New regular M-band orthogonal wavelet filter bank design usingzero-insertion method

A new regular M-band orthogonal wavelet filter bank (OWFB) is designed by inserting zeros into the filter transfer functions, which improves the characteristics of the frequency magnitude response. In an application of the sub-band coding of a still image, the new OWFB improves the PSNR by ~1 dB in the reconstructed image over the existing OWFB at the same bit rate     

Signal-adapted wavelet filter bank design

A method for designing wavelet filter banks that are adapted to the given signal is proposed. The method is based on optimising a certain cost function with constraint conditions. Gradient-descent optimisation techniques are not adequate for the minimisation of such a cost function. Evolutionary programming is used to resolve this difficult optimisation problem. Simulation results are given     

Design of IIR orthogonal wavelet filter banks using lifting scheme

The lifting scheme is well known to be an efficient tool for constructing second generation wavelets and is often used to design a class of biorthogonal wavelet filter banks. For its efficiency, the lifting implementation has been adopted in the international standard JPEG2000. It is known that the orthogonality of wavelets is an important property for many applications. This paper presents how to implement a class of infinite-impulse-response (IIR) orthogonal wavelet filter banks by using the lifting scheme with two lifting steps. It is shown that a class of IIR orthogonal wavelet filter banks can be realized by using allpass filters in the lifting steps. Then, the design of the proposed IIR orthogonal wavelet filter banks is discussed. The designed IIR orthogonal wavelet filter banks have approximately linear phase responses. Finally, the proposed IIR orthogonal wavelet filter banks are applied to the image compression, and then the coding performance of the proposed IIR filter banks is evaluated and compared with the conventional wavelet transforms.     

New perspectives and improvements on the symmetric extension filter bank for subband/wavelet image compression.

In subband/wavelet image coding, size-limited subband decompositions are ordinarily used to avoid increasing the number of samples that need to be coded. To reduce coding distortions that can occur at the borders, the symmetric extension filter bank is typically employed. This paper introduces some new perspectives and improvements to that decomposition. The symmetric extension filter bank is couched in the cyclic frequency domain, providing a framework that accommodates FIR and IIR filters in a natural way, all with perfect reconstruction. IIR filters with both rational and irrational transfer functions can be implemented and, in the context of symmetric extension, can accommodate IIRs that effectively have perfect stopband suppression. Enhancements to the filter bank at a tree-structured system level are also presented and include the application of spectral reversal correction and a transition band normalization approach to designing the constituent filters of the symmetric extension wavelet packet transform.     

Multiscale Wiener filter for the restoration of fractal signals:wavelet filter bank approach

A filter bank design based on orthonormal wavelets and equipped with a multiscale Wiener filter is proposed in this paper for signal restoration of 1/f family of fractal signals which are distorted by the transmission channel and corrupted by external noise. First, the fractal signal transmission process is transformed via the analysis filter bank into multiscale convolution subsystems in time-scale domain based on orthonormal wavelets. Some nonstationary properties, e.g., self-similarity, long-term dependency of fractal signals are attenuated in each subband by wavelet multiresolution decomposition so that the Wiener filter bank can be applied to estimate the multiscale input signals. Then the estimated multiscale input signals are synthesized to obtain the estimated input signal. Some simulation examples are given for testing the performance of the proposed algorithm. With this multiscale analysis/synthesis design via the technique of the wavelet filter bank, the multiscale Wiener filter can be applied to treat the signal restoration problem for nonstationary 1/f fractal signals     

The analysis and design of two-dimensional nearly-orthogonal symmetric wavelet filter banks

The design and analysis of two-channel two-dimensional (2D) nonseparable nearly-orthogonal symmetric wavelet filter banks with quincunx decimation is studied. The basic idea is to impose multiple zeros at the aliasing frequency to a symmetric filter and minimize the deviation of the filter satisfying the orthogonal condition to obtain a nearly-orthogonal FIR filter bank. Since multiple zeros are imposed, a scaling function may be generated from the minimized filter. With this filter, a semi-orthogonal filter bank is constructed. Methods for analyzing the correlation of the semi-orthogonal filter banks are proposed. The integer translates of the wavelet and scaling function are nearly-orthogonal. The integer translates of the wavelet at different scale are completely orthogonal. The semi-orthogonal filter bank can be efficiently implemented using the corresponding nearly-orthogonal FIR filter bank.     

M-ary wavelet transform and formulation for perfect reconstructionin M-band filter bank

The binary wavelet transform is generalized and extended to the M-ary biorthonormal case. The computational equivalence between the discrete wavelet analysis and the M-band multirate signal filtering is indicated. The equivalence allows the perfect reconstruction requirement in a filter bank to be investigated from the vector space decomposition/reconstruction in wavelet analysis. From the construction of the biorthonormal wavelet bases, the necessary and sufficient condition for the filters in a perfect reconstruction filter bank is formulated. Under this formulation, an additional optimization procedure is then used to model the frequency domain requirement in filter bank design     

New technique for designing nearly orthogonal wavelet filter bankswith linear phase

A new technique based on nonlinear optimisation to design nearly orthogonal wavelet filter banks with linear phase is proposed. The main idea is to impose a certain number of zeros at z=-1 for a symmetric filter and make it satisfy the power complementary condition as accurately as possible. From this filter, a semi-orthogonal wavelet filter bank which is nearly orthogonal can be constructed. This semi-orthogonal filter bank can be approximately implemented using a filter bank consisting of only one prototype filter. The frequency selectivity can also be designed at the same time by using a weighted cost function     

Synthesis filter bank optimization in two-dimensional separablesubband coding systems

Subband coding is a popular and well established technique used in visual communications, such as image and video transmission. In the absence of quantization and transmission errors, the analysis and synthesis filters in a subband coding scheme can be designed to obtain perfect reconstruction of the input signal, but this is no longer the optimal solution in the presence of quantization of the subband coefficients. We presuppose the use of a two-dimensional (2-D) separable subband scheme and we address the problem of designing, for a given analysis filter bank and assuming uniform quantization of the subband coefficients, the set of row and column synthesis filters that minimize the mean squared reconstruction error at the output of the subband system. Since the corresponding optimization problem is inherently nonlinear, we propose a suboptimal solution that extends a one-dimensional (l-D) optimal filter design procedure, already presented in the literature, to a 2-D separable synthesis filter bank. The separable 2-D extension is not trivial, since the processing in one direction, e.g., the rows, alters the statistics of the signals for the design of the filters in the other direction, e.g., the columns. To further simplify the filter design, we propose to model the input image as a 2-D separable Markov process plus an additive white component. Several design examples using both synthetic signals and real world images are presented, showing that the filters designed using the proposed technique can give a significant gain with respect to the perfect reconstruction solution, especially when the dither technique is used for quantization. The simulation results also show that the proposed image model can be conveniently used in the synthesis filter design procedure.     

Multidimensional orthogonal filter bank characterization and design using the Cayley transform.

We present a complete characterization and design of orthogonal infinite impulse response (IIR) and finite impulse response (FIR) filter banks in any dimension using the Cayley transform (CT). Traditional design methods for one-dimensional orthogonal filter banks cannot be extended to higher dimensions directly due to the lack of a multidimensional (MD) spectral factorization theorem. In the polyphase domain, orthogonal filter banks are equivalent to paraunitary matrices and lead to solving a set of nonlinear equations. The CT establishes a one-to-one mapping between paraunitary matrices and para-skew-Hermitian matrices. In contrast to the paraunitary condition, the para-skew-Hermitian condition amounts to linear constraints on the matrix entries which are much easier to solve. Based on this characterization, we propose efficient methods to design MD orthogonal filter banks and present new design results for both IIR and FIR cases.     

A new class of orthonormal symmetric wavelet bases using a complexallpass filter

This paper considers the design of the whole sample symmetric (WSS) paraunitary filterbanks composed of a single complex allpass filter and gives a new class of real-valued orthonormal symmetric wavelet bases. First, the conditions that the complex allpass filter has to satisfy are derived from the symmetry and orthonormality conditions of wavelets, and its transfer function is given to satisfy these conditions. Second, the paraunitary filter banks are designed by using the derived transfer function from the viewpoints of the regularity and frequency selectivity. A new method for designing the proposed paraunitary filterbanks with a given degrees of flatness is presented. The proposed method is based on the formulation of a generalized eigenvalue problem by using the Remez exchange algorithm. Therefore, the filter coefficients can be easily obtained by solving the eigenvalue problem, and the optimal solution is attained through a few iterations. Furthermore, both the maximally flat and minimax solutions are also included in the proposed method as two specific cases. The maximally flat filters have a closed-form solution without any iteration. Finally, some design examples are presented to demonstrate the effectiveness of the proposed method     

Self-lifting scheme: new approach for generating and factoring wavelet filter bank

The authors presents a new lifting scheme, the self-lifting scheme, and prove that self-lifted wavelets based on orthogonal or biorthogonal wavelets remain biorthogonal. In contrast to self-lifting, the existing lifting scheme can be called cross-lifting. Compared with cross-lifting, the self-lifting scheme provides new approaches for constructing biorthogonal wavelets, as well as factorising wavelet filter bank (WFB). For constructing wavelets, the self-lifting-based method updates one part of a wavelet filter by the other part of the same filter and obtains two updated filters in one pass, whereas the cross-lifting based method updates one filter by another filter and obtains one updated filter in one pass. To factorise WFB, self-lifting takes one part of a filter as the factor to decompose the other part of the same filter and obtains two factorised filters in one pass, whereas crosslifting based one takes one part of a filter as the factor to decompose the corresponding part of the other filter and obtains one factorised filter in one pass. Several examples show how to use self-lifting scheme to produce new wavelets with desirable properties, how to factorise complex WFBs into simple lifting filter banks, how to implement self-lifting-based discrete wavelet transform (WT) in z-domain and in time domain and why lifting-based WT is superior to convolution-based one.     

Beat-to-Beat ECG ventricular late potentials variance detection by filter bank and wavelet transform as beat-sequence filter

This paper presents a novel method that employs a wavelet transform and filter bank to detect ventricular late potentials (VLPs) from beat to beat in order to keep its variance. Conventionally, three time-domain features, which are highly related to the QRS complex endpoint, are generally accepted as criteria for classifying VLPs. Signal averaging is a general and effective de-noising method in electroencephalogram late potentials detection, but it may also eliminate the beat-to-beat variance. Other types of filter applied to the time sequence may destroy the late potentials as well when trying to filter out the noise. To preserve the variance from beat to beat as well as late potentials as much as possible, the concept of a beat-sequence filter will be introduced and the wavelet transform can be directly applied to the beat sequence, as will be demonstrated in this paper. After de-noising, instead of applying the voltage comparison on the de-noised signal to determine the QRS complex endpoint, the signal will be processed by a filter bank, and the QRS complex endpoint will be determined by consideration of the correlation between two beats. Both simulation and clinical experimental results will be presented to illustrate the effectiveness of this method.     

Designs and architectures of filter bank trees for spectrally efficient multi-user communications: review, modifications and extensions of wavelet packet filter bank trees

A review is presented first of the evolution of transmultiplexers since about 1966, in the context of a long progression of theoretical advances and developments leading to recent proposals to fundamentally improve OFDM type systems using principles of perfect reconstruction filter (PRF) banks. The equivalence of transmultiplexers to OFDM type multi-user systems is discussed. The desirable goals for performance and implementation of transmultiplexers or multiband, multiuser communication systems that are addressed and met in this paper using filter bank trees are set down. Then modifications and extensions are presented of the designs and architectures of wavelet packet based synthesis and analysis pairs of filter bank trees (Sablatash and Lodge in Digital Signal Process 13: 58–92, 2003) that can be used as transmultiplexers. These exhibit a number of advantages over the previous designs and address three shortcomings of the designs used to illustrate basic principles in Sablatash and Lodge (Digital Signal Process 13:58–92, 2003). The first of these is the asymmetry of the magnitude frequency responses of the multiplexer channels, which is addressed using a symmetric design for a lowpass and highpass quadrature mirror filter (QMF) pair described herein. The second is the problem of minimizing the total delay of the signal in passing through the analysis and synthesis filter banks. This is addressed using an architecture involving DFT polyphase synthesis filter banks to replace the wideband VSB filters at the roots of the two identical synthesis filter bank trees, but results in the multiplexer having fewer levels. In this way a tradeoff is effected of lower delay and complexity with fewer levels of bandwidth on demand. At the receiver matching DFT polyphase analysis filters and the other matching analysis filters are implemented. The third shortcoming is the difficulty in designing a synchronization scheme if the filters in the synthesis and analysis filter banks have non-linear phase. This is addressed by designing linear phase filters that do not affect the ISI to any significant degree for communication purposes, although exact perfect reconstruction is lost, but greatly ease and improve the design of the synchronization scheme. Relationships of this paper and its advantages over recent research studies and IEEE 802.22 standards proposals using PR filter banks for multi-user systems to greatly improve on OFDM systems are discussed. Financial support under Industry Canada’s Spectrum Research Funding is gratefully acknowledged.     

Design of non-uniform filter bank transmultiplexer with canonical signed digit filter coefficients

Design of non-uniform filter bank transmultiplexer (NUFB TMUX) with canonical signed digit (CSD) coefficients is presented. NUFB TMUX is preferred in a multicarrier communication system when applications with different data rates are to be multiplexed. If the filter coefficients are represented in CSD format, the hardware complexity of the NUFB TMUX can be reduced. A continuous coefficient NUFB TMUX is designed and the coefficients of the filters are synthesised in CSD format using genetic algorithm (GA). Separate objective functions are formulated for the fitness evaluation of the filters. Chromosomes are encoded as ternary digit strings. New crossover and mutation techniques are introduced to preserve the canonical property of the signed power of two (SPT) representations. For the fast convergence of the GA, positiondependent probability of mutation is used. Simulation results show that the CSD coefficient NUFB TMUX designed using the proposed algorithm has better signal-to-interference ratio (SIR) than that of continuous coefficient NUFB TMUX and CSD coefficient NUFB TMUX obtained by rounding. Frequency responses of its filters are better than that of the filters in CSD coefficient NUFB TMUX obtained by rounding and comparable with that of continuous coefficient NUFB TMUX.     

基于凸优化的MIMO雷达的优化滤波器组设计

在正交波形MIMO雷达信号处理中,发射信号分离是其中的一个重要环节,一般可以通过匹配滤波器组来实现,而匹配滤波器组对信号分离是基于发射信号满足理想正交条件的,实际中由于很难得到理想的正交波形集,因此将会造成信号分离能力下降或分离不彻底,为此,提出一种优化滤波器组设计方法,以最小化滤波输出峰值旁瓣电平为目标函数,采用凸优化方法进行全局优化设计,计算机仿真表明,该方法所设计的优化滤波器组可以显著提高非理想正交波形MIMO雷达的信号分离能力。     

A MC-CDMA system based on orthogonal filter banks of wavelet transforms and partial combining

Multi Carrier Code Division Multiple Access (MC-CDMA) is an appropriate modulation technique for high data rates. In this modulation scheme, employing of combining techniques are unavoidable for restoring orthogonality between different user signals. In this paper, the combining techniques of a MC-CDMA based on wavelet transform are studied. The partial combining of the wavelet based MC-CDMA system is suggested and its performance is compared with the maximum ratio combining (MRC), equal gain combining (EGC), orthogonality restoring combining (ORC) and the minimum mean square error (MMSE) techniques. Orthogonal filter banks of the wavelet transforms provide orthogonality between the wavelets and scaling functions, subcarriers and spreading sequences. Therefore, they provide new dimensions in combatting multipath fading, inter carrier interference (ICI) and narrowband interference in MC-CDMA systems. Furthermore, analysis of partial combining shows that coefficients of this technique can be computed in a simple manner. Simulations results indicate that the bit error rate (BER) performance of the proposed scheme is almost comparable with the MMSE combining scheme and the proposed system has a proper performance in terms of BER versus the signal to noise ratio (SNR) in frequency selective fading channels.     

FIR窄带滤波器组在现代雷达中的实现和优化方法

提出了一种动目标检测滤波器组在FPGA中的设计方法,给出了FIR滤波器组的设计原则和滤波器的设计步骤,并给出一组滤波器的频响曲线,运用该滤波器对某雷达回波数据进行了处理。实现了滤波器组在FPGA中的应用,并就实现过程作出了优化。     

航空图像压缩的双正交小波滤波器整数化设计

在航空图像压缩中,通常采用具有线性相位、正则性、消失矩和完全重构,及适于硬件实现、实时等特性的小波。根据小波滤波器设计,提出了一种基于图像压缩的构造整数双正交小波滤波器的设计方法。从选择小波基的原则为出发点,以CDF9-7小波基为参考,以压缩效果为准则来构造出更优的双正交整数小波基,并且采用航空图像为标准训练图像,以压缩比、峰值信噪比、压缩后保留能量百分比为参数,来寻找最优的小波基。试验结果证明,此方法可以实施非常简单的、无浮点乘法的运算,因而减少运算复杂性以及降低小波硬件实现的难度。