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首页> 外文期刊>WSEAS Transactions on Signal Processing >Design of Minimum-length, Minimum-phase, Low-group-delay FIR Filter Using Convex Optimization Method
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Design of Minimum-length, Minimum-phase, Low-group-delay FIR Filter Using Convex Optimization Method

机译：使用凸优化方法设计最小长度，最小相位，低组延迟FIR滤波器

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摘要

This paper proposes a new method for optimal design of minimum-length, minimum-phase, low-group-delay FIR filter by employing convex optimization, discrete signal processing (DSP), and polynomial stabilization techniques. The design of a length-N FIR filter is formulated as a convex second-order cone programming (SOCP). In order to design a minimum-phase FIR filter as the necessary condition for having low group delay, the algorithm guarantees that all the filter's zeros are inside the unit circle (minimum-phase). In addition, the quasiconvex optimization problem is developed to minimize the length of minimum-phase, low-group-delay FIR filter. To this end, for a typical low-pass FIR filter, the length of the filter is minimized such that the optimum magnitude response is satisfied, the minimum-phase characteristic is maintained, and the low-group-delay is achieved. The proposed design algorithm only relies on one parameter (cut-off frequency) and the rest of filter parameters are automatically optimized as the trade-off between having minimum-length, minimum-phase, maximum stopband attenuation and low group delay. The effectiveness and performance of proposed approach is demonstrated and compared with other approaches over a set of examples. It is illustrated that this approach converges to the optimal solution in a few iterations.
机译：本文提出了一种通过采用凸优化，离散信号处理（DSP）和多项式稳定技术来实现最小长度，最小相位，低组延迟FIR滤波器的新方法。长度-N FIR滤波器的设计配制为凸二阶锥编程（SOCP）。为了设计最小相位FIR滤波器作为具有低组延迟的必要条件，算法保证所有过滤器的零位于单位圆圈（最小相位）。此外，开发了QuasicOnvex优化问题以最小化最小相，低组延迟冷冻滤波器的长度。为此，对于典型的低通FIR滤波器，滤波器的长度最小化，使得满足最佳幅度响应，保持最小相位特性，并且实现了低组延迟。所提出的设计算法仅依赖于一个参数（截止频率），其余的滤波器参数自动优化为具有最小长度，最小相位，最大停机衰减和低组延迟之间的权衡。所提出的方法的有效性和性能被证明并与一组例子中的其他方法进行了比较。示出了该方法在几个迭代中收敛于最佳解决方案。

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