Complex Filter Bank Research Articles

An Improved Rational Approximation of Bark Scale Using Low Complexity and Low Delay Filter Banks

An Improved Rational Approximation of Bark Scale Using Low Complexity and Low Delay Filter Banks

IIR Cascaded-Resonator-Based Complex Filter Banks

The use of a filter bank of IIR filters for the spectral decomposition and analysis of signals has been popular for many years. As such, a new filter-bank resonator-based structure, representing an extremely hardware-efficient structure, has received a good deal of attention. Recently, multiple-resonator (MR)-based and general cascaded-resonator (CR)-based filters have been proposed. In comparison to single-resonator-based analyzers, analyzers with a higher multiplicity of resonators in the cascade provide lower side lobes and a higher attenuation in stopbands. In previous works, it was shown that the CR-based filter bank with infinite impulse response (IIR) filters, which is numerically more efficient than one with finite impulse response (FIR) filters, is suitable for dynamic harmonic analysis. This paper uses the same approach to design complex digital filter banks. In the previous case, the optimization task referred to the frequency responses of harmonic filters. In this work, the harmonic filters of the mother filter bank are reshaped so that the frequency response of the sum (or difference, depending on the parity of the number of resonators in the cascade) of two adjacent harmonic filters is optimized. This way, an online adaptive filter base can be obtained. The bandwidth of the filters in the designed filter bank can be simply changed online by adding or omitting the output signals of the corresponding harmonics of the mother filter.

A digital bandwidth interleaved structure correction method based on itemized correction.

To satisfy the input bandwidth and sampling rate requirements of data acquisition systems, digital bandwidth-interleaved analog-to-digital converters (DBI-ADCs) offer a practical parallel structure. However, the existing DBI-ADC correction methods are broadly inadequate in terms of design, testing, and implementation. Moreover, the evaluation and correction of the most significant feature of the DBI-ADC structure-wideband acquisition performance-is also imperfect. This paper proposes an itemized correction method for DBI-ADC structures. The proposed method simplifies the complex correction filter bank designalgorithm into multiple simple correction filters and then separates and corrects the various errors of the DBI-ADC system. This dramatically simplifies the design, testing, and implementation process of the system, resulting in a highly convenient method for practical engineering. In addition, this method achieves a good correction effect, with an appropriate balance between the correction effect and the project implementation. Simulation results and experimental results verify the effectiveness of the proposed method.

Improvement on the image rejection ratio via phase error equalization and adaptive DC tuning in Hartley receivers: A practical approach

This paper presents a novel tunable method to improve the image rejection ratio in image-reject down-converters. The proposed technique is based on the phase equalization and amplitude error mitigation through proper biasing of mixers. With the aid of the proposed technique, amplitude, and phase imbalances, resulting in unwanted images, were minimized. Therefore, significant improvement in the image rejection ratio was attained without using complex filter banks. Phase equalization is accomplished by introducing a delay line to force the phase error to be zero at the center of the frequency band.A frequency down-converter was designed and built with discrete components for an L-band Hartley receiver, which operates over 950–1450 MHz. Image rejection performance of the proposed technique was shown by simulation and prototype-measurements. It is exhibited that the proposed easy to apply technique provides a considerable improvement in the entire band without disturbing the system. Consequently, an average of 50 dB and a maximum 77 dB image rejection ratio can be obtained in Hartley image rejection and dual-IF receivers without using traditional filters.

Harmonic PMU Algorithm Based on Complex Filters and Instantaneous Single-Sideband Modulation

Phasor measurement units (PMUs) have become powerful monitoring tools for many applications in smart grids. In order to address the different issues related to harmonics in power systems, the fundamental phasor estimator in a PMU has been extended to the harmonic phasor estimator by several researchers around the world. Yet, the development of harmonic phasor estimators is a challenge because they have to consider time-varying frequencies since the frequency deviation in the harmonic components is proportional to the harmonic order in a dynamic way. In this work, a new algorithm for harmonic phasor estimation using an instantaneous single-sideband (SSB) modulation is presented. Unlike other SSB-based approaches, its implementation in this work is based on concepts of instantaneous phase and instantaneous frequency. In general, the proposed algorithm is divided into two stages. Firstly, the estimation of the fundamental phasor is carried out by means of a complex finite impulse response (FIR) filter which provides the analytic signal used to compute the instantaneous magnitude, phase, and frequency. Secondly, a complex FIR filter bank is proposed for the estimation of the harmonic components, where the instantaneous SSB modulation technique is applied in order to center the harmonic components into specific narrow bands for each complex filter when an off-nominal frequency occurs. The validation of the proposed algorithm is carried out by means of the current standards of phasor measurement units, i.e., Std. C37.118.1-2011 and C37.118.1a-2014, which involve steady-state, dynamic, and time performance tests.

Design of complex adaptive multiresolution directional filter bank and application to pansharpening

This paper proposes a new 2-D transform design, namely complex adaptive multiresolution directional filter bank, to represent the spatial orientation features of an input image adaptively. The proposed design is completely shift invariant and represents the input image by one low-pass and multiscale N directional band-pass subbands. Here, N represents estimated number of dominant directions present in the input image. Our design consists of two main filter bank stages. A fix partitioned complex-valued directional filter bank (CDFB) is at the core of the design followed by a novel partition filter bank stage. Fine partitioning of the CDFB subbands is used to get the adaptive nature of the proposed transform. The partitioning decision is made based on the directional significance of range of CDFB subband angle selectivity in the input image. Partition filter bank stage which nonuniformly partitions the CDFB subbands provides total N dominant direction selective subbands. Local orientation map of the input image is used to determine the dominant directions and hence N. For better sparsity properties, we design the multiresolution stage with filters having high vanishing moments and better frequency selectivity. Applicability of the proposed adaptive design is shown for pansharpening of multispectral images. Our proposed pansharpening approach is evaluated on images captured using QuickBird and IKONOS-2 satellites. Results obtained using the proposed approach on these datasets show considerable improvements in qualitative as well as quantitative evaluations when compared to state-of-the-art pansharpening approaches including transform-based methods.

Automated defect detection in uniform and structured fabrics using Gabor filters and PCA

This paper describes an algorithm for texture defect detection in uniform and structured fabrics, which has been tested on the TILDA image database. The proposed approach is structured in a feature extraction phase, which relies on a complex symmetric Gabor filter bank and Principal Component Analysis (PCA), and on a defect identification phase, which is based on the Euclidean norm of features and on the comparison with fabric type specific parameters. Our analysis is performed on a patch basis, instead of considering single pixels. The performance has been evaluated with uniformly textured fabrics and fabrics with visible texture and grid-like structures, using as reference defect locations identified by human observers. The results show that our algorithm outperforms previous approaches in most cases, achieving a detection rate of 98.8% and a false alarm rate as low as 0.20–0.37%, whereas for heavily structured yarns misdetection rate can be as low as 5%.

A SUFFICIENT AND NECESSARY CONDITION FOR CONSTRUCTION OF 3-BAND DUAL TREE COMPLEX WAVELET

To desire expectable applications in image processing, the construction of 3-band dual tree complex wavelet is a meaningful and constructive topic. In this paper, a sufficient and necessary condition 2π/3-periodic of phase difference between the prime and dual filter banks is proposed. With this condition, it is proposed that the phase function θl(ω) of wavelet filters can be uniquely determined by the phase function θ0(ω) of the scaling filters. Imposed on a necessary constraint to θ0(ω), phase function θl(ω) can be obtained which results in the analytical of the 3-band dual tree complex wavelet. Furthermore, the complex filter banks are obtained using the wavelet matrix factorization approach. Then the dual tree 3-band complex wavelet is analytical that indicates approximately shift invariance property. In addition, it also has more direction selectivity because there are more sub-bands than dyadic wavelet transform is frequency domain.

Decimation-Whitening Filter in Spectral Band Replication

MPEG-4 High-Efficiency Advanced Audio Coding (HE-AAC) has adopted spectral band replication (SBR) to efficiently compress the high-frequency part of the audio. In SBR, linear prediction is applied to low-frequency subbands to suppress tonal components and smooth the associated spectra for replicating to high-frequency bands. Such a tone-suppressing process is referred to as whitening filtering. In SBR, to avoid the alias artifact incurred by spectral adjustment, a complex filterbank instead of real filterbank is adopted. For QMF subbands, this paper demonstrates that the linear prediction defined in the SBR standard results in a predictive bias. A new whitening filter, called the decimation-whitening filter, is proposed to eliminate the predictive bias and provide advantages in terms of noise-to-signal ratio measure, frequency resolution, energy leakage, and computational complexity for SBR.

基于复滤波器组的红外弱小目标检测算法

基于复滤波器组的红外弱小目标检测算法

Estimation of the instantaneous amplitude and the instantaneous frequency of audio signals using complex wavelets

This work presents a method of analyzing and synthesizing audio signals that uses complex wavelets. In the method, the input signal is filtered by a complex bandpass filter bank through a discrete version of the complex continuous wavelet transform. A general theoretical signal with time-dependent amplitude and phase has been analyzed. The analysis of the information provided by the modulus and the phase of the complex continuous wavelet transform was used to develop an additive analysis/synthesis algorithm for audio signals called complex wavelet additive synthesis. To illustrate the method, this new algorithm has been used to analyze the following four synthetic, non-stationary signals that have different frequency variation laws: a linear chirp, a quadratic chirp, a hyperbolic chirp and an FM signal with a sinusoidal excursion. Finally, the validity of the algorithm has been tested by comparing the results of an analysis of two real sounds with the proposed algorithm and with one existing technique, namely spectral modelling synthesis (SMS).

Human action recognition using extreme learning machine based on visual vocabularies

This paper introduces a novel recognition framework for human actions using hybrid features. The hybrid features consist of spatio-temporal and local static features extracted using motion-selectivity attribute of 3D dual-tree complex wavelet transform (3D DT-CWT) and affine SIFT local image detector, respectively. The proposed model offers two core advantages: (1) the framework is significantly faster than traditional approaches due to volumetric processing of images as a ‘3D box of data’ instead of a frame by frame analysis, (2) rich representation of human actions in terms of reduction in artifacts in view of the promising properties of our recently designed full symmetry complex filter banks with better directionality and shift-invariance properties. No assumptions about scene background, location, objects of interest, or point of view information are made whereas bidirectional two-dimensional PCA (2D-PCA) is employed for dimensionality reduction which offers enhanced capabilities to preserve structure and correlation amongst neighborhood pixels of a video frame.

Optimization of Synthesis Oversampled Complex Filter Banks

An important issue with oversampled FIR analysis filter banks (FBs) is to determine inverse synthesis FBs, when they exist. Given any complex oversampled FIR analysis FB, we first provide an algorithm to determine whether there exists an inverse FIR synthesis system. We also provide a method to ensure the Hermitian symmetry property on the synthesis side, which is serviceable to processing real-valued signals. As an invertible analysis scheme corresponds to a redundant decomposition, there is no unique inverse FB. Given a particular solution, we parameterize the whole family of inverses through a null space projection. The resulting reduced parameter set simplifies design procedures, since the perfect reconstruction constrained optimization problem is recast as an unconstrained optimization problem. The design of optimized synthesis FBs based on time or frequency localization criteria is then investigated, using a simple yet efficient gradient algorithm.

Filter Bank Channelizers for Multi-Standard Software Defined Radio Receivers

The ability to support multiple channels of different communication standards, in the available bandwidth, is of importance in modern software defined radio (SDR) receivers. An SDR receiver typically employs a channelizer to extract multiple narrowband channels from the received wideband signal using digital filter banks. Since the filter bank channelizer is placed immediately after the analog-to-digital converter (ADC), it must operate at the highest sampling rate in the digital front-end of the receiver. Therefore, computationally efficient low complexity architectures are required for the implementation of the channelizer. The compatibility of the filter bank with different communication standards requires dynamic reconfigurability. The design and realization of dynamically reconfigurable, low complexity filter banks for SDR receivers is a challenging task. This paper reviews some of the existing digital filter bank designs and investigates the potential of these filter banks for channelization in multi-standard SDR receivers. We also review two low complexity, reconfigurable filter bank architectures for SDR channelizers based respectively on the frequency response masking technique and a novel coefficient decimation technique, proposed by us recently. These filter bank architectures outperform existing ones in terms of both dynamic reconfigurability and complexity.

부반송파간 간섭과 도플러 효과에 강한 WFMT 변조 방식의 성능 분석

OFDM(Orthogonal Frequency Division Multiplexing)은 고속 통신 시스템에 매우 효과적이다. 그러나 OFDM은 단일 반송파 시스템과 달리 높은 PAPR(Peak to Average Power Ratio)과 심각한 ICI(Inter Subcarrier Interference) 문제를 갖는다. 특히 ICI는 OFDM 신호들의 부반송파 사이에 직교성을 깨드려 시스템의 성능을 저하시킨다. 본 논문에서는 ICI에 대해 좋은 성능을 보이는 WFMT(Wavelet Filtered Multitone) 시스템을 연구하고, 위상 잡음과 반송 주파수 오프셋에 대한 성능 분석한다. WFMT 시스템은 멀티 채널 신호를 생성하고 분석하기 위하여 필터 뱅크 기술과 웨이블렛 이론을 기반으로 한다. 그러므로 WFMT 시스템은 필터 뱅크 시스템의 장점을 유지한다. 이 논문에서는 반송 주파수와 위상 잡음으로 인한 WFMT 시스템과 OFDM 시스템의 ICI와 ISI(Inter Symbol Interference)를 비교한다. 또한, 이 시스템들에서 PAPR 성능과 도플러 효과가 미치는 영향을 수식적으로 분석하고, HPA와 위상 잡음, 도플러 효과가 시스템에 존재할 때 각 시스템들의 BER 성능을 보인다. OFDM is very effective for the high speed communication system. However, OFDM has the problems of high PAPR and serious ICI, which is different from the single carrier system. Especially, ICI problem caused by phase noise, Doppler effect and frequency offset is main reason for poor performance since it breaks down the orthogonality between subcarriers in OFDM communication system. Therefore, WFMT modulation scheme is studied and the effect of the carrier frequency offset and phase noise is analyzed. WFMT modulation scheme is based on the wavelet theory and complex filter banks for synthesis and analysis of multichannel signal. WFHT modulation scheme keeps on the advantage of filter banks system and can be easily possible for the implementation of filter banks. In this paper, we compare ISI and ICI distortions of the WFMT and OFDM system due to the carrier frequency offset and phase noise. Also, we analyze the PAPR and BER performances in the HPA and ICI situation caused by the Doppler frequency shift and the frequency offset.

2M-BAND INTERLEAVED DFT MODULATED FILTER BANKS WITH PERFECT RECONSTRUCTION

In this paper, we propose a new family of perfect reconstruction (PR) complex filter banks, named interleaved discrete Fourier transform modulated filter banks (Interleaved DFT-FBs). In the filter banks, the analysis filters are generated by interlaced exponential modulating two different analysis prototype filters, and the synthesis filters are generated by two different synthesis prototype filters via the same manner. The filter banks have a simple polyphase structure similar to DFT modulated filter banks (DFT-FBs). More importantly, the proposed Interleaved DFT-FBs can achieve critically sampled PR complex filter bank with FIR analysis and synthesis filters, which is impossible for DFT-FBs. We give and prove the PR condition for 2M-band Interleaved DFT-FBs. Utilizing the result, the design procedure of the prototype filters is presented. In addition, by the theoretic analysis and numerical examples, it is shown that the analysis and synthesis filters cannot simultaneously provide good stopband attenuation for the critically sampled PR Interleaved DFT-FBs. Although the limitation always exits, the filter banks can find applications in some subband coding systems of high bit rate.

Critically sampled and oversampled complex filter banks via interleaved DFT modulation

This paper presents a new class of complex modulated filter banks, namely, interleaved discrete Fourier transform (DFT) modulated filter banks, where analysis filter bank comprises interleaved exponentially modulated versions of two lowpass analysis prototype filters and synthesis filter bank is generated from two lowpass synthesis prototype filters in the same manner. As compared with DFT modulated filter banks, interleaved DFT modulated filter banks are more flexible in structure and provide more degrees of freedom for design. It is shown that 2 M-channel critically sampled interleaved DFT modulated filter banks can be perfect reconstruction (PR) and FIR. However, critical sampling limits stopband attenuation of the filter banks. Further, we investigate the structure of oversampled interleaved DFT modulated filter banks and a bi-iterative quadratic programming algorithm is developed for designing oversampled nearly perfect reconstruction (NPR) interleaved DFT modulated filter banks. Owing to more degrees of freedom for design, oversampled interleaved DFT modulated filter banks achieve better total performance than oversampled DFT modulated filter banks do.

Three-band biorthogonal interpolating complex wavelets with stopband suppression via lifting scheme

Wavelet research has primarily focused on real-valued wavelet bases. However, the complex filterbanks provide much convenience for complex signal processing. For example, in radar and sonar signal processing, the complex signals from the I/Q receiver can be efficiently processed with complex filterbanks rather than real filterbanks. Specifically, the positive and negative Doppler frequencies imply different physical content in the moving target detector (MTD) and moving target identification (MTI); therefore, it is significant to design complex multiband filterbanks that can partition positive and negative frequencies into different subbands. We design two novel families of three-band biorthogonal interpolating complex filterbanks and wavelets by using the three-band lifting scheme. Unlike the traditional three-band filterbanks, the novel complex filterbank is composed of three channels, including the lowpass channel, the positive highpass channel whose passband distributes in the positive frequency region, and the negative highpass channel in the negative frequency region. Such a filterbank/wavelet naturally provides the ability to extract positive frequency components and negative frequency components from complex signals. Moreover, a novel set of design constraints are introduced to manipulate the stopband characteristic of highpass filters and are referred to as stopband suppression, which strengthens the traditional constraints of vanishing moments. Finally, a numerical method is given to further lower stopband sidelobes.

Subband adaptive filtering decimation constraints for oversampled nonuniform filterbanks

To avoid significant inband aliasing, the decimation factors for a real filterbank must satisfy strict constraints. These decimation constraints decrease the real filterbank's computational efficiency by requiring higher subband data rates. To combat this, a set of modified pseudo-quadrature mirror filter equations are proposed which easily construct complex near-perfect reconstruction filterbanks that can be utilized to build both uniform and nonuniform filterbanks with no significant inband aliasing. With a properly designed real or complex filterbank, subband adaptive filters illustrate low m.s.e. after convergence. However, the computational complexity and convergence time associated with the complex filterbank is significantly less. Several numerical simulations are included to illustrate the conclusions.

Genetic synthesis of reduced complexity filters and filter banks using primitive operator directed graphs

Using integer coefficient filters, which can be efficiently implemented using primitive operator directed graphs, a multi-objective optimisation using genetic algorithms is used to jointly optimise filter performance and complexity. Complexity is measured using a variation of the RAG-n algorithm (Dempster and MacLeod, 1995). The optimisation maintains a non-dominated set of best-compromise solutions, which allows the designer greater choice. A flexible design tool is described which allows the designer to interactively vary many of the optimisation parameters. The proposed techniques are demonstrated for the design of both one- and two-dimensional linear phase FIR filters with both low-pass and band-pass characteristics. The method is shown to provide significantly better results than previous methods. Also considered is the design of perfect reconstruction filter pairs, which are the main building block within discrete wavelet transforms. To achieve this the use of a combination of transformation and factorisation approaches is proposed. In this way, the problem is significantly simplified, allowing a GA to successfully find high performance filter banks with significantly better results than previous methods.