MATLAB Questions and Answers – Z Transform – 2

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This set of MATLAB Puzzles focuses on “Z Transform – 2”.

1. The unit delay operator can be thought of in the z-domain as ___________
a) Multiplication by z-1
b) Multiplication by z
c) Multiplication by z-2
d) Multiplication by z2
View Answer

Answer: a
Explanation: If a signal is delayed by one unit in time, the Z-transform of the resultant signal is the Z-transform of the original signal which gets multiplied by z-1. Hence, the correct option is Multiplication by z-1.
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2. The convolution of a signal in time domain can be viewed as __________
a) Multiplication in z-domain
b) Squaring in z-domain
c) Doubling the signal in z-domain
d) Convolution in z-domain
View Answer

Answer: a
Explanation: This is observed from the fact that a signal can be represented as a summation of impulses and while we perform convolution in a time domain, we can represent the entire output in the form of z-n.

3. The impulse response of a discrete time system is the inverse Z-transform of the transfer function of the system in z-domain.
a) True
b) False
View Answer

Answer: a
Explanation: The Z-transform of the impulse response of discrete time system gives the transfer function of the system in z-domain. This can also be achieved from the impulse invariance transformation. Hence, the converse should be true and the above statement is true.
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4. What will be seen in the scope if the step time is 1 second in the following Simulink Model?
matlab-puzzles-q4
a) A unit step signal delayed by 2 units in time
b) u[n-3]
c) A ramp function
d) An impulse function
View Answer

Answer: b
Explanation: Since the step time is 1, the input step signal is delayed by 1 unit already. Moreover, multiplying the signal by z-2 delays the signal further by 2 units.

5. What will be seen in the scope if the step time is 0 seconds in the following Simulink Model?
matlab-puzzles-q4
a) A unit step signal delayed by 2 units in time
b) u[n-3]
c) A ramp function
d) An impulse function
View Answer

Answer: a
Explanation: The delay block will delay the signal by 2 units in time.
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6. What will be seen in the Scope if the step time is 0 seconds in the following Simulink Model and the limit of x axis is n=10?
matlab-puzzles-q6
a) A delayed ramp function
b) r[n-1]
c) r[n-2]
d) Error
View Answer

Answer: b
Explanation: The output of the transfer function has a the function r[n+1] and it gets delayed by two units in time to become r[n-1]. This is why the Display of the model shows 9 at n=10.

7. How much does the delay change, if the step time is taken as two units in time, in r(t-m), in scope 1 and 3?
matlab-puzzles-q7
a) 1 and 3
b) 2 and 3
c) 3 and 1
d) Error
View Answer

Answer: a
Explanation: In scope 1, the input of the Transfer function block is u(t-2) and the step response leads to multiplication in z-domain which shows that the ramp output gets advanced by 1 unit and the result of scope1 is r(t-1). After going through Delay of z-2, the output is r(t-3).
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8. This is the output of scope1.
matlab-puzzles-q8
What is the transfer function1?
a) z/(z-1)2
b) z2/(z-1)2
c) A parabola
d) A impulse function
View Answer

Answer: a
Explanation: Since the output of scope 1 is a parabola and it has come from a system where the step response is seen at the output. Now, the step response is the convolution of a step signal with the impulse response of the system. In z domain, the step response becomes the product of the z-domain step signal and the transfer function of the system in z domain. Hence, it should be a ramp function whose transfer function is given by a. Option z2/(z-1)2 cannot be the answer since the graph shows the output delayed by 1 unit in time while option z2/(z-1)2 would’ve made the graph advance by 2 units in time.

9. The Discrete Transfer Fcn1 is using a ramp function.
matlab-puzzles-q9
a) True
b) False
View Answer

Answer: a
Explanation: The three delays received by the output of the transfer function suggests that the response of the transfer function is a parabola itself. Thus the above statement is necessary for this case.
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10. What will be seen in the scope?
matlab-puzzles-q10
a) A ramp function
b) A step function
c) A parabola
d) A hyperbola
View Answer

Answer: a
Explanation: The transfer function is a step function and the step response of a step function is a ramp function. Hence, the output in the scope is just a ramp function.

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