Nonuniform Filter Banks Research Articles

Time-Varying Time–Frequency Tilings Using Non-Uniform Orthogonal Filterbanks Based on MDCT Analysis/Synthesis and Time Domain Aliasing Reduction

Time Domain Aliasing Reduction (TDAR) is a method to improve the impulse response compactness of non-uniform orthogonal Modified Discrete Cosine Transforms (MDCT). Previously, TDAR was only possible between frames of identical time-frequency tilings, however in this letter we describe a method to overcome this limitation. This method enables the use of TDAR between two consecutive frames of different time-frequency tilings by introducing another subband merging or subband splitting step. Consecutively, this method allows more flexible and adaptive filterbank tilings while retaining compact impulse responses, two attributes needed for efficient perceptual audio coding.

Analysis of Signals via Non-Maximally Decimated Non-Uniform Filter Banks

This paper addresses the important problem of reconstructing a signal from multiple multirate observations. The observations are modeled as the output of an analysis bank, and time-domain analysis is carried out to design an optimal FIR synthesis bank. We pose this as a minimizing the mean-square problem and prove that at least one optimal solution is always possible. A parametric form for all optimal solutions is obtained for a non-maximally decimated filter bank. The necessary and sufficient conditions for an optimal solution, that results in perfect reconstruction (PR), are derived as time-domain pseudocirculant conditions. This represents a novel theoretical contribution in multirate filter bank theory. We explore PR in a more general setting. This results in the ability to design a synthesis bank with a particular delay in the reconstruction. Using this delay, one can achieve PR in cases where it might not have been possible otherwise. Further, we extend the design and analysis to non-uniform filter banks and carry out simulations to verify the derived results.

Decimations of intrinsic mode functions via semi-infinite programming based optimal adaptive nonuniform filter bank design approach

Abstract A signal can be represented as the sum of the intrinsic mode functions via performing the empirical mode decomposition. For the discrete time signals, the lengths of the intrinsic mode functions are equal to the lengths of the input signals. As there is usually more than one intrinsic mode function, the total numbers of discrete points of all the intrinsic mode functions are usually more than the lengths of the input signals. In other words, the empirical mode decomposition is an oversampled representation. For some applications such as the compression application, the oversampled representation is not preferred. Therefore, this paper proposes an optimal adaptive nonuniform filter bank design approach for performing the decimations on the intrinsic mode functions. In particular, the passbands of the intrinsic mode functions are estimated based on an adaptive gradient algorithm. Then, the intrinsic mode functions are nonuniformly downsampled and upsampled with the sampling integers derived based on their estimated passbands. Next, a bank of filters is employed to reconstruct the original signal. Here, the passbands of the filters are also derived based on those of the intrinsic mode functions. After that, the nonuniform filter bank design problem is formulated as a semi-infinite programming problem such that the total ripple energies of all the filters are minimized subject to the specifications on the absolute maximum values of both the real part and the imaginary part of the reconstruction error. The semi-infinite programming problem is approximated by a semi-definite programming problem. Computer numerical simulation results show that our proposed system could achieve a very small reconstruction error at a very small oversampling ratio.

Baseline Wander Removal from ECG Using Multiband Structured Sub band Adaptive Filter LMS Algorithm

This paper investigates the new detailed adaptive noise canceller (ANC) system for Electrocardiogram (ECG) enhancement with robustness based on multiband structured sub band adaptive filter (MSAF). The proposed design is probably a new realization form of algorithm which guaranteed a more stable transformation and solves the structured problems in conventional sub band adaptive filter (SAF). The objective of the examination is to give arrangement keeping in mind the end goal to improve the execution of ANC as far as filter parameters which are procured with the assistance of uniform filter banks (UFB) and non uniform filter banks (NUFB) structured MSAF's using LMS algorithm. Computer simulation demonstrates that the proposed system gives improved performance and achieves good adaptation. NUFB structured MSAF algorithms are applied on ECG records obtained from standard MIT-BIH data base and the performance is compared with UFB structured MSAF algorithms in terms of parameters SNR, MSE, RMSE and distortion. The SNR for various NUFB structured MSAF's was found to be higher than the UFB structured MSAF's. The five channel NUFB structures with decimation factors (16, 16, 8, 4, 2) has on average SNR of 17.67064 dB is obtained using LMS algorithm which is superior to existing algorithms.

Modeling and Simulation of Frequency Response Masking FIR Filter Bank using Approximate Multiplier for Hearing Aid Application

The tremendous increase in the use of portable electronic devices is due to the development in the fields of signal processing and electronic technology. These battery operated devices needs reduction in power consumption with increased performance and long battery life. Since CMOS technology scaling fast approaches its physical limit of minimum supply voltage and smaller feature size, the hardware designer has to opt for new multiplier architectures for achieving low power and high speed performance. This paper proposes an area and power efficient approximate multiplier architecture. The error metrics are estimated to verify its performance advantage over other approximate multipliers. Using Frequency Response masking approach, a 6-band non-uniform digital FIR filter bank is developed using approximate multiplier for hearing aid application. Audiogram matching is done with audiograms of two different types of hearing losses and the matching error is computed. Simulation results show that the audiogram matching error falls within +/- 4 dB range.

The Design of Low-Power 16-Band Nonuniform Filter Bank for Hearing Aids.

A computationally efficient, low-power (107.6 μW@1.1V), small core area (2.82[Formula: see text]@0.35 μm), 16-band nonuniformly spaced digital filter bank with stop-band attenuation of more than 60dB is designed and implemented for hearing aid applications using a 0.35 μm CMOS process. The low computational complexity of the filter bank is achieved using a frequency response masking technique with multiple band-edge shaping filters. The proposed filter bank yields significant improvements in both power consumption and group delay. By coefficient sharing scheme, the implementation of such a filter bank requires only three multipliers.

Constrained least square nonuniform dynamic filter bank for delay and Hardware efficient digital hearing aids

Hearing aid design requires a set of filters that provides reasonable audiogram matching for the specific type of hearing loss. Various fixed and reconfigurable filter banks are reported for different sound wave decomposition plans. But the delay and complexity of these structures are relatively large for a real hearing aid system. In this paper, a constrained least square, finite impulse response filter bank with low group delay and low hardware complexity is proposed. The method has considerable reduction in multiplications per sample and is more suitable for systems where the spectra of desired and undesired signals are overlapped. Coefficient decimation technique is used to vary the edge frequencies of the filters to make the system dynamic to accommodate the changes which can happen in future in the audiogram pattern due to aging of user. The proposed delay and hardware efficient filter structure has synthesized using Xilinx software.

Design of Low-redundant Cosine-modulated Nonuniform Filter Bank with Flexible Frequency Division

In this paper, a low-redundant cosine-modulated nonuniform filter bank (LR-CMNFB) and its design method are proposed. The proposed LR-CMNFB consists of two parallel subsystems which have the same frequency division scheme. The nonuniform analysis and synthesis filters of the first subsystem are formed by directly merging the consecutive cosine-modulated versions of a lowpass prototype filter, and the filters of the second subsystem are derived to meet the aliasing cancelation condition. Since the aliasing of the two subsystems is structurally canceled without guardband constraint on the filter location, the shift-invariance and flexible nonuniform frequency division, two important properties in many signal and image processing applications, can be achieved simultaneously at the cost of low redundancy (that is less than 2). From a particular analysis on the filter characteristic and the reconstruction error of the whole system, it is found that the good characteristics of filters and the good reconstruction performance of LR-CMNFB can be jointly obtained by constraining the prototype filter to be the linear-phase spectral factor of a 2 Mth band filter. Several design examples are given to illustrate the performance of the proposed LR-CMNFB and its potential in practical applications.

High performance continuous variable bandwidth digital filter design for hearing aid application

A low complexity, low delay reconfigurable digital filter structure for hearing aids is proposed in this paper. The main objective is to match a given human audiogram, with minimum error. The high computational complexity in the conventional uniform and non-uniform filter bank techniques, probes to shift the design paradigm towards variable filter structure. In this paper, Farrow structure based design is used to realize an arbitrary sample rate converter, making use of a differentiator based model, by which the bandwidth can be continuously varied. The proposed design also considers the importance of the power, area, and” delay in such a critical scenario. Exhaustive comparisons are performed with the existing literature on audiogram matching, and our design is very competitive when compared to the designs in the literature, not only with respect to the matching error but also with respect to area, power dissipation, and hardware complexity.

Low complexity reconfigurable channelizers using non-uniform filter banks

A Software Defined Radio (SDR) channelizer needs reconfigurable sharp filter banks with low implementation complexity. In this paper, the design of non-uniform Modified Discrete Fourier Transform filter bank (MDFT FB) is proposed to be used in SDR channelizer. The frequency response masking technique is used to design the prototype filter which gives sharp filters with lower hardware complexity, compared to the finite impulse response filters. The canonic signed digit (CSD) representation is used in the design, to convert the continuous filter coefficients into discrete coefficients. Multi-objective artificial bee colony algorithm is utilized to improve the performance degradation when the CSD represented filter coefficients are used. Further, the shift inclusive differential technique with common sub-expression elimination is used to reduce the number of adders. Xilinx ISE is used to verify the hardware requirement, for the implementation of the non-uniform MDFT FB. Hence low complexity reconfigurable SDR channelizers using non-uniform MDFT FB is proposed in this paper.

Optimal design of finite precision and infinite precision non-uniform cosine modulated filter bank

This paper investigates the design of non-uniform cosine modulated filter bank (CMFB) with both finite precision coefficients and infinite precision coefficients. The finite precision filter bank has been designed to reduce the computational complexity related to the multiplication operations in the filter bank. Here, non-uniform filter bank (NUFB) is obtained by merging the appropriate filters of an uniform filter bank. An efficient optimization approach is developed for the design of non-uniform CMFB with infinite precision coefficients. A new procedure based on the discrete filled function is then developed to design the filter bank prototype filter with finite precision coefficients. Design examples demonstrate that the designed filter banks with both infinite precision coefficients and finite precision coefficients have low distortion and better performance when compared with other existing methods.

비균일 이진트리 필터뱅크 시스템에 기반한 전력품질 사건의 특이점 검출 기법

비균일 이진트리 필터뱅크 시스템에 기반한 전력품질 사건의 특이점 검출 기법

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.

Design of hardware-efficient digital hearing aids using non-uniform MDFT filter banks

This paper proposes the design of a simple digital hearing aid using non-uniform modified discrete Fourier transform filter bank. Here, the non-uniform filter bank is obtained by first designing a uniform filter bank and then merging suitable bands to obtain the desired non-uniform structure. In hearing aids, narrow channels with adjustable gains can be allocated to those frequency regions of the audiogram with sharp transition, whereas wider passband channels can be allocated to frequency regions with slower transitions. The latter can be done by merging the bands in those regions. It is shown in this paper that matching error, delay and hardware complexity in terms of the number of multipliers required for the prototype filter are lower than the existing techniques for all types of hearing losses.

Design of hardware-efficient digital hearing aids using non-uniform MDFT filter banks

Design of hardware-efficient digital hearing aids using non-uniform MDFT filter banks

Design of oversampled nonuniform filter banks with arbitrary rational frequency partitioning

Among the theory and design of oversampled nonuniform filter banks (NUFBs), most of the existing works only consider the cases with integer decimators, and up to now the issue with rational sampling factors has not been discussed yet. In this paper, we generalize the partial modulation technique to realize arbitrary rational frequency partitioning of oversampled NUFBs with highly desired linear-phase (LP) property. Further for the subbands with sampling factors violating the guard band restriction, a phase-modification scheme is derived to avoid uneliminable large aliasing and meanwhile preserving the LP characteristics of shifted analysis/synthesis filters. By using the proposed method, the design issue of LP oversampled NUFBs can be reduced to that of several prototypes, decreasing the design complexity largely. As illustrated by examples, the proposed algorithm is more general in terms of arbitrary rational decimation and thus has broad application prospects.

Hypercomplex polynomial wavelet-filter bank transform for color image

Starting from a link with the discrete polynomial decomposition, we propose an extension of the non-uniform filter bank framework to vector-valued signals to carry out a non marginal color wavelet transform. Recently quaternions or Clifford algebras have been used to perform color image processing. This paper uses the embedding of color information into the imaginary part of a Quaternion. From this coding strategy, discrete Hypercomplex 2D polynomial transform is presented as generalizing the real polynomial transform to the Hypercomplex domain. We illustrate how this numerical approach can be used to define Wavelet filter bank transform for color image, with piecewise Hypercomplex polynomial. From this, the connection between discrete polynomial representation and multiscale, filter bank algorithm already defined for Grayscale image is described and the proposed color representation is discussed. This new hypercomplex polynomial-wavelet transform has an extra parameter: an imaginary unit quaternion corresponding to a privileged color direction. This new color representation satisfies the conditions of orthogonality, perfect reconstruction and linear phase filter. Moreover, a link between hypercomplex polynomial projections and discrete multiscale differentiators is studied. We also give a practical study of this new Hypercomplex transform in the contexts of image denoising, which validates the interest of our construction.

Performance Analysis of Non-uniform Filter Bank with Equi ripple Band pass Filter

In this paper we present a non-uniform filter bank (NUFB) matched to a given signal. To obtain matched M- channel NUFB, first, we choose the decimation set having M-down sampling/decimation factors for which perfect reconstruction NUFB exist and then using novel approach proposed in this paper, M-channel signal matched analysis bank is estimated. The outputs of all filters at the analysis side of proposed filter bank are mutually as well as across various channels are uncorrelated. By using well established theory of multirate filter bank, M-channel NUFB matched to signal is obtained. The equiripple band pass filter will provide better tradeoff compared to previous non uniform Filter bank obtained in this fashion will be useful to compress code or represent the signal or image in the best possible manner.

An Efficient Method for Designing Multiplier-Less Non-uniform Filter Bank Based on Hybrid Method Using CSE Technique

This paper presents an efficient method for optimal design of multiplier-less non-uniform tree-structured filter banks using hybrid evolutionary algorithm. Phenomenal reduction in number of adders is achieved by applying common sub-expression elimination (CSE) on canonic signed digits (CSD) and binary represented filter coefficients. The proposed methodology utilizes the proficiencies of particle swarm optimization and artificial bee colony algorithms to achieve magnitude response of a prototype filter for non-uniform filter bank (NUFB) of 0.7071 at quadrature frequency. Single optimization technique is employed for designing the computationally efficient, continuous and quantized coefficients of a prototype filter for NUFB. A comprehensive study on CSE technique such as vertical, horizontal and mixed CSE has been also made for designing NUFB. The simulation results reflect that the proposed method shows better performance in terms of adder gain and reconstruction error. The hybrid method yields 33 % of adder gain with CSD technique and 55 % adder gain in case of CSE technique.

Design of M ‐channel linear‐phase non‐uniform filter banks with arbitrary rational sampling factors

The majority of the existing work on designing non-uniform filter banks (NUFBs) cannot realise arbitrary rational frequency partitioning, due to the ineliminable large aliasing caused by the non-feasible permutation of rational sampling factors. In this study, the authors extend the efficient modulation technique to non-feasible partitioned NUFBs and then generalise the phase modification structure to the case of rational decimators to achieve the linear-phase (LP) property. Through a step-by-step analysis on the aliasing elimination of both feasible and non-feasible subbands, it is proved that when the symmetry of filters and phase modification factors are chosen to meet the derived matching conditions, the non-LP characteristic of shifted filters can be transferred to LP one and further the non-feasible partitioned NUFB is obtained with highly desired LP property. Compared with the existing typical NUFB designs, the proposed approach can achieve comparable performance with much lower system delay and implementation complexity.