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

xin]=xa(t)nr=xa(nT) EXAMPLE Sampling the analog waveform △A 32 (a) 256 samples (b) Figure 2.2

7 Figure 2.2 EXAMPLE Sampling the analog waveform x[n] x (t) | x (nT)  a tnT  a

Basic Sequence operations ◆ Sum of two sequences xln+ vln Product of two sequences x{nm]·y{n] Multiplication of a sequence by a number a a·x[n] Delay shift) of a sequence yIn=xn-nol no: integer 8 1/30/2021 Zhongguo Liu_Biomedical Engineering_ Shandong Univ

8 1/30/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. uSum of two sequences uProduct of two sequences uMultiplication of a sequence by a number α uDelay (shift) of a sequence Basic Sequence Operations x[n] y[n] [ ] [ ] :integer 0 0 y n  x n  n n x[n] y[n]   x[n]

Basic sequences ◆ Unit sample sequence 0n≠0 (discrete-time impulse, o(n H=0 impulse, Unit impulse) ◆离散时间单位脉冲(样本)序列,区别连续时间单位冲激 EK=(continuous-time unit impulse function &(t)) Unit sample 1/30/2021 Zhongguo Liu_Biomedical Engineering_ Shandong Univ

9 1/30/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Basic sequences uUnit sample sequence (discrete-time impulse, impulse, Unit impulse)         1 0 0 0 n n  n u离散时间单位脉冲(样本)序列, 区别连续时间单位冲激 函数(continuous-time unit impulse function δ(t) )

Basic sequences 4-20134568n 2 A sum of scaled delayed impulses =a3Dn+]+aoz-1]+a6-2]+a ◆ arbitrary sequence xm=∑xk[m-k k 10 1/30/2021 Zhongguo Liu_Biomedical Engineering_ Shandong Univ

10 1/30/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Basic sequences [ ] [ ] [ ] k x n x k  n k      uarbitrary sequence    3  1  2  7 p n  a 3 n   a1 n   a2 n   a7 n  A sum of scaled, delayed impulses

Basic sequences 1n≥0 AUnit step sequence unI 0n<0 nit step 6[k 10. when n <0 n=∑[k ,henn≥0 0k≠0 k=-∞ since s k=0 l]=8团]+8[n-11+6{m-2]+…=∑8[n-k k=0 an=uln-uln-l First backward difference 1/30/2021 Zhongguo Liu_Biomedical Engineering_ Shandong Univ

11 1/30/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Basic sequences uUnit step sequence       0 0 1 0 [ ] n n u n [ ]   n k u n  k    0 [ ] [ ] [ 1] [ 2] [ ] k u n  n  n  n  n k             [n]  u[n]u[n 1] First backward difference       0, 0 , 1, 0 0 0 1 0 since n k when n k when n k k k                