基于QPSO算法的准完全重构余弦调制滤波器组的优化设计

提出了一种准完全重构的余弦调制滤波器组的设计方法,使用优化方法设计原型滤波器。该方法固定原型滤波器的阻带截止频率为ωs=π/M,以通带截止频率ωp为参数变量,用量子粒子群优化算法(QPSO)优化满足重构条件的目标函数,间接设计原型滤波器,然后通过调制得到余弦调制滤波器组。稍微放宽余弦调制滤波器组的精确条件,从而大大降低了设计的复杂性,减少运行时间。仿真实验结果表明,该算法简单有效,可获得具有高阻带衰减、低混叠误差和重构误差的余弦调制滤波器组。     

利用频率掩蔽法设计均匀和非均匀余弦调制滤波器组

给出了一种均匀非均匀余弦调制滤波器组的设计方法。采用了频率掩蔽法设计原型滤波器,利用迭代算法优化原型滤波器的脉冲响应系数,目标函数表示为脉冲响应系数的四次方,非均匀余弦调制滤波器组通过合并均匀余弦调制滤波器组的相邻的滤波器得到,这种方法简单有效。最后的Matlab实例仿真验证了此算法的有效性。     

基于QPSO优化算法的余弦调制滤波器组设计

提出了一种新的余弦调制滤波器组设计方法,此方法以原型滤波器的阻带衰减作为目标函数,用改进型量子粒子群算法(QPSO)设计最接近满足重构条件的原型低通滤波器,然后在此基础上通过余弦调制得到分析滤波器组和综合滤波器组.实验仿真结果表明,用此方法设计的余弦调制滤波器组(CMFB)具有良好的阻带衰减特性和精确重构性能,在满足性...     

余弦调制滤波器组的原型滤波器设计

该文提出了一种近似重构的余弦调制滤波器组的原型滤波器设计方法。该方法将原型滤波器表示成A(z2)B(z)的形式(其中B(z)是最平坦FIR滤波器),通过优化低阶FIR滤波器A(z)的通带边缘频率,间接设计原型滤波器。文中给出的设计例子表明,该方法可获得很高阻带衰减的滤波器组。     

一种设计近似完全重构非均匀余弦调制滤波器组的新算法

该文提出了一种设计近似完全重构非均匀余弦调制滤波器组的新算法。针对现有合并算法中非均匀滤波器组性能无法直接控制优化的缺点,新算法把非均匀滤波器组的设计问题归纳为一个关于原型滤波器的无约束优化问题,其中目标函数是非均匀滤波器组传递失真与原型滤波器阻带能量的加权和,最后利用线性迭代算法求解该优化问题。理论分析和数值实验表明,新算法获得的非均匀余弦调制滤波器组比现有算法设计的滤波器组整体性能更佳。     

M带余弦调制滤波器组的迭代设计算法

余弦调制滤波器组的设计问题通常是关于原型滤波器系数的非凸优化问题,设计的优劣很大程度上取决于设计问题的归结和所采用的求解算法.本文提出了一种基于迭代的设计方法,用于设计近似完全重构的余弦调制滤波器组.该方法通过松弛完全重构条件和运用迭代的思想,将余弦调制滤波器组的设计归结为一个易于求解的优化问题.在该优化问题中,原型滤...     

具有重构特性的原型滤波器的设计

针对传统单参数优化法设计的原型低通滤波器存在设计复杂,性能不理想的问题,提出了一种利用窗函数截取平方根升余弦函数获取滤波器系数的设计方法。该方法将具有功率互补特性的平方根升余弦函数作为原型函数,通过迭代算法来确定滤波器长度,进而利用窗函数设计原型低通滤波器。仿真结果表明,该方法设计的原型滤波器的阻带衰减达到了-116dB,滤波器组的重构误差在5×10-4dB以内,性能优于传统单参数法设计的滤波器组,具有良好的重构特性。     

M带余弦调制滤波器组的设计

本文提出了一种近似重构的M带余弦调制滤波器组的设计方法.该方法将原型滤波器表示成A(z^L)B(z)的形式,通过优化低阶FIR滤波器A(z)的通带边缘频率,间接设计原型滤波器.在优化过程中,采用常用的Parks-McClellan算法设计滤波器A(z).文中给出的设计例子表明,该方法可获得很高阻带衰减的滤波器组.     

M带余弦调制正交小波的设计

本文提出了一种M带余弦调制正交小波的设计方法。该方法将原型滤波器表示成一个满足K正则度条件的滤波器和一个待定滤波器的级联。并且优化的目标函数和约束条件都是优化参数的二次函数。从而简化了优化问题并获得了频率选择性更好的M带余弦调制正交小波。     

设计余弦调制QMF组的一种新方法

通过适当矩阵变换，本文首先将精确重建余弦调制正交镜像滤波器组的设计转化为一种带约束的非线性优化问题，它是一种带二次型约束的最小二乘（ＱＣＬＳ）优化问题，然后，我们提出了一种变参量的罚函数方法来有效求解该类ＱＣＬＳ优化问题，通过直接采用原型滤波器系数为优化变量，我们构造了一个特殊的凸函数作优化代价函数，故可获得该问题的全局最小点，最后，采用本文提出的设计方法进行了一个具体实例设计，结果表明我们的方法     

一种余弦调制正交镜象滤波器组的设计方法

本文将具有精确重建特性的余弦调制正交镜象滤波器的设计问题转化为一种带二次约束的最小二乘（ＱＣＬＳ）优化问题,其中所有的约束矩阵都是对称正定的,为了有效地求解该类ＱＣＬＳ优化问题,文中构造了一个代价函数,从而很容易地获得了全局最优解,最后给出的两个设计实例验证了本文方法的正确性和有效性。     

Two-dimensional perfect reconstruction FIR filter banks withtriangular supports

We present a theory and design of two-dimensional (2-D) perfect reconstruction (PR) filter banks (FBs) (PRFBs) in which the supports of the analysis and synthesis filters consist of two triangulars. The two-triangular FB can be realized by designing an appropriate 2-D complex prototype whose passband support is a triangle that is a half of a parallelepiped-shaped passband support defined by the sampling matrix. Then a complex prototype filter is modulated by the DFT, and each analysis filter is derived by taking the real part of the modulated output. We show that the two-triangular FB satisfies the condition of permissibility. A necessary and sufficient condition for 2-D PRFBs is derived. Moreover, we present a design method of the 2-D PRFB that minimizes the cost function consisting of the frequency constraint and PR condition. Finally, a design example is presented to confirm the validity of the proposed method     

On the Design of Nearly-PR and PR FIR Cosine Modulated Filter Banks Having Approximate Cosine-Rolloff Transition Band

This paper proposes an efficient method for designing nearly perfect reconstruction (NPR) and perfect reconstruction (PR) cosine modulated filter banks (CMFBs) with prototype filters having an approximate cosine-rolloff (CR) transition band. It is shown that the flatness condition required for an NPR CMFB can be automatically satisfied by using a prototype filter with a CR transition band. The design problem is then formulated as a convex minimax optimization problem, and it can be solved by second-order cone programming (SOCP). By using the NPR CMFB so obtained as an initial guess to nonlinear optimizers such as Fmincon in Matlab, high-quality PR CMFBs can be obtained. The advantages of the proposed method are that it does not require a user-supplied initial guess of the prototype filter and bumps in the passband of the analysis filters can be effectively suppressed.     

Linear phase cosine modulated maximally decimated filter banks withperfect reconstruction

We propose a novel way to design maximally decimated FIR cosine modulated filter banks, in which each analysis and synthesis filter has a linear phase. The system can be designed to have either the approximate reconstruction property (pseudo-QMF system) or perfect reconstruction property (PR system). In the PR case, the system is a paraunitary filter bank. As in earlier work on cosine modulated systems, all the analysis filters come from an FIR prototype filter. However, unlike in any of the previous designs, all but two of the analysis filters have a total bandwidth of 2π/M rather than π/M (where 2M is the number of channels in our notation). A simple interpretation is possible in terms of the complex (hypothetical) analytic signal corresponding to each bandpass subband. The coding gain of the new system is comparable with that of a traditional M-channel system (rather than a 2M-channel system). This is primarily because there are typically two bandpass filters with the same passband support. Correspondingly, the cost of the system (in terms of complexity of implementation) is also comparable with that of an M-channel system. We also demonstrate that very good attenuation characteristics can be obtained with the new system     

Design of Oversampled Interleaved DFT Modulated Filter Bank Using 2Block Gauss-Seidel Method

In this paper, we present several new properties of the recently introduced interleaved DFT modulated filter bank and an efficient algorithm for designing the filter bank. The periodicity and symmetry properties of the overall transfer function and aliasing transfer functions are stated. Then the design of the filter bank is formulated into a constrained optimization problem that jointly minimizes the overall distortion and aliasing distortion subject to fixed bounds on the stopband energy, transition-band energy, and passband flatness of the prototype filters. The constrained optimization problem is solved by the 2block Gauss-Seidel method, which alternatively optimizes the analysis PF pair and the synthesis PF pair. Since the overall distortion and aliasing distortion are jointly minimized, the proposed algorithm can lead to filter banks with small reconstruction error, even when the filter banks behave with a low redundancy ratio and short PFs. The convergence of the proposed algorithm is proved. Numerical examples and comparisons with the existing method are included to demonstrate the performance of the proposed algorithm.     

Design of 2D oversampled linear phase DFT modulated filter banks via modified Newton's method

In this paper, the structure of the 2D oversampled DFT modulated filter banks is analyzed and a spatial-domain condition of a filter bank without transfer function distortion is derived. Based upon the spatial-domain condition, a modified Newton's method is presented for fast design of 2D oversampled linear phase (LP) DFT modulated filter banks with nearly perfect reconstruction (NPR). We formulate the design problem into an unconstrained optimization with a fourth-order objective function, which is the weighted sum of the transfer function distortion of the filter bank and the stopband energy of the prototype filter (PF). The optimization is solved by the modified Newton's method, where each of iterations updates the PF by a set of linear equations. It is proved that the iteration process fast converges to a stationary point of the objective function. Compared with the existing methods, the new method is fast in computation and can design 2D filter banks with a large number of subbands.