Linear-phase Filter Banks Research Articles

Low complexity reconfigurable modified FRM architecture with full spectral utilization for efficient channelizers

This paper proposes a design of low complexity, reconfigurable, and narrow transition band (NTB) filter bank (FB). In our proposed Modified Frequency Response Masking (ModFRM) architecture, the modal filter and complementary filter in the conventional FRM approach are replaced by a power complementary and linear phase FB. Additionally, a new masking strategy is proposed by which an M-channel FB can be designed by alternately masking even channels and odd channels. By using this masking strategy, it is only necessary to modulate the masking filters over the multiple spectra replicas appearing in [0,2π] to generate uniform ModFRM FB. Also, the reconfigurability of filter banks can be achieved by adjusting the interpolation values appropriately, to obtain more masking responses. The results indicate that the proposed method requires substantially fewer multipliers in comparison to the reconfigurable FB existing in the literature. Finally, nonuniform FB is generated from the uniform FB by combining nearby channels and are used for the extraction of different communication standards in the software defined radio (SDR) channelizer. When more channels are to be extracted, the proposed scheme can achieve a reduced hardware complexity in comparison to other filter bank based SDR channelizers.

Nearly symmetric orthogonal wavelets for time-frequency-shape joint analysis: Introducing the discrete shapelet transform’s third generation (DST-III) for nonlinear signal analysis

This article introduces the third generation of an interesting tool created for time-frequency-shape (TFS) joint analysis. Called Discrete Shapelet Transform (DST-III), it improves both its predecessors, i.e., DST-I and DST-II, in such a way that nearly symmetric major shapelet functions, and consequently almost linear-phase filterbanks, are obtained. Following a brief review on important concepts, the DST-III formulation is specified in detail and complemented with a numerical example. In addition, a prototype pattern matching strategy, where a comparison with ordinary wavelets takes place, and a spike sorting application are also presented and discussed. Notably, wavelet expansions use to provide very concise signal representations, thus simplifying subsequent nonlinear signal analysis in both time and frequency and, consequently, bringing advantages for non-stationary problem solving in science and engineering. This reassures the efficacy of this new tool.

Even Dispersion Design for a Compact Linear Loudspeaker Array with Adaptive Genetic Algorithm

Even dispersion is important for live sound reinforcement systems; however, it needs to be carefully designed when using a linear loudspeaker array. This is because the audience area is often large, while the loudspeakers are placed centrally in this case for convenience, and thus both the level and the frequency balance may not remain reasonably constant for all audiences. To solve this problem, the adaptive genetic algorithm is firstly introduced in the parameters optimization. Secondly, taking the radiation characteristics at different frequencies into account, a linear-phase non-uniform filter bank is proposed to decompose the broad frequency band into several sub-bands. The audio is re-synthesized with the optimized parameters in each frequency band for a linear loudspeaker array. To show the validity of the proposed method, the simulations and the experiments are conducted to demonstrate that the sound pressure level in the audience area is distributed within ± 1.33 dB, ranging from 200 Hz to 4000 Hz.

Design of linear-phase nonsubsampled nonuniform directional filter bank with arbitrary directional partitioning

In this paper, we propose a design method for linear phase (LP) nonsubsampled nonuniform directional filter bank (NUDFB) with arbitrary number of subbands and arbitrary directional partitioning. The proposed NUDFB is simply designed by windowing the analytical expressions of wedge-shaped filters in space domain. The direction and angular bandwidth of the filters are determined by only two angular parameters. It can extract directional information according to the directional distribution of images, making it efficient in the directional representation of images. In addition, the perfect reconstruction conditions are derived. Numerical experiments on image directional information extraction and image denoising are given to illustrate the performance of our NUDFB. The results show that our NUDFB outperforms various directional decomposition methods while possesses LP property and more flexibility.

A Multi Directional Perfect Reconstruction Filter Bank Designed with 2-D Eigenfilter Approach: Application to Ultrasound Speckle Reduction.

B-Mode ultrasound images are degraded by inherent noise called Speckle, which creates a considerable impact on image quality. This noise reduces the accuracy of image analysis and interpretation. Therefore, reduction of speckle noise is an essential task which improves the accuracy of the clinical diagnostics. In this paper, a Multi-directional perfect-reconstruction (PR) filter bank is proposed based on 2-D eigenfilter approach. The proposed method used for the design of two-dimensional (2-D) two-channel linear-phase FIR perfect-reconstruction filter bank. In this method, the fan shaped, diamond shaped and checkerboard shaped filters are designed. The quadratic measure of the error function between the passband and stopband of the filter has been used an objective function. First, the low-pass analysis filter is designed and then the PR condition has been expressed as a set of linear constraints on the corresponding synthesis low-pass filter. Subsequently, the corresponding synthesis filter is designed using the eigenfilter design method with linear constraints. The newly designed 2-D filters are used in translation invariant pyramidal directional filter bank (TIPDFB) for reduction of speckle noise in ultrasound images. The proposed 2-D filters give better symmetry, regularity and frequency selectivity of the filters in comparison to existing design methods. The proposed method is validated on synthetic and real ultrasound data which ensures improvement in the quality of ultrasound images and efficiently suppresses the speckle noise compared to existing methods.

Critically sampled graph filter banks with polynomial filters from regular domain filter banks

Graph signal processing deals with the processing of signals defined on irregular domains and is an emerging area of research. Graph filter banks allow the wavelet transform to be extended for processing graph signals. Sakiyama and Tanaka (2015) [22] recently proposed a technique to convert linear-phase biorthogonal filter banks for regular domain signals to biorthogonal graph filter banks. Perfect reconstruction is preserved using the technique but the resulting spectral filter functions are transcendental and not polynomial. Polynomial function filters are desired for the localization property and implementation efficiency. In this work we present alternative techniques to perform the conversion. Perfect reconstruction is preserved with the proposed techniques and the resulting spectral filters are polynomial functions.

Maximally Decimated Paraunitary Linear Phase FIR Filter Bank Design via Iterative SVD Approach

A necessary and sufficient condition for M-channel maximally decimated paraunitary FIR filter banks is derived when the lengths of all the filters are the same and they are integer multiples of M. Based on the derived condition, a family of this kind of filter banks is defined. These results are also applied to the corresponding linear phase filter banks. Then, the design of this type of filter banks with the linear phase property is formulated as two orthogonal Procrustes optimization problems. The analytical solution of each optimization problem is derived based on a singular value decomposition approach. Since no numerical optimization computer aided design tool is required for finding the analytical solution of each optimization problem, the computational power required for our proposed method is much lower than that for existing methods. Computer numerical simulation results show that our proposed method can obtain a design instantaneously.

Reversible symmetric nonexpansive convolution: an effective image boundary processing for <inline-formula> <tex-math notation="tex">$\mbi{m}$ </tex-math></inline-formula>-channel lifting-based linear-phase filter banks

We present an effective image boundary processing for M-channel (M ∈ IN, M ≥ 2) lifting-based linear-phase filter banks that are applied to unified lossy and lossless image compression (coding), i.e., lossy-to-lossless image coding. The reversible symmetric extension we propose is achieved by manipulating building blocks on the image boundary and reawakening the symmetry of each building block that has been lost due to rounding error on each lifting step. In addition, complexity is reduced by extending nonexpansive convolution, called reversible symmetric nonexpansive convolution, because the number of input signals does not even temporarily increase. Our method not only achieves reversible boundary processing, but also is comparable with irreversible symmetric extension in lossy image coding and outperformed periodic extension in lossy-to-lossless image coding.

Design and Simulation of Two Channel QMF Filter Bank using Equiripple Technique

In this paper a design of a two channel FIR QMF bank for perfect reconstruction is presented. The QMF design has multicriterion constraints such as minimal of reconstruction error and minimal of iterations are among the most important problems in filter bank design. The main problem of filter bank design is to find adequate coefficients for the prototype filter H0 such that the prototype filter has minimum error in stopband, passband and transition band. The proposed QMF filter bank has been developed using equiripple linear phase FIR filters with MATLAB. The developed equiripple linear phase filter bank performance has been compared with kaiser window based filter bank in terms of peak reconstruction error. The results show that equiripple based filter bank provides better PRE ranging from 16.45% to 17.31% as compared to kaiser window based filter bank.

Phase Watermarking of Images with Complex-Valued Linear-Phase Subband Filter Banks

A new algorithm is proposed for digital watermarking by applying complex-valued linear-phase filter banks to low frequency-band coefficients of images in the DCT domain. The watermark is conveyed in the phase spectrum of the subband coefficients. The robustness of the algorithm is examined in JPEG encoding with different qualities and compared with the DFT-based approach. Because only low frequency-band DCT coefficients are applied to complex-valued filter banks, the computational load introduced by the complex-valued filter banks is kept low. The watermark decoding is only accessible to users with the key information, i.e., impulse responses of the complex-valued linear-phase filter banks that designed with time-frequency spread property.

Design of Linear-Phase Filter Banks with Multiplier-Less Lattice Structures

Abstract In this paper, a new multiplier-less algorithm is proposed for the design of perfectreconstruction linear-phase (PR LP) filter banks by using multiplier-less lattice structures. The coefficients in the multiplication operations have been replaced with limited number of additions and the computational complexity is reduced significantly. The property of perfection reconstruction, however, is preserved regardless the multiplier-less approximation of lattice structures in the factorization of polyphase matrix. The coefficients in the 2x2 rotation matrices of the lattice structures are expressed as sum-of-powers-of-two (SOPOT) coefficients in the parameterization processes. By using the multiplier-less rotation matrices, the unitary matrices are constructed for the lattice factorization of perfect-reconstruction linear-phase filter banks. Design examples of 5-channel and 8-channel multiplier-less linear-phase filter banks are included to validate the algorithm and implementation.

Design of Biorthogonal Filter Banks Using a Multi-objective Genetic Algorithm for an Image Coding Scheme

In this paper, we present an optimization method based on a multi-objective Genetic Algorithm (GA) for the design of linear phase filter banks for an image coding scheme. To be effective, the filter banks should satisfy a number of desirable criteria related to such a scheme. Instead of imposing the entire PR condition as in conventional designs, we introduce flexibility in the design by relaxing the Perfect Reconstruction (PR) condition and defining a PR violation measure as an objective criterion to maintain near perfect reconstruction (N-PR) filter banks. Particularly in this work, the designed filter banks are near-orthogonal. This has been made possible by minimizing the deviation from the orthogonality in the optimization process. The optimization problem is formulated as a constrained multi-objective, and a modified Nondominated Sorting Genetic Algorithm NSGAII is proposed in this work to find the Pareto optimal solutions that achieve the best compromise between the different objective criteria. The experimental results show that the filter banks designed with the proposed method outperform significantly the 9/7 filter bank of JPEG2000 in most cases. Furthermore, the filter banks are near orthogonal. This is very helpful, especially where embedded coding is required.

A hybrid method for designing linear-phase quadrature mirror filter bank

In this work, a hybrid method in frequency domain for design of a linear-phase quadrature mirror filter bank is proposed. The nonlinear least square hybrid method based on Levenberg-Marquardt (LM) and Quasi-Newton (QN) is developed for the design of a low-pass prototype filter whose responses in the passband and stopband are ideal, and the filter bank response at quadrature frequency is 0.707. The proposed method is employed to optimize the quadratic measure of ideal characteristics of the prototype filter and filter bank at quadrature frequency. Performance and effectiveness of the proposed method in terms of peak reconstruction error (PRE), mean squares error in passband and stopband regions, and error in transition band at quadrature frequency are shown through numerical examples and comparison of the results with other existing method. It was found that the proposed method is very simple and easy to implement for QMF bank design problem.

Design of Linear Phase Nonuniform Filter Banks with Interpolated Prototype Filters

Most of nonuniform filter banks designed by existing methods are not linear phase. In order to solving the problem, a novel method for designing linear-phase nonuniform filter banks is proposed in this paper. By analyzing the filter banks structure with block decimation transformed to rational decimation, we get an interpolated filter banks structure which removes the mirror frequency brought from interpolation. The filter banks are obtained by cosine modulation in this paper, and the prototype filters are interpolated and filtered before modulation. To make sure the significant aliasing distortions are cancelled completely, all prototype filters are designed with consistent transition band performance, using the optimization algorithm. Simulation results demonstrate that the linear-phase nonuniform filter banks designed by the proposed method have small amplitude distortions and aliasing distortions.

An Efficient Nonuniform Cosine Modulated Filter Bank Design Using Simulated Annealing

In this paper, a new approach for the design of non-uniform frequency spacing filter bank using Simulated Annealing has been presented. The filter bank structure is obtained by merging the relevant bands of a uniformly shifted filter bank with integer sampling factors. The design problem is formulated as a single objective unconstrained optimization problem for reducing the amplitude distortion of the overall filter bank for a specified pass-band ripple and stop-band attenuation of the prototype filter. The prototype filter coefficients are optimized using block update method to reach global optimum very quickly and the near perfect reconstruction of the filter bank is also preserved. Simulation results demonstrate that the linear-phase non-uniform filter banks designed by the proposed method have small amplitude distortions and aliasing distortions. Using this technique to minimize design objective is suitable for filter banks applied in sub-band filtering because linear phase property is assured here.

Maximally flat differentiators through WLS Taylor decomposition

Instantaneous derivative estimates of a signal are obtained using the wighted least square (WLS) approximation of a Taylor (WLST) signal model, using classical windows as weighting factors. The WLST approximation in time corresponds to a Taylor approximation at the origin of the windowed signal spectrum. And the successive application of the WLST approximation leads to a filter bank whose frequency responses approach the set of ideal differentiator gains on the baseband, providing maximally flat differentiators on that band. Examples of these differentiator banks are designed with the Rectangular, Kaiser and Hamming windows, and their frequency and impulse responses are illustrated. Due to the strong symmetry of the signal model, this method achieves linear phase filter banks with equal delay for all the derivative estimates, which are very useful in applications where synchronized derivative of a bandlimited signal are desired.

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.

Symmetric extension for lifted filter banks and obstructions to reversible implementation

Symmetric pre-extension is a standard approach to boundary handling for finite-length input vectors with linear phase filter banks. It works with both conventional linear implementations and the so-called reversible, or integer-to-integer, implementations of odd-length linear phase ( whole-sample symmetric) filter banks. In comparison, significant difficulties arise when using symmetric pre-extension on reversible filter banks with even-length ( half-sample symmetric) linear phase filters. An alternative approach is presented using lifting step extension, in which boundary extensions are performed in each step of a lifting factorization, avoiding some of these difficulties while preserving reversibility and retaining the nonexpansive property of symmetric pre-extension. Another alternative that is capable of preserving both reversibility and subband symmetry for half-sample symmetric filter banks is developed based on ideas from the theory of lattice vector quantization. The practical ramifications of this work are illustrated by describing its influence on the specification of filter bank algorithms in Part 2 of the ISO/IEC JPEG 2000 image coding standard.

$M$-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

Design of linear-phase recombination nonuniform filter banks

This correspondence proposes a novel method for designing a class of recombination nonuniform filter banks (RNFBs) with the linear-phase (LP) property. In the structure of the proposed nonuniform filter bank (FB), certain channels of an M-channel uniform FB are merged by synthesis filters of transmultiplexers (TMUXs), yielding nonuniform subbands. By a detailed analysis of the frequency characteristics of the RNFBs, we derive the existence and matching conditions that are necessary for constructing the proposed RNFBs having good frequency responses. With those conditions being satisfied, the design problem becomes that of a set of LP uniform FBs. By using the Parks-McClellan algorithm, we are able to design the near-perfect-reconstruction LP RNFBs in a very simple and efficient way as demonstrated by two examples