The authors propose a method for constructing the chebyshevapproximation of multivariable functions by the rational expression with the interpolation condition. The idea of the method is based on constructing the lim...
详细信息
The authors propose a method for constructing the chebyshevapproximation of multivariable functions by the rational expression with the interpolation condition. The idea of the method is based on constructing the limiting power mean approximation by a rational expression with an interpolation condition in the norm of space L-p as p -> infinity. To construct such an approximation, an iterative scheme based on the least squares method with two variable weight functions is used. One weight function ensures the construction of a power mean approximation with the interpolation condition, and the second one specifies the parameters of the rational expression according to its linearization scheme. The convergence of the method is provided by the original method of sequential specification of the values of weight functions, which takes into account the approximation results at previous iterations. The results of test examples confirm the fast convergence of the proposed method of constructing the chebyshevapproximation by a rational expression with a condition.
constrained least-squares design and constrainedchebyshev design of one-and two-dimensional nonlinear-phase FIR filters with prescribed phase error are considered in this paper by a unified semi-infinite positive-def...
详细信息
constrained least-squares design and constrainedchebyshev design of one-and two-dimensional nonlinear-phase FIR filters with prescribed phase error are considered in this paper by a unified semi-infinite positive-definite quadratic programming approach. In order to obtain unique optimal solutions, we propose to impose constraints on the complex approximation error and the phase error. By introducing a sigmoid phase-error constraint bound function, the group-delay error can be greatly reduced. A Goldfarb-Idnani based algorithm is presented to solve the semi-infinite positive-definite quadratic program resulting from the constrained least-squares design problem, and then applied after some modifications to the constrainedchebyshev design problem, which is proved in this paper to be equivalent also to a semi-infinite positive-definite quadratic program. Through design examples, the proposed method is compared with several existing methods. Simulation results demonstrate the effectiveness and efficiency of the proposed method.
The design of FIR filters in the complex domain is performed by complex chebyshevapproximation where the continuous complex approximation problem is considered as a convex semi-infinite programming problem, This appr...
详细信息
The design of FIR filters in the complex domain is performed by complex chebyshevapproximation where the continuous complex approximation problem is considered as a convex semi-infinite programming problem, This approach permits the filter design under (in)finitely many additional convex constraints on the system function of the filter. For the solution of the semi-infinite programming problem a new method is presented which can be interpreted as a further development of the well-known Kelley-Cheney-Goldstein cutting plane method for finite convex programming. This method is simpler and as reliable as the authors' method in [30, 31], the only other method until now which likewise has proved convergence and can solve continuous design problems with constraints, Filters designed by the method are presented, in particular one with 1000 coefficients. For a number of test examples the method is compared with that in [30, 31].
This paper considers the design of finite impulse response (FIR) filters with equation constraints in the frequency domain and proposes a design algorithm. The design problem is formulated as chebyshevapproximation s...
详细信息
This paper considers the design of finite impulse response (FIR) filters with equation constraints in the frequency domain and proposes a design algorithm. The design problem is formulated as chebyshevapproximation subject to equation constraints. The optimal filter is proved to have a characteristic property that there exists a set of frequencies including extremal frequencies where the weighted error takes a maximum value, and constraint frequencies where the response takes a given magnitude. According to this property, an orthogonal projection-based Remez exchange algorithm is proposed to solve the constrainedchebyshev design problem. As its application, the algorithm is applied to the design of FIR lowpass filters and notch filters. Simulation examples demonstrate the effectiveness and good performance of the proposed algorithm.
A class of low-pass filter functions of even degree is presented having equal ripple delay response and chebyshev stopband attenuation. A special type of equal ripple delay approximation, referred to as the constraine...
详细信息
A class of low-pass filter functions of even degree is presented having equal ripple delay response and chebyshev stopband attenuation. A special type of equal ripple delay approximation, referred to as the constrained chebyshev approximation, that was previously employed to construct filter functions of odd degree, is modified so that it can also be used advantageously in the design of even-ordered lowpass filters. A comparison of results reveals that by this method a considerable amount of performance improvement of the resulting filter can be obtained. Tables are presented giving the zero and pole locations of these filters for n = 4, 6, 8 and 10 together with some other important parameters both in the frequency and in the time domain.
暂无评论