Filter Bank Design Problem Research Articles

Design of FRM-Based Nonuniform Filter Bank With Reduced Effective Wordlength for Hearing Aids.

This paper presents a design method for frequency response masking (FRM)-based nonuniform filter bank with reduced effective wordlength. Instead of designing prototype filters separately, we propose to model the filter bank design problem as a nonlinear programming problem and jointly design the prototype filters in the FRM structure. Moreover, in this work, all the filters are designed directly in the finite wordlength space, such that they can be directly implemented using efficient fixed-point arithmetic without any quantization. By simultaneously considering all the subband constraints during optimization, the proposed method is able to guarantee the desirable stopband attenuation for all subbands and achieve optimal effective wordlength (EWL) for the coefficients, reducing the hardware complexity for very large-scale integration (VLSI) implementation. Experimental results show that the hardware complexity of filter banks can be reduced without sacrificing the audiogram compensation performance for hearing aid applications.

Optimal maximally decimated <i>M</i>-channel mirrored paraunitary linear phase FIR filter bank design via norm relaxed sequential quadratic programming

It is worth noting that the conventional maximally decimated M-channel mirrored paraunitary linear phase finite impulse response condition is defined in the frequency domain. As the frequency domain is a continuous set, it is expressed as a matrix functional (a continuous function of the frequency) equation. On the other hand, this paper expresses the condition as a finite number of discrete (a set of functions of the sampled frequencies) equations. Besides, this paper proposes to sample the magnitude responses of the filters with the total number of the sampled frequencies being more than the filter lengths. Hence, the frequency selectivities of the filters can be controlled more effectively. This filter bank design problem is formulated as an optimization problem in such a way that the total mirrored paraunitary linear phase error is minimized subject to the specifications on the magnitude responses of the filters at these sampling frequencies. However, this optimization problem is highly nonconvex. To address this difficulty, a norm relaxed sequential quadratic programming approach is applied for finding its local optimal solution. By iterating the above procedures using different initial conditions, a near global optimal solution is obtained. Computer numerical simulation results show that our proposed design outperforms the existing designs.

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.

Application of an optimal class of antisymmetric wavelet filter banks for obstructive sleep apnea diagnosis using ECG signals

Obstructive sleep apnea (OSA) is a sleep disorder caused due to interruption of breathing resulting in insufficient oxygen to the human body and brain. If the OSA is detected and treated at an early stage the possibility of severe health impairment can be mitigated. Therefore, an accurate automated OSA detection system is indispensable. Generally, OSA based computer-aided diagnosis (CAD) system employs multi-channel, multi-signal physiological signals. However, there is a great need for single-channel bio-signal based low-power, a portable OSA-CAD system which can be used at home. In this study, we propose single-channel electrocardiogram (ECG) based OSA-CAD system using a new class of optimal biorthogonal antisymmetric wavelet filter bank (BAWFB). In this class of filter bank, all filters are of even length. The filter bank design problem is transformed into a constrained optimization problem wherein the objective is to minimize either frequency-spread for the given time-spread or time-spread for the given frequency-spread. The optimization problem is formulated as a semi-definite programming (SDP) problem. In the SDP problem, the objective function (time-spread or frequency-spread), constraints of perfect reconstruction (PR) and zero moment (ZM) are incorporated in their time domain matrix formulations. The global solution for SDP is obtained using interior point algorithm. The newly designed BAWFB is used for the classification of OSA using ECG signals taken from the physionet's Apnea-ECG database. The ECG segments of 1 min duration are decomposed into six wavelet subbands (WSBs) by employing the proposed BAWFB. Then, the fuzzy entropy (FE) and log-energy (LE) features are computed from all six WSBs. The FE and LE features are classified into normal and OSA groups using least squares support vector machine (LS-SVM) with 35-fold cross-validation strategy. The proposed OSA detection model achieved the average classification accuracy, sensitivity, specificity and F-score of 90.11%, 90.87% 88.88% and 0.92, respectively. The performance of the model is found to be better than the existing works in detecting OSA using the same database. Thus, the proposed automated OSA detection system is accurate, cost-effective and ready to be tested with a huge database.

An improved method for the design of quadrature mirror filter banks using the Levenberg–Marquardt optimization

This paper presents an improved and efficient method for the design of a two-channel quadrature mirror filter (QMF) bank. In the proposed method, the filter bank design problem is formulated as a low-pass prototype filter design problem, whose responses in the passband and stopband are ideal and their filter coefficients value at quadrature frequency is 0.707. A new method is developed for the design of a low-pass prototype filter which minimizes the objective function by optimizing the filter taps weights using the Levenberg–Marquardt method. When compared with other existing algorithms, it significantly reduces peak reconstruction error (PRE), error in passband, stopband and transition band. Several design examples are included to show the increased efficiency and the flexibility of the proposed method over existing methods. An application of this method is considered in the area of subband coding of the ultrasound images.

Reconstruction of Nonuniformly Sampled Bandlimited Signals by Means of Time-Varying Discrete-Time FIR Filters

This paper deals with reconstruction of nonuniformly sampled bandlimited continuous-time signals using time-varying discrete-time finite-length impulse response (FIR) filters. The main theme of the paper is to show how a slight oversampling should be utilized for designing the reconstruction filters in a proper manner. Based on a time-frequency function, it is shown that the reconstruction problem can be posed as one that resembles an ordinary filter design problem, both for deterministic signals and random processes. From this facts, an analytic least-square design technique is then derived. Furthermore, for an important special case, corresponding to periodic nonuniform sampling, it is shown that the reconstruction problem alternatively can be posed as a filter bank design problem, thus with requirements on a distortion transfer function and a number of aliasing transfer functions. This eases the design and offers alternative practical design methods as discussed in the paper. Several design examples are included that illustrate the benefits of the proposed design techniques over previously existing techniques.

Design of optimal shift-invariant orthonormal wavelet filter banks via genetic algorithm

Although the orthonormal discrete wavelet transform offers the advantage of computation efficiency, it is generally not shift-invariant thereby yielding different transform coefficient values when applied to the same signal with different time shifts. Proposed in this paper is a new design method based on the genetic algorithm for the construction of orthonormal wavelet filter banks with an optimal shift-invariant property. In particular, the paper presents transformation of the multi-objective filter bank design problem to a single-objective constrained optimisation problem, chromosome representation of filter coefficients, the shift-invariant objective function for chromosome fitness evaluation, as well as a special constraint to discard infeasible solutions thereby confining the search for the optimum, based on the natural evolution mechanisms, within the wavelet sub-space. Furthermore, using denoising as an example, the performance of the wavelet filter bank constructed is compared with the classical wavelet filter banks to demonstrate its optimality.

Linear phase filter bank design using LMI-based H/sub ∞ optimization

This paper is concerned with the design of nearly linear phase two-channel filter banks. Exactly linear phase finite-impulse response or nearly linear phase infinite-impulse response (IIR) filters are employed in analysis filter banks, and nearly linear phase IIR synthesis filter banks are designed such that the overall filter banks are also nearly linear phase. The filter bank design problem is formulated as a H/sub /spl infin// norm minimization of the difference between the pure delay and the products of some polyphase components. The H/sub /spl infin// norm optimizing problem is converted to a series of linear matrix inequalities (LMIs) and solved using semidefinite programming. The magnitude, phase and aliasing distortions are all incorporated in the design procedure.

An efficient algorithm to design weighted minimax perfect reconstruction quadrature mirror filter banks

An efficient algorithm is presented to design lattice structure two-channel perfect reconstruction quadrature mirror filter (PR-QMF) banks. We formulate the filter bank design problem as an unconstrained weighted least squares problem with respect to the coefficients of the lattice structure. The proposed iterative algorithm optimizes the lattice coefficients and provides flexible control of the filters' stopband ripple profiles. Typically, only a few iterations of the algorithm are needed to obtain an optimal solution in the weighted minimax sense. We include a set of practical design rules for use with our algorithm. These rules allow very good estimation of important filter bank characteristics, such as the filter length and the number of signed digits for quantization of the lattice coefficients into canonic signed digit representation, to meet a given set of PR-QMF bank specifications.

Digital filter bank design quadratic-constrained formulation

Formulate the filter bank design problem as an quadratic-constrained least-squares minimization problem. The solution of the minimization problem converges very quickly since the cost function as well as the constraints are quadratic functions with respect to the unknown parameters. The formulations of the perfect-reconstruction cosine-modulated filter bank, of the near-perfect-reconstruction pseudo-QMF bank, and of the two-channel biorthogonal linear-phase filter bank are derived using the proposed approach. Compared with other design methods, the proposed technique yields PR filter banks with much higher stopband attenuation. The proposed technique can also be extended to design multidimensional filter banks. >

Subband decomposition of signals with generalized sampling

The authors generalize down and up-sampling operations by proposing block sampling. Perfect reconstruction conditions for two-band subband coding with block sampling are derived. By generalizing the sampling operation, new degrees of freedom are introduced and as a result, filter banks which were not previously possible become possible. Generalized down-sampler introduces different aliasing components than that of the traditional down-sampler. This can be used to ease some the requirements of the filter bank design problem. A constructive sampling method is proposed so that coprimeness of the transfer functions of the analysis filter banks is not only a necessary but also sufficient condition for perfect reconstruction. The results are extended to the case where the filter banks are linear periodically time-varying. The multichannel case is analyzed and the relation between unimodular matrices and perfect reconstruction filter banks is discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>