Design Of Nonuniform Filter Banks Research Articles

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.

An optimized cosine-modulated nonuniform filter bank design for subband coding of ECG signal

A simple iterative technique for the design of nonuniform cosine modulated filter banks (CMFBS) is presented in this paper. The proposed technique employs a single parameter for optimization. The nonuniform cosine modulated filter banks are derived by merging the adjacent filters of uniform cosine modulated filter banks. The prototype filter is designed with the aid of different adjustable window functions such as Kaiser, Cosh and Exponential, and by using the constrained equiripple finite impulse response (FIR) digital filter design technique. In this method, either cut off frequency or passband edge frequency is varied in order to adjust the filter coefficients so that reconstruction error could be optimized/minimized to zero. Performance and effectiveness of the proposed method in terms of peak reconstruction error (PRE), aliasing distortion (AD), computational (CPU) time, and number of iteration (NOI) have been shown through the numerical examples and comparative studies. Finally, the technique is exploited for the subband coding of electrocardiogram (ECG) and speech signals.

An optimized design of nonuniform filter bank using variable-combinational window function

This paper proposes an optimized tree structure technique for the design of near perfect reconstruction (NPR) non-uniform filterbank. Popular variable window functions like Kaiser, Dolph-Chebyshev (DC) and Parzen-cos6 (nπ/N) (PC6) are used in the design of prototype filter. The NPR condition, results the distortion at the output. Therefore a linear iterative optimization technique is used to minimize the distortion. The proposed algorithm provides lowest value of distortion parameter than earlier reported publications with minimum computation overhead.

Analysis of realizable rational decimated nonuniform filter banks with direct structure

In the design of nonuniform filter banks (NUFBs) with direct structure, the location of each analysis filter, corresponding to the sampling factor satisfying maximal decimation condition, should be set properly to avoid large aliasing. In this paper, a necessary and sufficient condition for the setting of the location of each analysis filter is derived. The NUFBs, we focus on, have rational decimation factors. Based on the derived condition, the frequency support of each analysis filter for the realizable NUFBs can be determined directly in such a way that the analysis filters can extract the corresponding bands of the input signal. This provides a guideline for the design of NUFBs with direct structure in choosing proper locations of analysis filters.

On characterization of linear phase nonuniform filter banks

In this paper, a condition termed as linear phase condition (LPC), which ensures that the filters of a nonuniform filter bank are linear phase, is presented. It is observed that the proposed LPC is also applicable to the uniform filter bank case. Further, the utility of this LPC to find (i) necessary restrictions on the filters lengths, (ii) the number of symmetric and antisymmetric filters in the filter bank and (iii) filter bank decimation factors is also investigated. The results obtained for the different cases are also presented in the form of tables. These tables will facilitate the design of nonuniform filter bank by ruling out the non-solvable cases and by reducing the search space, thus saving the designers’ precious time.

Oversampled nonuniform filter banks using quadratic optimisation and transition filters

A new approach to nonuniform filter bank design is introduced. The designed filter bank is composed of many different uniform sections which are joined together by transition filters. Oversampled complex modulated uniform filter banks are calculated by means of quadratic optimisation. This way, analysis and synthesis stages are designed separately, each one fulfilling its own set of constraints. Later on, uniform sections with different frequency resolutions are joined together by transition filters. The results show that the designed filter bank exhibits nearly perfect reconstruction behaviour. An example with frequency resolution similar to the first 18 critical bands is implemented.

Eigenfilter design of real and complex coefficient QMF prototypes

In this brief, we propose a new method to design pseudo-QMF prototypes to implement near perfect reconstruction (NPR) modulated filter banks. The proposed method is based on the eigenfilter approach, simple to implement, but nevertheless, very efficient in designing high attenuation filters. The method also allows one to design complex coefficient prototypes that may be used to build nonuniform filter banks. Several examples of both uniform and nonuniform filter bank design are presented.

Nonuniform filter bank design with noises

This work solves the signal reconstruction problem involving nonuniform filter bank systems with rational decimation factors and noise. Three main nonuniform filter bank systems, i.e., filter-block decimator (FBD) structure, upsampler-filter-downsampler (UFD) structure, and tree structure, are included in this study. According to different operating conditions, two different signal reconstruction problems for nonuniform filter bank systems with noise under the unknown but identifiable input signal model and the unknown input signal model are discussed, respectively. At the first stage, a unified block state space model for different nonuniform filter bank systems with noise is developed. Then, by incorporating the identified input signal model with this unified state space model and appropriate choice of the augmented state vector, the signal reconstruction problem is reduced to an equivalent state estimation problem for resulting augmented systems if the input signal is identifiable. If the input signal is lacking in modeling, the signal reconstruction is discussed from the minimax estimation point of view. Two state estimation techniques involving robust Kalman filtering and H/sub /spl infin// filtering are employed, respectively, to treat the signal reconstruction problem of nonuniform filter bank systems according to different a priori knowledge of the input signal. Finally, several numerical examples are presented to illustrate the proposed algorithms and exhibit the performances.