance of the adaptive filter. In this paper, we propose a delayless adaptive IFIR filterbank structure for wideband and narrowband active noise control. The proposed delayless adaptive filter has improved mean square error (MSE) convergence rate and shows marginally better noise cancellation in the wideband and narrowband ANC domain when compared with the conventional fullband adaptive structure. The computational complexity of the proposed structure is compared with the fullband structure.

A delayless adaptive IFIR filterbank structure for wideband and narrowband active noise control

Active noise control (ANC) applications involve adaptive filters with hundreds of taps. These filters are associated with high computational burden depending on the number of taps in the filter and may suffer from slow convergence if the reference signal spectrum has a large dynamic range. Subband and filterbank techniques have been proposed to address these problems. It is known that linear systems can be modeled exactly using a set of filter bank basis functions. Filter bank adaptive filter (FBAF) is one such model in adaptive filterbank techniques. The FBAF model is a parallel bank of filters with each bank (channel) comprising of cascade of a set of short length filter called interpolator followed by adaptive sparse filter also called the model filter. The interpolator-sparse model filter cascade in each channel is identical to the classical interpolated finite impulse response (IFIR) filter. Hence, the structure is called IFIR filterbank structure. The filterbank basis functions are orthonormal, which introduces delay in the signal path, thereby, degrading the performance of the adaptive filter. In this paper, we propose a delayless adaptive IFIR filterbank structure for wideband and narrowband active noise control. The proposed delayless adaptive filter has improved mean square error (MSE) convergence rate and shows marginally better noise cancellation in the wideband and narrowband ANC domain when compared with the conventional fullband adaptive structure. The computational complexity of the proposed structure is compared with the fullband structure.

3-D IIR filtering using decimated DFT-polyphase filter bank structures

Two three-dimensional (3-D) under-decimated uniform discrete Fourier transform polyphase filter bank structures are proposed along with two applications: first, the sub-pixel motion discrimination of two-dimensional spatial objects moving with approximately constant local velocity in a noisy 3-D spatio-temporal image sequence and, second, the selective filtering of 3-D spatio-temporal broad-band plane waves based on their directions of arrival. The desired 3-D filter passband shapes are realized utilizing combinations of highly selective first-order 3-D infinite-impulse response frequency-planar filters in each band between the analysis and synthesis sections. Measured spatio-temporal performance confirms the high-quality broad-band transmission of passband signals, high directional selectivity and low computational complexity.

Optimal block boundary pre/postfiltering for wavelet-based image and video compression

This paper presents a pre/postfiltering framework to reduce the reconstruction errors near block boundaries in wavelet-based image and video compression. Two algorithms are developed to obtain the optimal filter, based on boundary filter bank and polyphase structure, respectively. A low-complexity structure is employed to approximate the optimal solution. Performances of the proposed method in the removal of JPEG 2000 tiling artifact and the jittering artifact of three-dimensional wavelet video coding are reported. Comparisons with other methods demonstrate the advantages of our pre/postfiltering framework.

Multiresolution direction filterbanks: theory, design, and applications

This paper presents new developments of directional filterbanks (DFBs). The motivation for the paper is the existence of multiresolution and multidirection orthogonal transform for two-dimensional (2-D) discrete signals. Based on the frequency supports of the ideal transform, a new uniformly, maximally decimated DFB with six highpass directional subbands and two lowpass subands is introduced. The uniform DFB (uDFB) can be implemented by a binary tree structure of two-channel filterbanks. The filterbank employed in the tree is shown to be alias-free decimation and permissible. The uDFB is then extended to a nonuniform case (nuDFB), which is still maximally decimated, by combining the two lowpass subbands. The nuDFB yields nonuniform frequency division, which composes of one lowpass filter with a decimation factor of one fourth and six highpass directional filters with a decimation factor of one eighth. The new DFBs offer alternative image decompositions, which overcome the limited directional selectivity of the separable wavelets and the limited multiresolution of the conventional DFB. The lowpass subband of the nuDFB can be used to obtain a multiresolution representation by simply reiterating the same nuDFB decomposition. On the other hand, the directional subbands can also be further refined by simply applying a two-channel conventional DFB at each highpass component. A simple design method yielding near orthogonal uniform and nonuniform multidimensional filterbanks is presented. Finally, the performances of the newly proposed nuDFB are compared with other conventional transforms in nonlinear approximation, image denoising, and texture classification to demonstrate its potential.

Channel noise robust transmit power optimized linear precoder for ISI channel with minimal complexity equalizer

A special class of linear precoder-equalizer pair with equalizers formed by simple tapped delay lines is proposed. With this special equalizer structure, the equalizer of this system not only can enjoy the minimal implementation complexity, but also can avoid the noise amplification effect. Moreover, using nonmaximally decimated filterbank structure, this precoder-equalizer pair is proven to be able to guarantee intersymbol interference (ISI)-free communication by zero-forcing approach, even if spectral nulling exists in the physical channel. Another advantage of this system is that the length of the guard period introduced by the precoder can be any positive integer values, thus the guard period can be designed to maximize the spectral efficiency by selecting it to be as short as one symbol per block of transmitted signal. A systematic method for designing a minimal transmit power finite-impulse response (FIR) precoder under the proposed precoder-equalizer pair structure is presented. Under the ISI channel with independent additive white Gaussian noise, the design of this minimal transmit power FIR precoder is shown to be a minimum mean square error precoder design. Simulation results are presented to illustrate the performance of the proposed precoder-equalizer structure and that of the transmit power minimized precoder.