2.1 Discrete-Time Signals: Sequences Discrete-Time signals are represented as x=nj) 00<n<∞,n: Integer Cumbersome, so just use xIn OIn sampling of an analog signal xat) xn=x(nr), T: sampling period ◆1/T(〔 reciprocal of T): sampling frequency 2/6/2021 Zhongguo Liu_Biomedical Engineering_shandong Univ
12 2/6/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. 2.1 Discrete-Time Signals: Sequences ◆Discrete-Time signals are represented as ◆In sampling of an analog signal xa (t): ◆1/T (reciprocal of T) : sampling frequency x =xn, − n , n:integer xn= xa (nT), T :sampling period Cumbersome, so just use x n
Figure 2.1 Graphical representation of a discrete-time signa -2 2 7891011 94-7-6-54-3-2-10123456 Abscissa continuous line is defined only at discrete instants 2/6/2021 Zhongguo Liu_ Biomedical Engineering_ shandong Univ
13 2/6/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Figure 2.1 Graphical representation of a discrete-time signal Abscissa: continuous line x n : is defined only at discrete instants
rI n x(t C t=nt x, (nT) EXAMPLE Sampling the analog waveform 32m 256 samples (b) Figure 2.2
14 Figure 2.2 EXAMPLE Sampling the analog waveform x[n] x (t) | x (n T ) = a t =n T = a
Basic Sequence Operations ◆ Sum of two sequences xn+yn Product of two sequences x{n]·yn] Multiplication of a sequence by a number a a·x[m] Delay shift) of a sequence n=xIn-n Integer 2/6/2021 Zhongguo Liu_Biomedical Engineering_shandong Univ
15 2/6/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. ◆Sum of two sequences ◆Product of two sequences ◆Multiplication of a sequence by a number α ◆Delay (shift) of a sequence Basic Sequence Operations x[n]+ y[n] [ ] [ ] :integer n n0 n0 y n = x − x[n] y[n] x[n]
Basic sequences ◆ Unit sample sequence (discrete-time impulse, S/1sJo ≠0 n=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 8(t))o Unit sample 16 2/6/2021 Zhongguo Liu_Biomedical Engineering_shandong Univ
16 2/6/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Basic sequences ◆Unit sample sequence (discrete-time impulse, impulse, Unit impulse) = = 1 0 0 0 n n n ◆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) )