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We study a class of composite filters (C-filters), each is composed of a prototype filter and a shaping filter in cascade, where the shaping filter is constructed by cascading several complementary comb filters. In particular, the problem of designing a C-filter with equiripple passband and least-squares stopband subject to peak stopband gain is formulated and an algorithm for designing such a class...
We present a unified approach to minimax design of interpolated and frequency-response-masking FIR filters which are well-known classes of computationally efficient digital filter. The highly nonconvex minimax designs of these filters are carried out by jointly optimizing the subfilters involved using a convex-concave procedure (CCP). We explain why CCP is well-suited for the design problems at hand...
We study a class of composite digital filters, each has a dominating FIR component of order N and an extremely simple IIR component of order r with r-C N that are connected in parallel. We show that a constrained optimization setting known as convex-concave procedure (CCP) is naturally suited for the design of stable composite filters where the FIR and IIR components are jointly optimized in frequency-weighted...
Sparse digital filters are of importance as they offer improved implementation efficiency relative to their nonsparse counterparts. This paper examines the design of minimax sparse IIR filters from a sparse representation point of view. The result is a new algorithm that accomplishes a design with three phases — identification of the whereabouts of zero coefficients; optimal design subject to the...
Implementing a variable fractional delay (VFD) filter in Farrow model is costly as each coefficient of a VFD filter is a polynomial rather than a numerical scalar as in a conventional digital filter. This paper presents a method for the design of VFD filters with sparse coefficients which admits efficient implementation. The design is accomplished in two phases with the first phase identifying locations...
Coefficient sparsity of digital filters is of importance as it is directly related to implementation efficiency and cost. To date most work in the field has been focused on finite-impulse-response filters. In this paper, the design of sparse digital filters is investigated for a class of IIR filters. We propose a two-phase algorithm that promotes coefficient sparsity, maintains filter's stability,...
Designing perfect-reconstruction orthogonal cosine-modulated filter banks is essentially a nonconvex problem and to date only local solutions can be claimed. By virtue of the recent progress in global polynomial optimization, this paper describes an attempt of developing a global design method using an order-recursive strategy combined with a technique that identifies a desirable initial point in...
Is sparsity an issue in filter design problems? and why is it important? How a digital filter can be designed to have a sparse impulse response for efficient implementation while achieving improved performance relative to its non-sparse counterpart? In an attempt to address these questions, this paper comes up with a design technique for optimal linear-phase FIR filters with sparse impulse responses.
This paper analyzes the requirements of algorithms in AKA, which is the authenticated key exchange mechanism of 3G mobile communication system. An AKA security algorithm based on chaotic mapping is proposed. We establish a one-way Hash function based on chaotic mapping as the kernel function. Then all the encryption functions in AKA are redefined. Simulation results show that this method possesses...
This paper investigates several design issues concerning two-channel conjugate quadrature (CQ) filter banks and orthogonal wavelets. It is well known that optimal designs of CQ filters and wavelets in least squares or minimax sense are nonconvex problems and to date only local solutions can be claimed. By virtue of recent progress in global polynomial optimization and direct design techniques for...
This paper presents a new method for the design of two-channel conjugate quadrature (CQ) filter banks in which halfband filter and spectrum factorization are not required. Instead, a CQ filter is directly optimized subject to the perfect reconstruction and possibly other constraints (such as number of vanishing moments (VM)). We develop a design strategy in that the solution is approached sequentially...
This paper investigates several design issues concerning two-channel conjugate quadrature (CQ) filter banks and orthogonal wavelets. It is well known that optimal designs of CQ filters and wavelets in the least squares (LS) or minimax sense are nonconvex problems and to date only local solutions can be claimed. By virtue of recent progress in global polynomial optimization and a direct design technique...
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