信号与系统习题课

8
System Properties
Linear, Causal, Time-invariant, Stable, Memoryless
• Ex. 2.3 (2011)
Determine the following signals which have finite total energy
9
System Properties
• Ex. 4.4 (2012)
Consider an LTI system whose input x[n] and unit impulse response h[n] are given by Determine the output of this system.
15
Convolution
27
2.23
Chapter 2
28
Chapter 2
2.24
29
Chapter 2
3.15
30
Chapter 2
3.34
31
Chapter 2
4.32
32
2
Signal Properties
Fundamental Period • Ex. 1.1 (2011’)
The fundamental period of
3
Signal Properties
Fundamental Period • Ex. 1.2 (2011’)
The fundamental period of the signal
x(t) 1
-1
0
1
t
6
System Properties
Linear, Causal, Time-invariant, Stable, Memoryless
• Ex. 2.1 (2012)
Consider a continuous-time system with input x(t) and output y(t) related by
Properties
• Ex. 5.2 (2012)
Let and
The Fourier series coefficients of x(t) may be ( )
19
Fourier Series
The output of an LTI system
• Ex. 5.1 (2011)
Consider a continuous-time LTI system whose frequency response H(jw) is illustrated in Fig.1. If the input is , determine the output.
22
Chapter 1
1.9
Determine whether or not each of the following signals is periodic. If yes, the fundamental period?
23
Chapter 1
1.17
The following system, causal? Linear?
• Ex. 4.2 (2011)
Tห้องสมุดไป่ตู้e convolution integral
14
Convolution
Sum----discrete-time signal
• Ex. 4.3 (2011)
Consider an LTI system whose input x[n] and unit impulse response h[n] are given by Determine the output of this system.
• Ex. 3.2 (2006’)
12
Properties of Delta function
• Ex. 3.3 (2007’)
• Ex. 3.4 (2012’)
13
Convolution
Integral----continuous-time signal
• Ex. 4.1 (2011)
The convolution integral
The output of an LTI system
• Ex. 2.4 (2012)
Consider an LTI system whose response to the signal in Fig.2 is the signal in Fig.3. Determine and sketch the response of the system to the input depicted in Fig.4
Properties
• Ex. 4.5 (2011)
Consider an LTI system with unit impulse response h(t) illustrated in Fig.1. If the input is , the output is
1 0 -1 1 2 t
16
-2
-1
Convolution
Properties
• Ex. 4.6 (2006)
17
Fourier Series
Properties
• Ex. 5.1 (2011)
Let and
The Fourier series coefficients of x(t) may be ( )
18
Fourier Series
24
Chapter 1
1.19
The following system, Linear? Time-invariant?
25
Chapter 1
1.27 (a)
Memoryless? Linear? Time-invariant? Causal? Stable?
26
Chapter 2
2.5
is an integer Determine the value of N, given that
Linear? Time-invariant? Causal? Memoryless? Stable?
7
System Properties
Linear, Causal, Time-invariant, Stable, Memoryless
• Ex. 2.2 (2011)
Which of the following systems are causal and stable systems?
2
1
1
1
0
1
2
t
0
1
t
-1
0
1
2
3
10
t
System Properties
The output of an LTI system
• Ex. 2.5 (2011)
1
1
1
0
1
2
t
0
1
t
0
1
2
3
t
11
Properties of Delta function
Sifting Property (筛选) • Ex. 3.1 (2011’)
4
Signal Properties
Fundamental Period • Ex. 1.3 (2007’)
The fundamental period of the signal
5
Signal Properties
Even and Odd • Ex. 1.4 (2012)
A continuous-time signal of it? is illustrated in Fig.1, the odd part
1
0
t
20
Signals and Systems
Exercise Lesson
(Part II) Youxin Lv & Junjie Wu
School of Electronic Engineering
21
Chapter 1
1.6 (a)
Determine whether or not each of the following signals is periodic.
Signals and Systems
Exercise Lesson
(Part I) Youxin Lv & Junjie Wu
School of Electronic Engineering
1
Main Points of Mid-term Exam
• Signal Properties ----Periodic, Even and Odd • System Properties ----Linear, Causal, Stable, Time-invariant, Memoryless • Properties of Delta function • Convolution ----Integral, Sum, Properties • Fourier Series ----Properties, System output of an LTI