ABSTRACT

In this paper, a new transformation polynomial for $$s$$-to-$$z$$ plane is presented. This third-order transformation is derived by optimizing the coefficients of the logarithmic series followed by utilizing the multirate technique to extend its bandwidth. In terms of magnitude and phase response, the proposed transform correlates well with the ideal and shows mean absolute magnitude error and mean absolute phase error as $$-40$$ dB and $$-132.04$$ dB respectively. The proposed transform is compared with the existing operators to demonstrate its performance. In addition, an example is also conferred, which establishes the viability of the transform in terms of the overall frequency response, when applied for analog-to-digital transformation.

摘要

在本文中，一个新的变换多项式为 $$秒$$-到-$$z$$平面呈现。这种三阶变换是通过优化对数级数的系数，然后利用多速率技术扩展其带宽来推导出来的。在幅度和相位响应方面，所提出的变换与理想的相关性很好，并显示平均绝对幅度误差和平均绝对相位误差为$$-40$$ 分贝和 $$-132.04$$分贝分别。将提议的转换与现有运算符进行比较以证明其性能。此外，还提供了一个示例，当应用于模数转换时，该示例根据整体频率响应建立了转换的可行性。