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首页> 外文期刊>WSEAS Transactions on Signal Processing >Separating Magnitude Response into Real and Imaginary Parts by Mellin Convolution Filters
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Separating Magnitude Response into Real and Imaginary Parts by Mellin Convolution Filters

机译：通过MELLIN卷积过滤器将幅度响应分成真实和虚部

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摘要

The paper is devoted to the determination of the real and imaginary parts from the magnitude responses for causal linear time-invariant systems having monotonic impulse responses. We demonstrate that the problem can be considered as a special filtering task in the Mellin transform domain having a diffuse magnitude response. The theoretical background is given for the separating the magnitude response into the real and imaginary parts by discrete-time Mellin convolution filters processing geometrically sampled magnitude responses and the appropriate finite impulse response (FIR) filters are designed. To compensate exponential shortening frequency ranges of the real and imaginary parts due to the end-effects of FIR filters processing geometrically sampled magnitude responses, the multiple filtering mode is used, where the sets of the first and last input samples are repeatedly processed by the filters having impulse responses with the shifted origins, which gradually vary the number of coefficients with negative and positive indices on each side of the origin. The performance of the designed filters are evaluated in terms of the accuracy of the generated real and imaginary parts and the noise amplification.
机译：本文致力于确定具有单调脉冲响应的因果线性时间不变系统的幅度响应的真实和虚部的确定。我们证明问题可以被认为是具有漫反射幅度响应的MELLIN变换域中的特殊滤波任务。通过离散时间MELLIN卷积滤波器处理几何采样幅度响应，设计了理论背景，将幅度响应分离成真实和虚部，并设计了适当的有限脉冲响应（FIR）滤波器。为了补偿Real和虚部的指数缩短频率范围由于FIR滤波器处理几何采样幅度响应的终端效应，使用多个过滤模式，其中第一滤波器的集合由滤波器重复处理具有脉冲响应与移位的起源，这逐渐改变原点的每一侧的负面索引的系数数量。在所产生的实部和虚部的准确性和噪声放大的准确性方面评估设计过滤器的性能。

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