アナログフィルタの合成特性 I : バタワースフィルタ

概要

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The "combined" characteristics of the analog filter are investigated，where the combined characteristics means the feature of the filters that represents how accurately the original signal divided by the low pass filter (LPF）and high pass filter（HPF）will be reproduced when summed after passing through these filters．The combined characteristics are important in the field of audio engineering，where the audio signal is often divided into two or more frequency bands，amplified separately，and finally we hear the vector sum of them in sound pressure. In this paper，the existence of the filter that has perfect combined－characteristics is discussed at first，and it has been proved that no stable filter with perfect combined characteristics exists of order N≧2，except for the first order delay element. Then the combined characteristics of the Butterworth filter are investigated analytically. It has been proved that the Butterworth filter of odd order has the perftct "amplitude"characteristics，namely，lGT（jw）l＝1，where GT is the sum of the transfer functions of LPF and HPF，but their group delay characteristics and impulse response functions are not good，in contrast to the Bessel filter，which will be reported elsewhere.