数字信号处理-讲义_2_2

DT Systemsin Time-domain
DSP MOOC Course
DSP: Discrete Signal and System in Time-
1/ 21
Discrete (Continuous) -time System
Discrete-time System:
x[n]
H
y[n] =H(x[n])
DT Systems in Time-
DSP MOOC Course
DSP: DiscreteSignalandSystemin Time-domain
6/ 21
Shift (time) Invariant
x[n]
H
y[n]
x[n−n0]
H
y[n−n0]
DT Systemsin Time-domain
12/ 21
...
LT I
y[n]
Impulse Resp.:
Shift Invariant:
Linearity:
δ[n] −→ h[n] δ[n −k] −→ h[n−k] x[k]δ[n−k] −→ x[k]h[n−k]
DT Systemsin Time-domain
x[n]
LTI
y[n]
Impulse Resp.: Shift Invariant:
δ [n] −→ h[n] δ [n−k] −→ h[n−k]
DT Systemsin Time-domain
DSP MOOC Course
DSP: Discrete Signal and System in Time-
DT Systemsin Time-domain
DSP MOOC Course
DSP: DiscreteSignalandSystemin Time-domain
4/ 21
Linearity
x1 [n] −H→ y1[n] x2[n] −H→ y2[n] αx1[n] + β x2[n] −→H αy1[n]+ βy2[n]
n−1
= ∑ x[l] + x[n] l=−∞
= y[n− 1]+ x[n]
x[n]
y[n]
z−1
DT Systemsin Time-domain
DSP MOOC Course
DSP: Discrete Signal and System in Time-
3/ 21
... properties
• Linearity • Shift (time) Invariant
《数字信号处理》：时域中的离散时间信号与系统
Digital Signal Processing: Discrete Signal and System in Time-domain
Discrete-time Systems inTime-domain
DSP MOOC Course
Outline
• Discrete-time System • LTI DT System
DSP MOOC Course
DSP: DiscreteSignalandSystemin Time-domain
12/ 21
... input-output relation
x[n]
LT I
y[n]
Impulse Resp.:
δ[n] −→ h[n]
Shift Invariant:
Continuous-time System:
x(t)
H
y(t)= H(x(t))
DT Systemsin Time-domain
DSP MOOC Course
DSP: DiscreteSignalandSystemin Time-domain
2/ 21
... accumulator
n
y[n] = ∑ x[l] l=−∞
此一时，彼一时、时过境迁、物是人非 少壮不努力，老大徒伤悲
A classical time-invariant system with physical mean is our COMPUTER!
DT Systemsin Time-domain
DSP MOOC Course
DSP: Discrete Signal and System in Time-
DT Systemsin Time-domain
DSP MOOC Course
DSP: DiscreteSignalandSystemin Time-domain
5/ 21
Example of Linearity
Linear system is very common, for instance • savings of your bank account • microphone • filtering .
10/ 21
LTI DT System
x[n]
LTI
y[n]
scale
addition
delay/shift
DT Systemsin Time-domain
DSP MOOC Course
DSP: DiscreteSignalandSystemin Time-domain
11/ 21
... input-output relation
x[n]
LTI
y[n]
Impulse Resp.:
δ [n] −→ h[n]
DT Systemsin Time-domain
DSP MOOC Course
DSP: DiscreteSignalandSystemin Time-domain
12/ 21
... input-output relation
DSP MOOC Course
DSP: DiscreteSignalandSystemin Time-domain
7/ 21
... time-variant
y[n] = H(x[n]) = x[−n]
DT Systemsin Time-domain
DSP MOOC Course
DSP: DiscreteSignalandSystemin Time-domain
8/ 21
... time-invariant
y[n] = H(x[n]) = x[n−n0] + ax[n]
DT Systemsin Time-domain
DSP MOOC
DSP: DiscreteSignalandSystemin Time-domain
9/ 21
... time-(in)variant