信号与系统习题课

-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
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
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
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
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
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?
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?
• 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
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
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
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
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’)
• 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
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
1
0
t
20
Signals and Systems
Exercise Lesson
(Part II) Youxin Lv & Junjie Wu
School of Electronic Engineering
21
Chapter 1
1.源自文库 (a)
Determine whether or not each of the following signals is periodic.
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
• Ex. 4.2 (2011)
The 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.
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.