2.2 Discrete-Time System Discrete-Time System is a trasformation or operator that maps input sequence xIn] into an output sequence yIn] ByIn]=Txn] xin] yln]: discrete-time signal xn yn T y Discrete-Time System 22 1/30/2021 Zhongguo Liu_Biomedical Engineering_ Shandong Univ
22 1/30/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. 2.2 Discrete-Time System uDiscrete-Time System is a trasformation or operator that maps input sequence x[n] into an output sequence y[n]. uy[n]=T{x[n]}, x[n], y[n]: discrete-time signal T{‧ } x[n] y[n] Discrete-Time System
EX 2.2 The Ideal Delay System n]=xn-n],-<n<0 If n, is a positive integer the delay of the system, Shift the input sequence to the right by na samples to form the output If na is a negative integer: the system wi shift the input to the left by nd samples, corresponding to a time advance 1/30/2021 Zhongguo Liu_Biomedical Engineering_ Shandong Univ
23 1/30/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. EX. 2.2 The Ideal Delay System y[n] x[n nd ], n uIf 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 uIf is a negative integer: the system will shift the input to the left by samples, corresponding to a time advance. d n nd
EX 2.3 Moving Average ∑n-l M+M2+12 0+8p+4++-++小+p +.1+xn-M forn=7,M1=0,M2=5 xm n-5 0 n ummy lindex m
24 1/30/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. EX. 2.3 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 x[m] n m n-5 dummy index m for n=7, M1=0, M2=5 y[7]
Properties of Discrete-time systems 2.2 1 Memoryless(memory) system ◆ Memoryless systems: the output yn] at every value of n depends only on the input x[n] at the same value of n Example 2. 4 A Memoryless System z]=(xn]) 25 1/30/2021 Zhongguo Liu_Biomedical Engineering_ Shandong Univ
25 1/30/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Properties of Discrete-time systems 2.2.1 Memoryless (memory) system uMemoryless 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] Example 2.4 A Memoryless System
Properties of Discrete-time systems 22.2 Linear Systems nHTe] } ◆ and only If x+xT}一y+ additivity property homogeneity or scaling 同(齐)次性 propert principle of superposition xa[n]=ax, n+bxn +by In 1/30/2021 Zhongguo Liu_Biomedical Engineering_ Shandong Univ
26 1/30/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Properties of Discrete-time systems 2.2.2 Linear Systems uIf y n x1n 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 x1n x2n T{‧ } 1 2 additivity property homogeneity or scaling 同(齐)次性 property uprinciple of superposition uand only If: