2.2 Discrete-Time System Discrete-Time System is a trasformation or operator that maps input sequence XIn] into a unique yIn] yln]=tiN, Xin] yln]: discrete-time signa XIn] yn Discrete-Time System 22 2/2/2021 Zhongguo Liu_ Biomedical Engineering_shandong Univ
22 2/2/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. 2.2 Discrete-Time System ◆Discrete-Time System is a trasformation or operator that maps input sequence x[n] into a unique y[n] ◆y[n]=T{x[n]}, x[n], y[n]: discrete-time signal T{‧} x[n] y[n] Discrete-Time System
EX 2 3 The Ideal Delay System yn]=x{n-na,-00<n<∞ If n is a positive integer the delay of the system. Shift the input sequence to the right by n, samples to form the output If na is a negative integer: the system wi shift the input to the left by In, samples, corresponding to a time advance. 2/2/2021 Zhongguo Liu_ Biomedical Engineering_shandong Univ
23 2/2/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. EX. 2.3 The Ideal Delay System y[n] = x[n − nd ], − n ◆If is a positive integer: the delay of the system. Shift the input sequence to the right by samples to form the output . d n d n ◆If is a negative integer: the system will shift the input to the left by samples, corresponding to a time advance. d n d n
EX2.4 Moving Average y[n M+M,+lk=m M,+M、+1 x[n+M]+x[n+M-1]+…+x]+x[n-1]+…+xn-M2]} forn=7,M1=0,M2=5 dummy index m x[m] n-5
24 2/2/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. x[m] n m n-5 dummy index m EX. 2.4 Moving Average 2 1 2 1 1 1 2 1 2 1 1 1 1 ... 1 ... 1 M k M y n x n k M M x n M x n M x n x n x n M M M = − = − + + = + + + − + + + − + + − + + for n=7, M1=0, M2=5
Properties of Discrete-time systems 2.2.1 Memoryless(memory) system ◆ Memoryless systems: the output yin] at every value of n depends only on the input xn] at the same value of n n=(xin 25 2/2/2021 Zhongguo Liu_ Biomedical Engineering_shandong Univ
25 2/2/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Properties of Discrete-time systems 2.2.1 Memoryless (memory) system ◆Memoryless systems: the output y[n] at every value of n depends only on the input x[n] at the same value of n ( ) 2 y n = x[n]
Properties of Discrete-time systems 2.2 Linear Systems 回]T十y ◆ and only If xn+ x2 T yin +y In additivity property T千}小 homogeneity or scaling 同(齐)次性 property principle of superposition axIn+ 一[T=+b团 26 2/2/2021 Zhongguo Liu_ Biomedical Engineering_shandong Univ
26 2/2/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Properties of Discrete-time systems 2.2.2 Linear Systems ◆If y n x1 n T{‧} 1 y n x n 2 2 T{‧} axn T{‧} ayn x n ax n bx n 3 = 1 + 2 y n ay n by n T{‧} 3 = 1 + 2 y n y n x1 n+ x2 n T{‧} 1 + 2 additivity property homogeneity or scaling 同(齐)次性 property ◆principle of superposition ◆and only If: