Special paraunitary matrices, Cayley transform, and multidimensional orthogonal filter banks.

We characterize and design multidimensional (MD) orthogonal filter banks using special paraunitary matrices and the Cayley transform. Orthogonal filter banks are represented by paraunitary matrices in the polyphase domain. We define special paraunitary matrices as paraunitary matrices with unit determinant. We show that every paraunitary matrix can be characterized by a special paraunitary matrix and a phase factor. Therefore, the design of paraunitary matrices (and thus of orthogonal filter banks) becomes the design of special paraunitary matrices, which requires a smaller set of nonlinear equations. Moreover, we provide a complete characterization of special paraunitary matrices in the Cayley domain, which converts nonlinear constraints into linear constraints. Our method greatly simplifies the design of MD orthogonal filter banks and leads to complete characterizations of such filter banks.     

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     

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_∞ 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     

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     

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.     

Directional lapped orthogonal transform: theory and design

This paper proposes a directional design method of 2-D nonseparable linear-phase paraunitary filter banks. The proposed method is based on a lattice structure consisting of the 2-D separable DCT block and nonseparable support extension processes. Because of the nonseparability, the bases are allowed to be directional with the critically fixed subsampling, overlapping, orthogonal, symmetric, real-valued, and compact support properties. First, a novel vanishing moment (VM) condition is introduced as a suitable directional constraint, where the moment is referred to as the trend VM. The condition forces wavelet filters, i.e., high-pass and bandpass filters, to annihilate trend-surface components. Second, some theoretical properties of TVMs are discussed for general 2-D paraunitary systems, and then, the properties are applied to the lattice parameters. In order to verify the significance, several design examples are shown, the trend-surface annihilation properties are numerically confirmed, and the denoising capability is evaluated for images through shrinkage. It is shown that our proposed transforms yield perceptually preferable results.     

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     

Design of almost symmetric orthogonal wavelet filter bank via direct optimization

It is a well-known fact that (compact-support) dyadic wavelets [based on the two channel filter banks (FBs)] cannot be simultaneously orthogonal and symmetric. Although orthogonal wavelets have the energy preservation property, biorthogonal wavelets are preferred in image processing applications because of their symmetric property. In this paper, a novel method is presented for the design of almost symmetric orthogonal wavelet FB. Orthogonality is structurally imposed by using the unnormalized lattice structure, and this leads to an objective function, which is relatively simple to optimize. The designed filters have good frequency response, flat group delay, almost symmetric filter coefficients, and symmetric wavelet function.     

Top-down design of a VLSI digital filter bank

This paper relates theoretical investigations in digital signal processing (DSP) to the design of a VLSI digital filter bank (DFB). Emphasis is on a top-down approach to identify multilevel parallelisms inherent in a generic DSP algorithm and a new VLSI architecture. System level control and communication requirements are examined. Finite word length effects on filter accuracy are identified. The complexity of filter modules is reduced by partitioning large filter functions into a sum of smaller subfunctions. A memory intensive architecture minimizes design time. Up to 100 DRF modules are configured in parallel to perform signal processing up to 20 MHz. This VLSI DFB out performs sequential von Neumann architectures by several orders of magnitude using the same level of VLSI technology.     

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.     

Multidimensional directional filter banks and surfacelets.

In 1992, Bamberger and Smith proposed the directional filter bank (DFB) for an efficient directional decomposition of 2-D signals. Due to the nonseparable nature of the system, extending the DFB to higher dimensions while still retaining its attractive features is a challenging and previously unsolved problem. We propose a new family of filter banks, named NDFB, that can achieve the directional decomposition of arbitrary N-dimensional (N > or =2) signals with a simple and efficient tree-structured construction. In 3-D, the ideal passbands of the proposed NDFB are rectangular-based pyramids radiating out from the origin at different orientations and tiling the entire frequency space. The proposed NDFB achieves perfect reconstruction via an iterated filter bank with a redundancy factor of N in N-D. The angular resolution of the proposed NDFB can be iteratively refined by invoking more levels of decomposition through a simple expansion rule. By combining the NDFB with a new multiscale pyramid, we propose the surfacelet transform, which can be used to efficiently capture and represent surface-like singularities in multidimensional data.     

用于多路MCP-EBPSK信号解调的冲击滤波器组设计

修正的随机极性连续相位扩展的二元相移键控调制（MCP-EBPSK）通过随机化调制指数的符号,并加入功率谱调节系数,进一步降低了连续相位扩展的二元相移键控(CP-EBPSK)调制信号功率谱中的线谱分量,使得功率谱占用带宽更窄,信息传输更加的高效高速。多载波作为高频谱利用率的复用调制方式,与MCP-EBPSK结合势必会带来更高的系统性能,因此本文对用于解调单路MCP-EBPSK信号的冲击滤波器进行初步改进,通过添加陷波零点来抑制旁路干扰,设计出带陷波的冲击滤波器组。引入量子粒子群优化算法对加入陷波的冲击滤波器组进行优化得到滤波器组系数,仿真显示即使时频混叠的子载波间不满足正交关系,利用各冲击滤波器中心频率处极陡峭的陷波选频特性依然可以实现各子载波的正确解调。因此, 设计的冲击滤波器组可以用于子载波无保护间隔的多路MCP-EBPSK信号解调。      

A.S.W. filter bank using a multistrip reflective array

A new frequency-sensitive a.s.w. structure is presented. The device, operating by reflection of acoustic surface waves, is used as a filter bank.     

Complex notch filter design using allpass filter

Complex coefficient IIR notch filter design problems are investigated. The specification of a notch filter is first transformed into that of an allpass filter. An effective approach to the design of this desired allpass filter is developed. The realisation of the proposed notch filter is equivalent to the realisation of an allpass filter. Owing to the mirror-image symmetry relation between the numerator and denominator polynomials of allpass filters, the notch filter can be realised by a computationally efficient lattice structure with very low sensitivity     

Two-dimensional filter bank design for optimal reconstruction usinglimited subband information

In this correspondence, we propose design techniques for analysis and synthesis filters of 2-D perfect reconstruction filter banks (PRFB's) that perform optimal reconstruction when a reduced number of subband signals is used. Based on the minimization of the squared error between the original signal and some low-resolution representation of it, the 2-D filters are optimally adjusted to the statistics of the input images so that most of the signal's energy is concentrated in the first few subband components. This property makes the optimal PRFB's efficient for image compression and pattern representations at lower resolutions for classification purposes. By extending recently introduced ideas from frequency domain principal component analysis to two dimensions, we present results for general 2-D discrete nonstationary and stationary second-order processes, showing that the optimal filters are nonseparable. Particular attention is paid to separable random fields, proving that only the first and last filters of the optimal PRFB are separable in this case. Simulation results that illustrate the theoretical achievements are presented.     

Deconvolution filter design for fractal signal transmissionsystems: a multiscale Kalman filter bank approach

A deconvolution filtering design is proposed for the 1/f fractal signal transmission systems, with its design philosophy being based on multiscale Kalman deconvolution filter bank equipped in the analysis/synthesis wavelet filter bank, The role of wavelet transformation for 1/f fractal signal process is exploited as a multiscale whitening filter for removing the properties of self-similarity and long-range dependence from the fractal signals     

A filter bank for the directional decomposition of images: theoryand design

The authors introduce a directionally oriented 2-D filter bank with the property that the individual channels may be critically sampled without loss of information. The passband regions of the component filters are wedge-shaped and thus provide directional information. It is shown that these filter bank outputs may be maximally decimated to achieve a minimum sample representation in a way that permits the original signal to be exactly reconstructed. The authors discuss the theory for directional decomposition and reconstruction. In addition, implementation issues are addressed where realizations based on both recursive and nonrecursive filters are considered     

Coherent orthogonal filter using pilot symbol-assisted channelestimation for DS-CDMA

A coherent orthogonal filter (COF) using pilot symbol-assisted channel estimation is proposed for DS-CDMA cellular mobile radio. In the proposed scheme, a complex fading envelope in the multi-path environment is estimated using pilot symbols, and tap coefficients of orthogonal filter are controlled for maximising the signal to interference ratio (SIR) of a RAKE combined signal. Computer simulation results show that the required E_b/N₀ of the proposed COF is reduced by ~10.0 dB compared to conventional matched filter receiver at an average BER of 3×10² when there are 10 users and processing gain is 31     

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。