单元二线性非时变系统之时域表示.PDF

單元二 線性非時變系統之時域表示 Time-Domain Representations of Linear Time-Invariance Systems 1 教學目標 瞭解 線性非時變系統(LTI )之 – Convolution 與LTI system – Convolution 之計算 – 基本性能 – 表示法 2 本單元進度  Convolution Sum – Convolution Sum Evaluation procedure  Convolution integral – Convolution integral Evaluation procedure  LTI system – LTIimpulse response – LTI step response  LTI representation – Differential difference – Block diagram – State variable description 3 下單元進度  Fourier representation of signal and LTI system  Fourier analysis – Property – Fourier signal operation – Fourier system operation 4 The Convolution Sum ∞ y [n] ∑x[k ]h[n −k ] x[n] ⊗h[n] x[n] ∗h[n] k −∞ 若有一LTI 系統 LTI 系統 { } y [n] H x[n] { } y [n] H x[n] , { }δ h n H n 且 [ ] [ ] { }δ 且h[n] H [n] ⇒ 則 y n可表示如下 [ ] 則 y [n可表示如下] ∞ y [n] x[n] *h[n] y n x k h n −k [ ] ∑ [ ] [ ] k −∞ h[n] *x[n]