# 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?

`ztrans(1,z)`

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

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)
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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)

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)
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3. What is the output of the following code?

`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)]

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

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

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.

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]

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|=∞

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))

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))

9. The bilateral Z-transform ranges from ____________
a) -∞ to ∞
b) 0 to ∞
c) -∞ to 0
d) Does not exist

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

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

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

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

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

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

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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