MATLAB Multiple Choice Questions on “Impulse Response – 2”.
1. The impulse response does not take account of the transient response of the system.
a) True
b) False
Answer: b
Clarification: Since the output of a system depends on int’s initial conditions, the laplace transform of the output would depend on the transient conditions. Hence, the impulse response of the system does take account of the transient response of the system.
2. The impulse response of a parabola _________
a) will have 3 poles in the s-plane
b) will have 2 poles in the s-plane
c) will have 4 poles in the s-plane
d) will have no poles in the s-plane
Answer: a
Clarification: The transfer function of a system, whose impulse response is a parabola, will have three roots which will satisfy the characteristic equation. Hence, only option will have 3 poles in the s-plane is correct.
3. The impulse response of a sinusoid ________
a) will have 2 poles in the s-plane
b) will have 3 poles in the s-plane
c) will have 1 pole frequency in the s-plane
d) will have only 1 conjugate pole in the s-plane
Answer: a
Clarification: The transfer function of the system, whose impulse response is a sinusoid, will have 2 roots which satisfy the characteristic equation. Hence, there will be two poles which are complex conjugate to each other.
4. The step response of the impulse response of a ramp function will be ________
a) a parabolic function
b) an exponential function
c) a sinusoidal function
d) a sinc function
Answer: a
Clarification: The step response of a system can be thought in the Laplace domain as multiplication with 1/s. Now, the impulse response of ramp function is the ramp function itself while the step response of ramp function results in a parabola.
5. In MATLAB, the impulse response of the step response of a system is ___ to the step response of the impulse response of the system.
a) Equal
b) Not Equal
c) Greater
d) Lesser
Answer: a
Clarification: The distributive property of convolution suggests that the A*(B*C)=(A*B)*C. Thus only option Equal is correct.
6. The impulse response of the transfer function 1 is ________
a) an impulse function
b) a step function
c) a pulse function
d) cannot be determined
Answer: a
Clarification: The laplace transform of only the impulse function is 1. Hence, the inverse laplace transform.
7. What is the output of the following code?
>>p=ilaplace(1); >>laplace(p)
a) 1
b) Impulse function
c) Error
d) Cannot be determined
Answer: c
Clarification: The ilaplace command doesn’t take double as an input. This would lead to an error and the correct option is Error.
8. What is the output of the following code?
>>p=ilaplace(s/s); >>laplace(p)
a) dirac(1,t)
b) dirac[1,t]
c) dirac{1,t}
d) Cannot be determined
Answer: a
Clarification: The ilaplace command observes that the input is actually 1. The inverse laplace transform of 1 is the impulse function which is represented as dirac(1,t) in MATLAB.
9. What is the output of the following code?
>>t=(0:17); >>o=dirac(t)==Inf; >>q=o*1; >>conv(q,t)
a) t followed with 17 zeros
b) t followed with 18 zeros
c) 1
d) Error
Answer: a
Clarification: In the above code, we’ve actually performed the impulse response of discrete system defined by a ramp function for [0,17]. Now, the output of the code is shown below which shows that the impulse function gets shifted for the time t and the total result of the convolution will be the entire value. Notice that the length of the convolution is 2N-1=35.
Output:
10. The impulse response is the result of the transfer function of the system.
a) True
b) False
Answer: b
Clarification: The impulse response is truly due to the impulse input given to a system. If we would’ve changed the input, the output would’ve been a different and the resulting expression in laplace domain will not be called the transfer function.
11. What is the output of the following code?
>>t=(0:17); >> p=dirac(0)==Inf; >> q=p*1; >> conv(q,t)
a) An impulse response of step for a time from 0:16
b) An impulse response of unit ramp function for a time from 0:17
c) An impulse response of ramp function for a time from 0:18
d) Error in 3rd line
Answer: b
Clarification: The function p exists for only t=0 and q has only 1 element in it which is 1. So, truly, we’ve derived the convolution of a system which results in a ramp function whose slope is 1 and is ranging from 0 to 17 units in time since t is defined as such.
Output:
12. What is the output of the following code?
>> p=dirac(0)==Inf; >> t=(0:.001:17); >> q=p*1; >> conv(q,sin(2*pi*t)); >> plot(t,ans)
a) A sinusoid of a frequency 1Hz
b) A sinusoid of a frequency of 17 Hz
c) A sinusoid of a frequency of .001 Hz
d) Error
Answer: a
Clarification: We’re only computing the impulse response of a system which behaves as a sinusoid on the input. The frequency of the system is 1 Hz as seen from the description. The output, shown below, contains 17 cycles.