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Projected Least-Squares Algorithms for Constrained FIR Filter Design

机译:约束FIR滤波器设计的投影最小二乘算法

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Constrained finite-impulse response (FIR) filter design with time- and frequency-domain linear constraints can be generally transformed into a, or a series of, constrained least-squares problems, which can be generally reformulated as positive definite quadratic programming (QP) problems. This paper presents a novel algorithm referred to as a projected least-squares (PLS) algorithm for the positive definite QP problems. The PLS algorithm essentially projects the unconstrained (least-squares) minimization solution successively onto the boundaries of active constraints that are identified by an active-set strategy. The PLS algorithm has been applied to the constrained least-squares design of FIR filters directly, and to the constrained Chebyshev design of FIR filters in an iterative fashion/The PLS algorithm is compared with the most widely used interior-point methods and an active-set method through design examples of low-pass filters with specified passband and stopband ripples, Nyquist filter constraints and step response constraints. All these examples demonstrate the high efficiency of the PLS algorithm.
机译:具有时域和频域线性约束的约束有限冲激响应(FIR)滤波器设计通常可以转换为一个或一系列约束最小二乘问题,通常可以将其重构为正定二次规划(QP)问题。本文针对正定QP问题提出了一种称为投影最小二乘(PLS)算法的新颖算法。 PLS算法本质上是将无约束(最小二乘)最小化解决方案相继投影到由活动集策略标识的活动约束的边界上。 PLS算法已直接应用于FIR滤波器的约束最小二乘法设计,并且以迭代方式应用于FIR滤波器的约束Chebyshev设计/ PLS算法与最广泛使用的内点法和有源通过具有指定通带和阻带纹波,奈奎斯特滤波器约束和阶跃响应约束的低通滤波器的设计示例来设置方法。所有这些例子证明了PLS算法的高效率。

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