Filter Bank Structure Research Articles

Filter bank property of variational mode decomposition and its applications

The variational mode decomposition (VMD) was proposed recently as an alternative to the empirical mode decomposition (EMD). To shed further light on its performance, we analyze the behavior of VMD in the presence of irregular samples, impulsive response, fractional Gaussian noise as well as tones separation. Extensive numerical simulations are conducted to investigate the parameters mentioned in VMD on these filter bank properties. It is found that, unlike EMD, the statistical characterization of the obtained modes reveals a different equivalent filter bank structure, robustness with respect to the nonuniformly sampling and good resolution in spectrum analysis. Moreover, we illustrate the influences of the main parameters on these properties, which provides a guidance on tuning them. Based on these findings, three potential applications in extracting time-varying oscillations, detrending as well as detecting impacts using VMD are presented.

Higher order feasible building blocks for lattice structure of multidimensional linear phase biorthogonal filter banks

A multidimensional (MD) linear phase biorthogonal filter bank (LPBOFB) with higher order feasible (HOF) building blocks is reported. Basically, there are two ways to design filter banks with large filter supports. One way is to use a cascade of degree-1 building blocks, and the other way is to use a cascade of order-1 building blocks. Unfortunately, both methods have high implementation costs in terms of the number of parameters, especially for the multidimensional case. A previously reported HOF building block has now been applied to MD LPBOFBs. Their generalized structural design supports both an even and odd number of channels. It is shown that the HOF structure cannot be factored into a cascade of order-1 building blocks. The proposed MD LPBOFB has larger filters and uses fewer building blocks than the traditional degree-1 and order-1 structures.

Extraction of adaptive wavelet packet filter‐bank‐based acoustic feature for speech emotion recognition

In this paper, a wavelet packet (WP)-based acoustic feature extraction approach is proposed for automatic speech emotion recognition (SER). First, the issue of optimising the WP filter-bank structure for giving classification task is presented as a tree pruning problem, and different tree-pruning criteria are investigated. On this basis, a novel WP-based feature is introduced for SER, namely discriminative band WP power coefficients. Finally, a SER system is built and extensive experiments are carried out. Experimental results show that the proposed feature considerably improves emotion recognition performance over conventional mel frequency cepstrum coefficient (MFCC) feature. The proposed feature extraction approach is promising since it can be easily extended to two-dimensional (2D) facial expression analysis with 2D WP quadtree structures, and further a high-quality audio–visual bimodal emotion recognition system is desirable.

Design of totally multiplier-less sharp transition width tree structured filter banks for non-uniform discrete multitone system

In this paper, a multiplier-less near perfect reconstruction tree structured non-uniform filter bank for discrete multitone (DMT) system is proposed. In DMT systems, filters with sharp transition width are required to reduce the inter-channel interference. When sharp transition width filter banks are to be implemented, the order of the filters will become very high. Frequency response masking technique is known to result in filters with sharp transition width with less complexity. To further reduce the complexity and power consumption, the filter bank is made totally multiplier-less by converting the continuous filter coefficients to finite precision coefficients in the canonic signed digit space. This may lead to performance degradation and calls for the use of suitable optimization techniques. Here, the search space consists of only integers. Hence, meta-heuristic algorithms are preferred as they can be tailor made to suit the problem under consideration. In this work, meta-heuristic algorithms such as, artificial bee colony, harmony search and gravitational search are deployed to improve the performance of the tree structured filter bank. Thus, the proposed method results in tree structured non-uniform filter banks which are simple, multiplier-less and have linear phase, sharp transition width, very low aliasing and reduced amplitude distortion.

Loss-Tolerant Allpass-Based Filter Bank Design Suitable for Integrated Optics

This paper presents a novel design algorithm for a filter bank structure that is suitable for photonic integrated circuits. The proposed design is entirely based on the principle of loss-exhibiting allpass filtering, which is a behavior naturally observed in a variety of microscale optical components. The setup and mathematical optimization of the system is explored in detail from a signal processing perspective, and an algorithm based on convex and nonlinear optimization techniques is subsequently presented. The algorithm methodologically utilizes the otherwise-undesirable effect of waveguide loss to derive an allpass-based filter bank structure that is amenable to photonic implementation. The proposed structure is ideal for applications in time-stretched analog-to-digital converters, WDM network channelizers, and general optical signal multiplexers.

Smooth affine shear tight frames with MRA structure

Finding efficient directional representations is one of the most challenging and extensively sought problems in mathematics. Representation using shearlets recently receives a lot of attention due to their desirable properties in both theory and applications. Using the framework of frequency-based affine systems as developed in [16], in this paper we introduce and systematically study affine shear tight frames which include all known shearlet tight frames as special cases. Our results in this paper resolve several important questions on shearlets. We provide a complete characterization for an affine shear tight frame and then use it to construct smooth directional affine shear tight frames with all their generators in the Schwartz class. Though multiresolution analysis (MRA) together with filter banks is the foundation and key features of wavelet analysis for the fast numerical implementation of a wavelet transform, most papers on shearlets do not concern the underlying filter bank structure and its connection to MRA. In order to study affine shear tight frames with MRA structure, following the lines developed in [16], we introduce the notion of a sequence of affine shear tight frames and then we provide a complete characterization for such a sequence. Based on our characterizations, we present two different approaches, i.e., non-stationary and quasi-stationary, for the construction of sequences of directional affine shear tight frames with MRA structure such that all their generators are smooth (in the Schwartz class) and they have underlying filter banks. Consequently, their associated transforms can be efficiently implemented using filter banks and are very similar to the standard fast wavelet transform. Moreover, we provide concrete examples of directional affine shear tight frames with filter banks and apply them to the image denoising problem. Our numerical experiments show that our constructed directional affine shear tight frames perform better than known directional multiscale representation systems such as curvelets and shearlets for the image denoising problem.

A method to initialize free parameters in lattice structure of arbitrary-length linear phase perfect reconstruction filter bank

The optimization of the free parameters in the lattice structure of linear phase perfect reconstruction filter bank (LPPRFB) is commonly highly nonlinear, therefore the free parameters should be carefully initialized. Such methods have been published for constrained-length LPPRFB (CLLPPRFB), i.e. LPPRFB with filter length MK, where M is the decimation factor and K is an integer. In contrast to CLLPPRFB, arbitrary-length LPPRFB (ALLPPRFB) [i.e. LPPRFB with filter length MK+β, where β is an integer between 0 and M] provides more choices of filter banks, offering better trade-off between filter length and filter performance. Nevertheless, as far as we know there is no systematic study on initializing the free parameters in the lattice structure of ALLPPRFB, and the required method cannot be easily generalized from those for CLLPPRFB. To address this issue, an initialization method will be described in this paper that initializes a longer ALLPPRFB by a shorter one, and the length difference between the longer and the shorter filter banks can be any number allowed by an ALLPPRFB system. The efficiency of the proposed method will be shown by design examples and image compression experiments.

Robust multi-scale orientation estimation: Directional filter bank based approach

Orientation estimation is considered as an important task in many subsequent pattern recognition and image enhancement systems. In a noisy environment, the gradient-based estimator provides poor results. A pre-smoothing Gaussian function with an appropriate scale is conventionally used to get improved gradients. Later on, a family of pre-smoothing Gaussian functions with a range of scales is employed for estimation, this is referred to as multi-scale orientation estimator. To provide groundwork for comparison, a more formal framework of multi-scale orientation estimation, based on scale-space axioms, in spatial domain is presented. Then for improvement purposes a Fourier domain approach, where directional filter bank (DFB) structure is embedded in multi-scale orientation estimation framework, is proposed. This is referred to as multi-scale DFB approach. The paper presents the comparison work for estimation of local orientations using multi-scale approaches both in spatial and Fourier domain. In the Fourier-domain approach, two linear combinations are deployed, one across the directional image, and the other across the scales. This is opposed to only one linear combination across the scales, used in simple spatial domain techniques. Further more, the DFB-based Fourier domain approach extracts the best local orientation by comparing and contrasting all possible orientations with their respective strength measures. The strength measure used in Fourier method is based on local variance, free from inaccurate gradient calculation. Simulations are conducted over noisy test images as well as real fingerprints. Our objective results indicate that multi-scale Fourier domain approach always yields better estimates at variable level of noise as compared to stand alone multi-scale spatial domain approaches. The improvements made by Fourier domain estimate can largely be attributed to the use of double linear combination both across the directional bands and across the scales.

Search for information-bearing components in neural data.

Multivariate empirical mode decomposition (MEMD) is an important extension of EMD, suitable for processing multichannel data. It can adaptively decompose multivariate data into a set of intrinsic mode functions (IMFs) that are matched both in number and in frequency scale. This method is thus holds great potential for the analysis of multi- channel neural recordings as it is capable of ensuring all the intrinsic oscillatory modes are aligned not only across channels, but also across trials. Given a plethora of IMFs derived by MEMD, a question of significant interest is how to identify which IMFs contain information, and which IMFs are noise. Existing methods that exploit the dyadic filter bank structure of white noise decomposition are insufficient since the IMFs do not always adhere to the presumed dyadic relationship. Here we propose a statistical procedure to identify information-bearing IMFs, which is built upon MEMD that allows adding noise as separate channels to serve as a reference to facilitate IMF identification. In this procedure, Wasserstein distance is used to measure the similarity between the reference IMF and that from data. Simulations are performed to validate the method. Local field potentials from cortex of monkeys while performing visual tasks are used for demonstration.

Binaural Signal Processing Motivated Generalized Analytic Signal Construction and AM-FM Demodulation

Binaural hearing studies show that the auditory system uses the phase-difference information in the auditory stimuli for localization of a sound source. Motivated by this finding, we present a method for demodulation of amplitude-modulated–frequency-modulated (AM-FM) signals using a signal and its arbitrary phase-shifted version. The demodulation is achieved using two allpass filters, whose impulse responses are related through the fractional Hilbert transform (FrHT). The allpass filters are obtained by cosine-modulation of a zero-phase flat-top prototype halfband lowpass filter. The outputs of the filters are combined to construct an analytic signal (AS) from which the AM and FM are estimated. We show that, under certain assumptions on the signal and the filter structures, the AM and FM can be obtained exactly. The AM-FM calculations are based on the quasi-eigenfunction approximation. We then extend the concept to the demodulation of multicomponent signals using uniform and non-uniform cosine-modulated filterbank (FB) structures consisting of flat bandpass filters, including the uniform cosine-modulated, equivalent rectangular bandwidth (ERB), and constant-Q filterbanks. We validate the theoretical calculations by considering application on synthesized AM-FM signals and compare the performance in presence of noise with three other multiband demodulation techniques, namely, the Teager-energy-based approach, the Gabor’s AS approach, and the linear transduction filter approach. We also show demodulation results for real signals.

A novel optimization design approach for Contourlet directional filter banks

A Contourlet transform, an expansion of a wavelet transform, is a double filter bank structure composed of Laplacian Pyramid and directional filter banks. Several wavelet filters of preferable performance have been developed for wavelet transforms, e.g. CDF (Cohen, Daubechies and Feauveau) 9/7 filter. However, there is still only a limited number of wavelet filters applicable for Contourlet transforms. Therefore, it has become an urgent issue to find effective contourlet filters and design methods in the field of multiscale geometric analysis. In order to design a new directional filter bank for Contourlet transforms, this paper uses parametric modeling to obtain a novel PKVA (See-May Phoong, Chai W. Kim, P. P. Vaidyanathan, and Rashid Ansari) filter, by first implementing Chebyshev best uniform approximation, and then reaching the optimal solution by means of Parks-McClellan algorithm. Using Brodatz standard texture image database for test images, and using image denoising treated with hidden Markov tree (HMT) models in the Contourlet domain, the optimal PKVA filter was obtained on the basis of the peak signal to noise ratio (PSNR) maximum criterion with human visual properties considered. Experiment results show that the image denoising performance of our filter is better than that of Po and Do’s. The PSNR obtained from the experiment is 1.011449 higher than that of Po and Do’s in average. Therefore, Contourlet transforms using the proposed PKVA filter as DFB can ensure that the local error in images is of a uniform minimum value, and that good overall visual effect can be achieved.

A method for initializing free parameters in lattice structure of linear phase perfect reconstruction filter bank

Since the optimization of the free parameters in the lattice structure of linear phase perfect reconstruction filter bank (LPPRFB) is commonly highly nonlinear, the initialization of the free parameters is important before starting the optimization. We systematically study the initialization of the free parameters, following the way that initializes the free parameters in a higher-order LPPRFB by those in a lower-order one. The proposed method is carried out in two steps: formulating the relation between the higher-order and the lower-order LPPRFBs in terms of polyphase matrices, and then implementing the initialization based on the relation. Design examples show that, compared with published LPPRFBs, the filter banks yielded by our method show comparable or even better performance.

Maximal-overlap adaptive multiwavelet for detecting transient vibration responses from dynastic signal of rotating machineries

Vibration signal is an important prerequisite for mechanical fault detection. However, early stage defect of rotating machineries is difficult to identify because their incipient energy is interfered with background noises. Multiwavelet is a powerful tool used to conduct non-stationary fault feature extraction. However, the existing predetermined multiwavelet bases are independent of the dynamic response signals. In this paper, a constructing technique of vibration data-driven maximal-overlap adaptive multiwavelet (MOAMW) is proposed for enhancing the extracting performance of fault symptom. It is able to derive an optimal multiwavelet basis that best matches the critical non-stationary and transient fault signatures via genetic algorithm. In this technique, two-scale similarity transform (TST) and symmetric lifting (SymLift) scheme are combined to gain high designing freedom for matching the critical faulty vibration contents in vibration signals based on the maximal fitness objective. TST and SymLift can add modifications to the initial multiwavelet by changing the approximation order and vanishing moment of multiwavelet, respectively. Moreover, the beneficial feature of the MOAWM lies in that the maximal-overlap filterbank structure can enhance the periodic and transient characteristics of the sensor signals and preserve the time and frequency analyzing resolution during the decomposition process. The effectiveness of the proposed technique is validated via a numerical simulation as well as a rolling element bearing with an outer race scrape and a gearbox with rub fault.

Metaheuristic algorithms for the design of multiplier-less non-uniform filter banks based on frequency response masking

In this paper, multiplier-less nearly perfect reconstruction tree structured non-uniform filter banks (NUFB) are proposed. When sharp transition width filter banks are to be implemented, the order of the filters and hence the complexity will become very high. The filter banks employ an iterative algorithm which adjusts the cut off frequencies of the prototype filter, to reduce the amplitude distortion. It is found that the proposed design method, in which the prototype filter is designed by the frequency response masking method, gives better results when compared to the earlier reported results, in terms of the number of multipliers when sharp transition width filter banks are needed. To reduce the complexity and power consumption for hardware realization, a design method which makes the NUFB totally multiplier-less is also proposed in this paper. The NUFB is made multiplier-less by converting the continuous filter bank coefficients to finite precision coefficients in the signed power of two space. The filter bank with finite precision coefficients may lead to performance degradation. This calls for the use of suitable optimization techniques. The classical gradient based optimization techniques cannot be deployed here, because the search space consists of only integers. In this context, meta-heuristic algorithm is a good choice as it can be tailor made to suit the problem under consideration. Thus, this design method results in near perfect NUFBs which are simple and multiplier-less and have linear phase and sharp transition width with very low aliasing. Also, different non-uniform bands can be obtained from the tree structured filter bank by rearranging the branches.

Reconstruction of N-th order nonuniformly sampled bandlimited signals using digital filter banks

In this paper, a digital filter bank structure is proposed for the reconstruction of uniformly sampled bandlimited signals from their N-th order nonuniform samples. The proposed filter bank structure is arrived at after incorporating polyphase-domain filtering operations and discrete Fourier transform (DFT) modulation to an existing filter bank framework.In this paper, an idea is also presented, so that uniform samples can be reconstructed from N-th order nonuniform samples using the structures based on recurrent nonuniform sampling. A comparison of the computational complexity and the signal-to-noise ratio (SNR) performance is also given for various structures existing in the literature.

Modified CIC 필터뱅크를 이용한 저전력 심장박동수 측정 알고리즘 및 구조

In this paper, low-power heart beat detection algorithm and structure is proposed. The proposed detection algorithm utilizes filter banks to display a specific beat per minute(BPM) from the heart beat signals. Since general filter banks need a lot of computation to calculate a BPM, we propose the filter banks structure using modified CIC(Cascaded Integrator Comb) filters. It is shown that the proposed modified CIC filter banks algorithm can display the BPM from the heart beat signals precisely and efficiently.

A pseudo wavelet system-based vibration signature extracting method for rotating machinery fault detection

The rotating machinery, as a typical example of large and complex mechanical systems, is prone to diversified sorts of mechanical faults, especially on their rotating components. Although they can be collected via vibration measurements, the critical fault signatures are always masked by overwhelming interfering contents, therefore difficult to be identified. Moreover, owing to the distinguished time-frequency characteristics of the machinery fault signatures, classical dyadic wavelet transforms (DWTs) are not perfect for detecting them in noisy environments. In order to address the deficiencies of DWTs, a pseudo wavelet system (PWS) is proposed based on the filter constructing strategies of wavelet tight frames. The presented PWS is implemented via a specially devised shift-invariant filterbank structure, which generates non-dyadic wavelet subbands as well as dyadic ones. The PWS offers a finer partition of the vibration signal into the frequency-scale plane. In addition, in order to correctly identify the essential transient signatures produced by the faulty mechanical components, a new signal impulsiveness measure, named spatial spectral ensemble kurtosis (SSEK), is put forward. SSEK is used for selecting the optimal analyzing parameters among the decomposed wavelet subbands so that the masked critical fault signatures can be explicitly recognized. The proposed method has been applied to engineering fault diagnosis cases, in which the processing results showed its effectiveness and superiority to some existing methods.

A New Design Method of the Starting Block in Lattice Structure of Arbitrary-Length Linear Phase Paraunitary Filter Bank by Combining Two Polyphase Matrices

Constructing the starting block is the core of designing an arbitrary-length linear phase paraunitary filter bank (ALLPPUFB), and lattice structure is an efficient approach of ALLPPUFB design. This brief proposes a new ALLPPUFB starting block design by combining two polyphase matrices of constrained-length linear phase paraunitary filter bank. The proposed design is much easier to be understood than existing ones due to the brief design process. Moreover, it might be modified and used for unaddressed topics in neighboring fields, such as starting block design for arbitrary-length oversampled linear phase paraunitary filter bank.

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.

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.