Generalized Pascal Matrices and Inverses Using One-to-One Rational Polynomial s-z Transformations

摘要

本論文では、我々は連続時間（s領域）IIRフィルタの伝達関数の係数と離散時間（z領域）IIRフィルタの伝達関数の係数の間の1対1写像法を痙案する。この1対1写像に基づき、様々な1次s-z変換の場合の一般化パスカル行列の逆行列を証明でき、一般化パスカル行列とその逆行列を用いれば、連続時間IIRフィルタと離散時間IIRフィルタの伝達関数の係数間の関係が1対1写像となる。%Abstract This paper proposes a one-to-one mapping between the coefficients of continuous-time (s-domain) and discrete-time (z-domain) IIR transfer functions such that the s-domain numerator/denominator coefficients can be uniquely mapped to the z-domain numerator/denominator coefficients, and vice versa. The one-to-one mapping provides a firm basis for proving the inverses of the so-called generalized Pascal matrices from various first-order s-z transformations.