瞬時スペクトラム操作のみを許すHilbert変換機の存在とその回路構造

概要

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Hilbert transform has been previouly studied in many fields, as it plays significant and indispensable rolles in Single Side Band (ab. in SSB) modulation to save occupied frequency bandwidth. It is unfortunate that the Hilbert transform has been realized to possess phase shifting characteristic by π/2 radians from the point of view for circuitry approximation. In this paper, an ideal and exact realization of the Hilbert transform is shown clearly by adopting instantaneous spectrum analysis and synthesis, namely Short Time DFT (ab. in ST-DFT). Where the instantaneous spectrum is given, the Hilbert transform on the frequency domain is precisely carried out via merely exchanging both original real or imaginary part of the spectrum into mapped imaginary or real part, respectively. The Hilbert transform is, therefore, performed as synthesizing the output signal correspondence with the transformed instantaneous spectrum via inverse ST-DFT (ab. in ST-IFT). A circuitry configuration and its characteristic of the short time DFT Hilbert transform are demonstrated to be ideal through unit sample responce.