MATLAB Questions and Answers – Z Transform – 1

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This set of MATLAB Multiple Choice Questions & Answers (MCQs) focuses on “Z Transform – 1”.

1. What is the output of the following code?

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ztrans(1,z)

a) 1/z-1
b) 1/z+1
c) z/(z-1)
d) z/(z+1)
View Answer

Answer: c
Explanation: The Z-transform of 1 or unit signal is simply z/(z-1). Hence, the correct option is z/(z-1).
Output: z/(z-1)

2. What is the output of the following code?

syms n;ztrans(2^n,z)

a) z/(z-2)
b) z/(z+2)
c) z/(2-z)
d) z/(2+z)
View Answer

Answer: a
Explanation: If the discrete signal, x[n], gets multiplied by a^n where a is an integer, the z transform of the resultant signal becomes X(az-1). Hence, in the above case- the Z-transform of 2n is actually the Z-transform of 2nu[n]; since the Z-transform of u[n] is z/(z-), the Z-transform of 2nu[n] becomes z/(z-2).
Output: z/(z-2)

3. What is the output of the following code?

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ztrans('[1 0 1 0 1]',z)

a) [ z/(z – 1), 0, z/(z – 1), 0, z/(z – 1)]
b) [ z/(z + 1), 0, z/(z – 1), 0, z/(z – 1)]
c) [ z/(z – 1), 0, z/(z – 1), 0, z/(z -+1)]
d) [ z/(z + 1), 0, z/(z – 1), 0, z/(z + 1)]
View Answer

Answer: a
Explanation: When the ztrans command gets such inputs, it calculate the Z-tranform of each element present in the vector. Hence, the correct answer should only be option [ z/(z – 1), 0, z/(z – 1), 0, z/(z – 1)] since the Z-transform of 1 or u[n] is z/(z-1).
Output: [ z/(z – 1), 0, z/(z – 1), 0, z/(z – 1)]

4. What is the output of the following code?

>>syms s;
>> ztrans('n',s)

a) s/(s-1)2
b) ns/(s-1)2
c) s/(ns-1)2
d) Error
View Answer

Answer: a
Explanation: The Z-transform of n*xx[n] is (-z ddz)m * X(z) where X(z) is the Z transform of x[n]. Here, x[n] is unit step function whose Z-transform is z/z-1. After differentiating it and multiplying it with -z, we get s/(s-1)2 with the variable changed to s since it has been specified in the ztrans command after the function is given as an input.
Output: s/(s-1)2

5. What is the output of the following code?

>> ztrans('n',s)

a) s/(s-1)2
b) ns/(s-1)2
c) Error
d) s/(s+1)2
View Answer

Answer: c
Explanation: We have not initialized s as symbolic, MATLAB won’t be able to realize the variable s which has been given as an input to the ztrans command. Thus, this leads to an error. If s was defined symbolic, the answer would’ve been s/(s-1)2.
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6. What is the output of the following code?

ztrans([1,2,3 4*z],z)

a) [ z/(z – 1), (2*z)/(z – 1), (3*z)/(z – 1), (4*z)/(z – 1)2]
b) [ z/(z + 1), (2*z)/(z + 1), (3*z)/(z + 1), (4*z)/(z – 1)2]
c) [ z/(z – 1), (2*z)/(z – 1), (3*z)/(z – 1), (4*z)/(z + 1)2]
d) [ z/(z – 1), (2*z)/(z – 1), (3*z)/(z – 1) (4*z)/(z – 1)2]
View Answer

Answer: a
Explanation: The ztrans command computes the Z-transform of every element. In doing so, the output it returns are separated by commas.
Output: [ z/(z – 1), (2*z)/(z – 1), (3*z)/(z – 1), (4*z)/(z – 1)2]

7. The R.O.C. of impulse function is _________
a) The entire z-plane
b) Interior to the unit circle |z|=1
c) Exterior to the unit circle |z|=1
d) Between the unit circle |z|=1 and |z|=∞
View Answer

Answer: a
Explanation: The impulse function has a Z-transform equal to 1.Since it is independent of z, it exists for all values of z. Hence, the Z-transform converges for all values of z. Thus, the R.O.C. of impulse function is the entire z-plane.

8. What is the output of the following code?

ztrans(exp(2*n),z)

a) z/(z – exp(2))
b) z/(z – exp(-2))
c) z/(z + exp(-2))
d) z/(z + exp(2))
View Answer

Answer: a
Explanation: The Z-transform of eanT*u[n] is z/(z-enT). exp(2*n) is taken as e2nu[n] whose Z-transform is given by option z/(z – exp(2)).
Output: z/(z – exp(2))
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9. The bilateral Z-transform ranges from ____________
a) -∞ to ∞
b) 0 to ∞
c) -∞ to 0
d) Does not exist
View Answer

Answer: a
Explanation: Unilateral Z-Transform ranges are provided in 0 to ∞ and -∞ to 0. For Bilateral Z-transform the signal can be defined in the range given in option -∞ to ∞.

10. The R.O.C. of a unit step function is __________
a) |z|>|1|
b) Entire z plane except z=0
c) Entire z plane except z=∞
d) Does not exist
View Answer

Answer: a
Explanation: The unit step function is a causal infinite duration signal. The R.O.C. of anu[n] is |z|>|a|. For a unit step function, a=1 and thus the R.O.C. is given by option only.

11. What is the relationship b/n laplace transform and z-transform of a function?
a) Impulse invariant transformation
b) z=e-sT
c) s=jw
d) s=σ
View Answer

Answer: a
Explanation: The Z-transform of a signal at z=esT yields the Laplace transform of the signal. This method of transformation is called Impulse Invariant Transformation.

12. If σ<0, the point in the z plane lies __ of the circle |z|=1.
a) Interior
b) Exterior
c) On the circumference
d) Nowhere near
View Answer

Answer: a
Explanation: For σ<0, |z| is less than 1. Hence, the point lies interior to the circle |z|=1.

13. What is the T in the relation z=esT?
a) Sampling Period
b) Time Period
c) Normal Period
d) Average Period
View Answer

Answer: a
Explanation: This equation is used to transform the signal from Laplacian domain to z domain. Here, T refers to the sampling period since the entire signal needs to be sampled at a period of T to be expressed in the z-domain.

14. The Z-transform is only for discrete signals.
a) True
b) False
View Answer

Answer: a
Explanation: The signal needs to be a sampled sequence so that it can be represented in terms of the complex frequency z. Hence, the above statement is true.

15. The Z-transform doesn’t follow the linearity principle.
a) True
b) False
View Answer

Answer: b
Explanation: The Z-transform does follow the principles of homogeneity and superposition. Hence, the linearity principle can be applied to check if a system is linear or not in the z-domain.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn