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首页> 外文期刊>Circuits, systems, and signal processing >FIR FILTERS WITH PUNCTURED RADIX-8 SYMMETRIC COEFFICIENTS: DESIGN AND MULTIPLIER-FREE REALIZATIONS
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FIR FILTERS WITH PUNCTURED RADIX-8 SYMMETRIC COEFFICIENTS: DESIGN AND MULTIPLIER-FREE REALIZATIONS

机译：具有固定RADIX-8对称系数的FIR滤波器：设计和无乘数实现

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摘要

In recent years, several approaches have been investigated to obtain multiplier-free realizations of digital filters. One approach makes use of periodically time-varying (PTV) structures. The idea is to distribute the computation in time and in space. Distribution in time provides reuse of the same hardware by means of PTV coefficients. Distribution in space increases the number of coefficients but simplifies the values of the coefficients. Computation distribution is based on radix-r number representation, and it can be carried out to the extent that each computation involves a simple coefficient that can be realized using only addition and shift (no hardware multiplier). Previous PTV realizations could not exploit the coefficient symmetry of finite impulse response (FIR) filters to reduce the number of coefficients. This paper proposes design and realizations of FIR filters with punctured radix-8 coefficients belonging to the septuple set {0, +- 1, +- 2, +- 4}, which can be implemented using only a shift operation without requiring any hardware multiplier. The realizations exploit the coefficient symmetry to reduce the hardware by about one-half. Due to a non-uniform grid of representation, we apply a modified Karmarkar's linear programming algorithm to find the optimum set of discrete coefficients that minimizes the weighted peak ripple error. Comparison with a conventional FIR filter with sum-of-powers-of-two (SOPOT) coefficients shows that the proposed filter is faster and uses less hardware than one with SOPOT coefficients. However, the punctured radix-8 system has a limit on the achievable ripple.
机译：近年来，已经研究了几种方法来获得数字滤波器的无乘数实现。一种方法利用周期性时变（PTV）结构。这个想法是在时间和空间上分布计算。时间上的分布通过PTV系数提供了相同硬件的重用。空间中的分布增加了系数的数量，但是简化了系数的值。计算分布基于基数-r数表示，并且可以在每次计算都涉及一个简单系数的情况下进行，该系数仅使用加法和移位即可实现（无需硬件乘法器）。先前的PTV实现无法利用有限冲激响应（FIR）滤波器的系数对称性来减少系数的数量。本文提出了属于基数集{0，+-1，+-2，2，+-4}的带打底基数8系数的FIR滤波器的设计和实现，可以仅使用移位运算来实现，而无需任何硬件乘法器。这些实现利用系数对称性将硬件减少了大约一半。由于表示的网格不均匀，因此我们应用了改进的Karmarkar线性规划算法来找到最佳的离散系数集，从而使加权峰值纹波误差最小。与具有2的幂和（SOPOT）系数的常规FIR滤波器的比较表明，与具有SOPOT系数的FIR滤波器相比，该滤波器速度更快且使用的硬件更少。但是，打底基8系统对可达到的纹波有限制。

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