山东大学：《生物医学信号处理 Biomedical Signal Processing》精品课程教学资源（PPT课件讲稿）Chapter 02 Discrete-Time Signals and Systems

Example of Linear System KEX. 2.5 Accumulator system y 以=∑x for arbitrary xIn and x2 k=-∞ y=∑x]y=∑x when x,/=ax,n+bx2I y=∑x=∑(ax]+bkl k ∑x]+b∑x]=q+b[ k k 1/30/2021 Zhongguo Liu_Biomedical Engineering_ Shandong Univ

27 1/30/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Example of Linear System uEx. 2.5 Accumulator system        n k y n x k          a x k b x k ay n by n y n x k ax k bx k n k n k n k n k 1 2 1 2 3 3 1 2                       n k y n x k 1 1        n k y n x k 2 2 x n and x n 1 2 for arbitrary x n ax n bx n when 3  1  2

Example 2.6 Nonlinear Systems Method: find one counterexample ◆For ◆ counterexample12+12≠=(+1) ◆For y7=10g( ◆ counterexample 10×1og101)≠1og10(10 28 1/30/2021 Zhongguo Liu_Biomedical Engineering_ Shandong Univ

28 1/30/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Example 2.6 Nonlinear Systems uMethod: find one counterexample   2 2 2 u counterexample 1 1  11     2 u For y n  x[n]   log  [ ] y n  10 x n 10 log 1 log 10 1  10  10  u counterexample u For

Properties of Discrete-time systems 2.2.3 Time-Invariant Systems Shift-Invariant Systems X,In r In=xuIn-n y2列=y1n=no 29 1/30/2021 Zhongguo Liu_Biomedical Engineering_ Shandong Univ

29 1/30/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Properties of Discrete-time systems 2.2.3 Time-Invariant Systems uShift-Invariant Systems     2 1 n n0 x n  x      2 1 0 y n  y n  n y n x1n T{‧ } 1 T{‧ }

Example of time-Invariant System Ex 2. 7 The accumulator as a Time-Invariant System y=∑x k =xn-no y=∑x]=∑水-n=∑xk]=yn=m k k k1 30 1/30/2021 Zhongguo Liu_Biomedical Engineering_ Shandong Univ

30 1/30/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Example of Time-Invariant System uEx. 2.7 The Accumulator as a Time-Invariant System        n k y n x k   1 0 x  x n  n           1 1 0 1 0 0 1 y n x k x k n x k y n n n n k n k n k             

EX2.8 The compressor system x[n - f y[n]=x[Mn] <n<0 yIn=xen y[n-1]=8[n-1]=x[2(n-1 0 =xM=xMm1≠y]=M(m-) 31 1/30/2021 Zhongguo Liu_ Biomedical Engineering_ Shandong Univ

31 1/30/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Ex. 2.8 The compressor system xn T{‧ } yn  xMn,    n   0 T{‧ } 0  n  2n  yn  x2n x1 n  xn  n0  0  n 1 T{‧ }  2n1 0 0 yn  n 0 yn1  n1 x2(n1) y1 n  x1 Mn  x Mn -n0    0    0     y n n x M n n