Zheng Junli's "Signals and Systems" (3rd Edition) (Volume 2) Supporting Question Bank [Selected Real Questions + Chapter Question Bank]
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Part I Selected Real Questions for Examination and Research
1. Multiple choice questions
2. Fill-in-the-blank questions
3. Judgment questions
4. Draw pictures
5. Calculation questions
Part II Chapter Question Bank
Chapter 7: Time Domain Analysis of Discrete-Time Systems
Chapter 8: z-Domain Analysis of Z-Transforms, Discrete-Time Systems
Chapter 9: Discrete Fourier Transforms and Other Discrete Orthogonal Transformations
Chapter 10: Analog and Digital Filters
Chapter 11: Feedback Systems
Chapter 12: Analysis of State Variables in Systems
Hongbo Learning Network ———— all kinds of examination materials
Synopsis
This book is a companion question bank to Zheng Junli's "Signals and Systems" (3rd Edition) (Volume 2), which mainly includes the following:
The first part is a selection of real questions for the examination. This section selects the classic examination questions of key universities (such as Chinese Academy of Sciences, Shanghai Jiaotong University, Nanjing University, Huazhong University of Science and Technology, Beihang University, Beijing University of Posts and Telecommunications, Beijing Institute of Technology, Shandong University, Communication University of China, Sun Yat-sen University, Sichuan University, Xidian University, Nanjing University of Posts and Telecommunications, etc.) and provides detailed explanations. Through the exercises in this part, you can become familiar with the propositional style and difficulty of the real questions.
The second part is the chapter question bank. Combined with the real questions and examination priorities of many well-known colleges and universities in China, according to the chapters of the textbook, typical exercises are selected and detailed answer analysis is provided for candidates to strengthen their exercises.
1. Multiple choice questions
The period of 1 signal x[k]=2cos[πk/4]+sin[πk/8]-2cos[πk/2+π/6] is ( ). [Sun Yat-sen University 2010 Research Institute]
A．8
B．16
C．2
D.4
【Answer】B View the answer
【Analysis】 According to the definition of the period T=2π/ω, cos(πk/4), sin(πk/8), cos(πk/2+π/6) The minimum positive period is 8, 16, and 4, respectively, taking the smallest common multiple, so the period of x[k] is 16.
2 multiple choice sequences and
Equal to ( ). [Research Institute of Beijing Jiaotong University]
A．1
B.δ[k]
C.k u [k]
D.(k+1)u[k]
【Answer】D View the answer
【Parsing】By
Know.
3 sequences and
[Sun Yat-sen University 2010 Research Institute]
A.4u[k]
B．4
C.4u[-k]
D.4u[k-2]
【Analysis】Defined by the unit sample signal,
。 When k ≠ 2, the sequence value is constant 0; when k=2, the sequence value is 4, and therefore
4 The system described by the following difference equation is ( ). [Research Institute of Xidian University]
A.y(k)+y(k-1)=2f(k)+3
B.y(k)+y(k-1)y(k-2)=2f(k)
C.y(k)+ky(k-2)=f(1-k)+2f(k-1)
D.y(k)+2y(k-1)=2|f(k)|
【Answer】C View the answer
【Analysis】 Term A, the constant 3 appears on the right side of the equation. Item B, where item y(k-1)y(k-2) appears. Term D, |f(k) | these are nonlinear relationships.
5 Describes the difference equation for a discrete system as y(k)+y(k-1) = 2f(k)+f(k-1), where the unit response h(k) is equal to ( ). [Xidian University 2013 Research Institute]
A.δ(k)+(-1)kε(k)
B.δ(k)+ε(k)
C.2δ(k)-ε(k)
D.δ(k)-(-1)kε(k)
【Answer】A View the answer
【Analysis】 According to the definition of the unit response h(k), h(k)+h(k-1)=2δ(k)+δ(k-1), using the linear property to first find h(k)+h(k-1)=δ(k),h0(k)=C(-1)k,h0(0)=1, so C=1, that is, h0(k)=(-1)kε(k), Using the linear property, h(k)=2h0(k)+h0(k-1)=2(-1)kε(k)+(-1)k-1ε(k-1)=2(-1)kε(k)-(-1)k[ε(k)-δ(k)]=δ(k)+(-1)kε(k).
6 The waveforms of signals f1(t) and f2(t) are shown in Fig. 1-1-1, let y(t)=f1(t)*f2(t), then y(4) equals ( ). [Xidian University 2013 Research Institute]
Figure 1-1-1
A．2
C．6
D.8
【Analysis】The definition of using convolutional integrals
therefore
This is shown in Figure 1-1-2
Figure 1-1-2
7 tests to determine whether the sequence f(k)=2sin(πk/3)+3cos(πk/4) is a periodic sequence. If so, its period N is ( ). [Xidian University 2013 Research Institute]
A． Not a periodic sequence
B.是,n=24
C.是,n=12
D.是,N=8
【Analysis】 The period N1=2π/3 of 2sin(πk/3) is π 6,the period N2=2π/(π/4) of 2sin(πk/3) is a rational number, so N=3N2=4N1=24.
8 Set the initial state of the system to x(0), and the relationship between the full response of each system y(·) and the excitation f(·) and the initial state is as follows. The following systems are linear ( ). [Xidian University 2013 Research Institute]
A．
B．
C.y(k)=kx(0)+f(k)f(k-1)
D.y(k)=f(k)+f(k-1)+2x(0)+3
[Analysis] B term, does not meet the decomposition nature, that is, y(t) can not be decomposed into zero input response and zero state response, so it is a nonlinear system; C term, there is f(k)f(k-1), so it is a nonlinear system; D term, due to the existence of constant 3 is a nonlinear system.
【Summary】The linear nature satisfies the following three points:
(1) Decompositivity: The full response y(t) can be decomposed into the sum of the zero input response yzi(t) and the zero state response yzs(t), that is, y(t)=yzi(t)+yzs(t).
(2) Flush-off: including zero input response flush-time and zero-state response flush-off, that is, if x(0)→yzi(t), then ax(0)→ayzi(t), if f(t) →yzs(t), then af(t) → ayzs(t).
(3) Adductability: including zero input response adductability and zero state response adductability, that is, if x1(0)→yzi1(t), x2(0)→yzi2(t), then ax1(0)+bx2(0)→ayzi1(t)+byzi2(t), if f1(0)→yzs1(t), f2(0)→yzs2(t), then af1(0)+bf2(0)→ayzs1(t)+byzs2(t).
9 known a bilateral sequence
, whose Z is transformed into ( ). [Beijing University of Posts and Telecommunications, 2009 Research Institute]
A.z(a-b)/[(z-a)(z-b)],a<|z|<b
B.(-z)/[(z-a)(z-b)],|z|≤a,|z|≤b
C.z/[(z-a)(z-b)],a<|z|<b
D.(-1)/[(z-a)(z-b)],a<|z|<b
【Analysis】From the meaning of the title, according to the common Z transformation, it is obtained:
a<|z|<b
10 The Z transform F(z) of the known causal signal f(k) = 1/[(z+0.5)(z+2)], then the convergence domain of F(z) is ( ). [Xidian University 2010 Research Institute]
A.|z|>0.5
B.|z|<0.5
C.|z|>2
D.0.5<|z|<2
【Analysis】 The convergence domain of the causal signal is in the form of | z|>a, and the convergence domain cannot contain poles. The poles of F(z) are z=-0.5 and z=-2, so the convergence domain of F(z) is |z|>2.
11 Known z transform of x(n)u(n) is X(z), then
The Z transformation Y(z) is ( ). [Beihang University 2007 Research Institute]
A.X(z)/(z+1)
B.zX(z)/(z+1)
C.X(z)/(z-1)
D.zX(z)/(z-1)
E． None of them
【Analysis】Use and function z transformation formula
Can.
12 For linearly shifted invariant discrete-time systems, the following statement is erroneous ( ). [Southeast University Research]
A． The poles are all within the z-plane unit circle is a stable system
B． The convergence domain, which includes the unit circle, is the stable system
C． The convergence domain is a system of ring-like regions that are non-causal
D． The unit function responds unilaterally to a causal system
【Analysis】 Item A, the poles are in the z-plane with the origin as the center of the circle within the circle is a stable system. Defined by a power-finite signal: if the average power of the signal f(t) satisfies 0<p<∞ (and E= ∞), f(t) is called a power signal.
13x(n)=a|n|, a is a real number, and the convergence domain of X(z) is ( ). [Sun Yat-sen University 2018 Research Institute]
A.|a|<1,|z|>|a|
B.|a|>1,|z|<1/|a|
C.|a|<1,|a|<|z|<1/|a|
D.|a|>1,|a|<|z|<1/|a|
[Analysis] According to the title, it can be obtained that x(n) is actually a bilateral sequence. Its corresponding expression is:
So the corresponding z transforms to
The answer is selected option C.
The period of the 14 signal x(n)=sin(nπ/4)-2cos(nπ/6) is ( ). [Research Institute of Beijing University of Posts and Telecommunications]
B．24
C.12p
D.12
【Analysis】The period of sin(nπ/4) is 8, the period of cos(nπ/6) is 12, and the two parts are in the form of addition, so the period is the least common multiple of the two cycles, that is, 24.
The period of the 15 sequence x[n]=sin(5πn/6) is ( ). [Huazhong University of Science and Technology 2009 Research Institute]
A．10
B．12
C．15
D.30
【Analysis】 Since 2π/(5π/6) = 12/5, and because the sequence period is an integer, the solved period is 12/5×5=12.
16 A signal is known to have power frequency interference and is usually removed with ( ). [Sun Yat-sen University 2018 Research Institute]
A． Low-pass filter
B． High-pass filter
C． Band-pass filter
D． Trap filters
【Analysis】ABC term, the main role of the low-pass filter, the high-pass filter and the pass filter is that the purposeful artificial selection of useful frequency range segments, according to the cutoff frequency to retain the desired frequency range, generally a certain frequency band, so the three options are wrong. Term D, a trap filter is a filter that can rapidly attenuate the input signal at a certain frequency point to prevent the signal from passing through this frequency. The power frequency interference is a single frequency of 50Hz, so a trap filter is selected.
17 Known causally stable systems H(z) and G(z) are both minimal phase, it is possible that which of the following systems is not the least phase ( ). [Communication University of China 2017 Research Institute]
A.H(z)G(z)
B.H(z)+G(z)
C.H(z)/G(z)
D.1/[H(z)G(z)]
【Analysis】The zero poles of the smallest phase of the discrete system are located within the unit circle, but the zero poles of H(z)+G(z) may appear outside the unit circle, and the multiplication and division operation will not bring this effect, so the answer is B.