Design of nonuniform near allpass complementary FIR filters via a semi-infinite programming technique

Abstract

Abstract-In this paper, we consider the problem of designing a set of nonuniform near allpass complementary FIR filters. This problem can be formulated as a quadratic semi-infinite programming problem, where the objective is to minimize the sum of the ripple energy for the individual filters, subject to the passband and stopband specifications as well as to the allpass complementary specification. The dual parameterization method is used for solving the linear quadratic semi-infinite programming problem.Index Terms-allpass complementary FIR filters, nonuniform frequency bands, semi-infinite programming, dual parameterization.

Design of interpolative sigma delta modulators via a semi-infinite programming approach

“…This is because the above configuration of fifth order SDM is enough for most applications, such as audio applications [17]. By selecting , the optimal SDM design problem can be formulated as SIP problems as discussed in Section II and these problems can be solved via our recently proposed dual parameterization method [16]. The magnitude responses of…”

“…Although the difference between the exact upper bound of a discretized constraint and that of the corresponding continuous constraint vanishes as the number of grid points increases, the computational complexity increases. To solve the problem, our recently developed dual parameterization method [16] is applied and this method guarantees to obtain a global optimal solution that satisfies the continuous constraint if the solution exists. Besides the characteristics of the noise output and input output transfer functions are captured in the design, the stability of these two transfer functions and the frequency characteristics of the loop filter should also be considered.…”

“…(28) It is worth noting that problem P 1 does not depend on the numerator coefficients, so the global optimal solution of problem P 1 can be obtained via our recently proposed dual parameterization method [16]. To solve problem P 2 , since the denominator coefficients are obtained from solving problem P 1 , the global optimal solution of problem P 2 can then be obtained similarly.…”

“…The optimization problems are actually quadratic SIP problems. By applying our recently proposed dual parameterization method for solving the problems [16], global optimal solutions that satisfy the corresponding continuous constraint are guaranteed. According to the simulations, the SDM produces a higher SNR compared to the existing designs.…”

Efficient Algorithm for Solving Semi-Infinite Programming Problems and Their Applications to Nonuniform Filter Bank Designs

“…In order to solve these problems, numerically efficient simplex extension algorithms were employed in [6] and [16], conventional dual parameterization approaches were employed in [5], [12], [17], [18] and [27], an extended active set strategy was employed in [4], an extended version of Remez algorithm was employed in [7] to generate a feasible starting condition for the dual method, discretization methods were employed in [9], [15] and [16], outer-approximation cutting plane algorithms were employed in [10], [15] and [30], penalty function approaches were employed in [11] and [26], and constraint transcription approaches were employed in [13] and [25]. Among them, the constraint transcription methods, the penalty function approaches, the discretization methods, the cutting plane methods and the conventional dual parameterization methods are the most common methods employed for solving engineering problems.…”