2.1 Discrete-Time Signals:Sequences Discrete-Time signals are represented as x=fxln), -oo<n<oo,n:integer Cumbersome, so just usexn In sampling of an analog signal x(t): xn=x,(nT),T:sampling period 1/T(reciprocal of T):sampling frequency 12 10/18/2022 Zhongguo Liu_Biomedical Engineering_Shandong Univ
12 10/18/2022 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 signal x-1,0网 x[-2] 。x[1] x(n] ◆x2] 7891011 -9-8-7-6-54-3-2-10123456$ Abscissa:continuous line x[n]:is defined only at discrete instants 13 10/18/2022 Zhongguo Liu_Biomedical Engineering_Shandong Univ
13 10/18/2022 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
x[n]=xa(t)li=nr=xa(nT) EXAMPLE Sampling the analog waveform 32 ms (a) lo 256 samples (b) 14 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,sample-by-sample,respectively x[n]+y(n]x(n]+y(n] sample-by-sample product of two sequences,respectively x[n],y(n] Multiplication of a sequence by a number a o·x[n] Delay (shift)of a sequence yIn =xn-no] n:integer 15 10/18/2022 Zhongguo Liu_Biomedical Engineering_Shandong Univ
15 10/18/2022 Zhongguo Liu_Biomedical Engineering_Shandong Univ. ◆Sum of two sequences, sample-by-sample,respectively ◆sample-by-sample product of two sequences,respectively ◆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] x[n]+ y[n]
Basic sequences ◆Unit sample sequence (discrete-time impulse, 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 函数(continuous-time unit impulse functionδ())。 Unit sample n 16 10/18/2022 Zhongguo Liu_Biomedical Engineering_Shandong Univ
16 10/18/2022 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) )