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An Approach to Accurate Inversion of Convolution Transforms by FIR Filters

机译：FIR滤波器对卷积变换进行精确反演的一种方法

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摘要

Inversion of convolution transforms is considered by FIR filters for aperiodic band- and time-unlimited signals from the perspective attaining maximum accurate inverted waveforms with controllable noise amplification of the filter. The difficulties hampering to gain this goal, such as a lack of knowledge how the digital filter shall deviate from ideal one to produce waveforms as accurately as possible, complexity to choose optimal sampling rate, necessity to sacrifice the accuracy for suppressing noise, etc. are analysed. Based on learning in the input-output signal domain and controlling noise amplification by varying sampling rate, an approach is developed for designing maximum accurate filters, which are specified only by two user's relevant parameters: (i) the desired noise gain and (ii) the continuous time support. Implementation of the approach is illustrated by designing a digital differentiator for the logarithmic derivative and a digital estimator of the distribution of relaxation times. Simulation results are presented demonstrating that the approach allows constructing more accurate FIR filters with predefined noise amplification and support sizes compared with those designed by other commonly used techniques.
机译：从FIR滤波器考虑到对非周期性频带和时间无限制信号的卷积变换的反转，从获得最大精确的反转波形和可控噪声放大的角度来看。阻碍实现这一目标的困难，例如缺乏对数字滤波器如何偏离理想滤波器以尽可能准确地产生波形的知识，选择最佳采样率的复杂性，必须牺牲抑制噪声的精度等。分析。基于对输入输出信号域的学习并通过改变采样率来控制噪声放大，开发了一种设计最大精度滤波器的方法，该滤波器仅由两个用户的相关参数指定：（i）所需的噪声增益和（ii）持续的时间支持。通过设计对数导数的数字微分器和弛豫时间分布的数字估计器来说明该方法的实现。仿真结果表明，与通过其他常用技术设计的滤波器相比，该方法可以构建具有预定义噪声放大和支持尺寸的更精确的FIR滤波器。

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