Multiplierless FIR filters (or other fixed linear combiners) are built as add/subtract networks operating on bit-shifted input data. Classically, the computational structure required is determined by simply expressing the coefficients in canonical-signed-digit (CSD) form. In this paper, expressing coefficients in a higher-radix number system instead results in a computational structure for a partial solution, one that reduces a large linear-combination problem to a smaller one. A well-chosen sequence of such number systems then leads to a cascade of these problem-reducing networks that together solve the original problem with remarkable overall computational efficiency, especially for larger filters. An example FIR filter with a real chirp impulse response 3000 samples in length (a matched filter for a pulse-compression radar) was easily realized with -95 dB rms approximation error using less than two add or subtract operations per coefficient. This is a reduction of approximately 60% relative to the usual CSD method.
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机译：无乘法器FIR滤波器（或其他固定的线性组合器）被构建为对位移后的输入数据进行操作的加/减网络。传统上，所需的计算结构是通过简单地以标准符号数字（CSD）形式表示系数来确定的。在本文中，用基数较高的系统表示系数会导致部分求解的计算结构，从而将较大的线性组合问题简化为较小的线性组合问题。然后，精心选择的此类数字系统序列会导致这些问题减少网络的级联，这些网络以显着的总体计算效率共同解决原始问题，尤其是对于较大的过滤器。具有真实的线性脉冲响应长度为3000个样本的示例FIR滤波器（用于脉冲压缩雷达的匹配滤波器）很容易实现，具有-95 dB rms逼近误差，每个系数使用少于两个加法或减法运算。相对于常规的CSD方法，这大约减少了60％。
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