EENG21000 SIGNALS AND SYSTEMS 2019
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January/February 2019
EENG21000
SIGNALS AND SYSTEMS
(a) 
Determine which of the following properties hold and which do not hold for systems (i) and (ii). Justify you answers.
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Properties |
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Systems |
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1. |
Memoryless |
(1 mark) |
i) |
y\n\ = n x\n\ |
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2. |
Causal |
(1 mark) |
ii) |
仰)=腿-1) |
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3. |
BIBO Stable |
(1 mark) |
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4. |
Linear |
(2 marks) |
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5. |
Time invariant |
(2 marks) |
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(14 marks)
(b) Consider the cascade interconnection of three causal LTI systems shown in Figure 1. The impulse response h^\n\ is: h^[n\ = u\n\ - u\n - 2] where 〃[〃] is the discrete-time unit step function.
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The overall impulse response is as shown in Figure 2:
10
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-1 01234567
Figure 2
i) Find the impulse response hi[n]
ii) Find the response of the overall system to the input: x\n\ = d\n\ - 8\n-\]
6 marks)
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Q2 (a) |
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A discrete-time linear system is described by the following difference equation |
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y\n\ — 0.9y[n-1] + 0.81y[n-2] = x\n\ + 1.1x[n-1] |
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What is the transfer function of this system? Comment on the stability of this system (3 marks) |
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Sketch a block diagram fbr the system described by the above difference equation |
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(3 marks) |
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Determine the frequency response of this system and sketch the normalised amplitude response. |
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(5 marks) |
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Sketch the pole-zero plot of the following transfer functions. By considering the geometric interpretation of the magnitude of the Fourier transform from the pole-zero plot, determine whether the corresponding system has an approximately lowpass, bandpass, or highpass frequency response. |
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(9 marks)
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The block diagram of a continuous time system is shown in Figure 3 where X(s) and Y(s) are the Laplace transforms of the input and output signals respectively.
(a) Find the system transfer function
(4 marks)
(b) Determine the value of 知 and % when the poles of this system are at s = 1 and s = -5. Comment on the stability of the system
(5 marks)
(c) Draw the system pole-zero plot and comment on the stability for ki=6 and k?=25
(5 marks)
(d) Find the impulse response of this system for ki=6 and k?=25
(6 marks)
2023-01-11