2 Linear Time-Invariant Systems 2. Linear Time-Invariant Systems 2.1 Discrete-time lti system: The convolution sum 2.1.1 The Representation of Discrete-time Signals in Terms of Impulses xn]=…+x-2]6n+2]+x[-16[n+1]+x[0j1[n]+x(1]n-1]+x{216[n-2]+ x{k16[n-k] If xIn]=u[n], then x[n]=>8[n-k
2 Linear Time-Invariant Systems 2.1 Discrete-time LTI system: The convolution sum 2.1.1 The Representation of Discrete-time Signals in Terms of Impulses 2. Linear Time-Invariant Systems + =− = − = + − + + − + + + − + − + k x k n k x n x n x n x n x n x n [ ] [ ] [ ] [ 2] [ 2] [ 1] [ 1] [0] [ ] [1] [ 1] [2] [ 2] If x[n]=u[n], then + = = − 0 [ ] [ ] k x n n k
2 Linear Time-Invariant Systems 32 xl-218[n,21 a-2:8:2 [-11Dn+1 …-3-2I525…
2 Linear Time-Invariant Systems
2 Linear Time-Invariant Systems 2.1.2 The Discrete-time Unit Impulse response and the Convolution Sum Representation of Lti Systems (1)Unit Impulse(Sample) Response xn=8n yIn=hn LTI Unit Impulse Response: hnI
2 Linear Time-Invariant Systems 2.1.2 The Discrete-time Unit Impulse Response and the Convolution Sum Representation of LTI Systems (1) Unit Impulse(Sample) Response LTI x[n]=[n] y[n]=h[n] Unit Impulse Response: h[n]
2 Linear Time-Invariant Systems 2) Convolution Sum of Lti System Question n LTI yin/=? Solution n]—>hn] i[n-k]—>hn-K] k]n-K]—>xk]h[n-k xn=∑xk6n-k]-→yn=∑xkhn-k
2 Linear Time-Invariant Systems (2) Convolution Sum of LTI System LTI x[n] y[n]=? Solution: Question: [n] ⎯→ h[n] [n-k] ⎯→ h[n-k] x[k][n-k] ⎯→x[k] h[n-k] + =− + =− = − − − → = − k k x[n] x[k][n k] y[n] x[k]h[n k]
2 Linear Time-Invariant Systems ho回o h1回
2 Linear Time-Invariant Systems