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Z反变换: x ( n ) = 1 2 π j ∮ c X ( z ) z n − 1 d z x(n)=\frac{1}{2πj}∮_cX(z)z^{n-1}dz x(n)=2πj1∮cX(z)zn−1dz
f ( z 0 ) = 1 2 π i ( ∮ c f ( z ) / ( z − z 0 ) d z ) f(z_0) =\frac{1}{2}πi (∮_c f(z)/(z-z_0) dz) f(z0)=21πi(∮cf(z)/(z−z0)dz)
1 2 π j ∮ c X ( z ) z n − 1 d z = ∑ k R e s [ X ( z ) z n − 1 , z k ] \frac{1}{2πj}∮_cX(z)z^{n-1}dz=\sum_{k}^{}Res[X(z)z^{n-1},z_k] 2πj1∮cX(z)zn−1dz=k∑Res[X(z)zn−1,zk]
X ( z ) = ∑ k = 1 N A k 1 − d k z − 1 X(z) =\sum_{k=1}^{N}\frac{A_k}{1-d_kz^{-1}} X(z)=k=1∑N1−dkz−1Ak
X ( z ) = ∑ n = − ∞ ∞ x ( n ) z − n X(z) =\sum_{n=-\infty}^{\infty}x(n)z^{-n} X(z)=n=−∞∑∞x(n)z−n
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有理系统函数的单位脉冲响应
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无限长单位脉冲响应系统（IIR系统）：系统的单位脉冲响应延伸到无穷长
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有限长单位脉冲响应系统（FIR系统）：系统的单位脉冲响应是一个有限长的序列
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Q 0 = ω 0 L r = 1 ω 0 C r = R 0 ω 0 L = R 0 ω 0 C Q_0=\frac{\omega_0L}{r}=\frac{1}{\omega_0Cr}=\frac{R_0}{\omega_0L}=R_0\omega_0C Q0=rω0L=ω0Cr1=ω0LR0=R0ω0C
