AUTHORS: Vairis Shtrauss, Aldis Kalpinsh, Uldis Lomanovskis

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ABSTRACT: 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.

KEYWORDS: Magnitude Response, Real Part, Imaginary Part, Mellin Convolution Filter, Diffuse Frequency Response, Geometrically Sampled Data, End-Effects, Multiple Filtering Mode

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