Free Printable EC 8352 SS IAT#3

1.

Compute the ZT of a DT signal x(n)= (1,2,3,4,0,1)

a)

1 + 2z + 3z² + 4z³ + z⁴

b)

1 + 2z + 3z² + 4z³ + z⁵

c)

1 + 2z^-1 + 3z^-2 + 4z^-3 + z^-5

d)

1z² + 2z + 3 +z^-1 + z^-3

2.

Z-transform of an impulse function is……

a)

z

b)

z²

c)

1

d)

z³

3.

The two signal x(n) = aⁿ u(n) and x(n) = -aⁿ u(-n-1) have ROC z>a and z<a respectively.

a)

True

b)

False

4.

The Dirichlet condition for (DTFT) is……

a)

DT Signal should be absolutely differentiable

b)

DT Signal should be absolutely multipliable

c)

DT Signal should be absolutely integrable

d)

DT Signal should be absolutely summable

5.

Fourier Transform is used to analyse any elementary signals at different frequencies due to?

a)

Convert from time domain to frequency domain

b)

Convert from frequency domain to time domain

c)

Both a & b

d)

None of the above

6.

If x(n) is a DT signal then the equation x (n – n₀ ) indicates the basic ………..property.

a)

Linearity

b)

Time Reversal

c)

Frequency Shifting

d)

Time Shifting

7.

If [x(n)↔X(z)] and [y(n)↔Y(z)]. The linearity property of Z-Transform states

a)

ax(n)+by(n) ↔ aX(z).bY(z)

b)

ax(n).by(n) ↔ aX(z)+bY(z)

c)

ax(n)+by(n) ↔ aX(z)+bY(z)

d)

ax(n).by(n) ↔ aX(z).bY(z)

8.

If FT{x₁(n)}=X₁(w) and FT{x₂(n)}=X₂(w) then FT{x₁(n)*x₂(n)}=?

a)

X₁(w).X₂(w)

b)

X₁(w)+X₂(w)

c)

X₁(w)*X₂(w)

d)

None of the mentioned

9.

What is the convolution x(n) of the signals x₁(n)={-1,0,1} and x₂(n)={1,0,1,0,1,2} ?

a)

{1,1,0,0,0,0,1,2}

b)

{-1,0,0,0,0,-2,1,2}

c)

{-1,1,0,0,0,0,1,-2}

d)

{1,-1,0,0,0,0,-1,2}

10.

Determine the Nyquist rate and Nyquist interval for Cos(4πt).

a)

4 Hz, 0.25 sec

b)

0.5 Hz, 0.5 sec

c)

0.5 Hz, 2 sec

d)

2 Hz, 0.5 sec

11.

The Nyquist theorem for sampling (choose from arguments given below)

1) Converts time domain to frequency domain

2) Helps in quantization

3) Limits the bandwidth requirement

4) Provide the spectrum of the signal

a)

only 3 is correct

b)

1 and 2 are correct

c)

1 and 3 are correct

d)

All the four are correct

12.

Region of Convergence is defined as

a)

Value of z for which the z transform converges

b)

Value of frequency for which the z transform exists

c)

range of frequency for which the signal gets transmitted

d)

range in which the signal is free of noise

13.

A discrete time system is said to causal and Linear Time Invariant when

a)

Its ROC covers outside the largest pole

b)

Its ROC covers inside the largest pole

c)

Its ROC covers outside the unit circle

d)

Its ROC covers inside the unit circle

14.

The causal sequences have ______ components in the right hand sequences.

a)

Positive

b)

Negative

c)

Both a and b

d)

None of the above

15.

Find x(∞) if X(z) = Z/(z−0.5)²

a)

1

b)

0.5

c)

∞

d)

0

16.

The DTFT is used to

a)

convert frequency spectrum domain to discrete time domain

b)

convert discrete time domain to continuous frequency

spectrum domain

c)

convert analog signal to digital signal

d)

convert digital signal to analog signal

17.

What is the DTFT of the four point sequence x(n)={1,0,1,0}?

a)

{-2, 0,-2,0}

b)

{2,-2-2j,2,-2+2j}

c)

{2,-2+2j,-2,-2-2j}

d)

{2,0,2,0}

18.

Given that W=e^-i(2π/N) , where N=3. Then F=W^N can be computed as F=

a)

0

b)

1

c)

-1

d)

e

19.

The circular convolution of two sequences in time domain is equivalent to

a)

Multiplication of DFTs of two sequences

b)

Summation of DFTs of two sequences

c)

Difference of DFTs of two sequences

d)

Square of multiplication of DFTs of two sequences

20.

The time system which operates with a continuous time signal and produces a continuous time output signal is

a)

CTF system

b)

DTF System

c)

Time invariant System

d)

Time variant System

21.

Discrete or continuous data?

a)

Discrete

b)

Continuous

22.

The transforming relations performed by DTFT are

1)Linearity

2) Modulation

3) Shifting

4) Convolution

a)

1, 2 and 3 are correct

b)

1, and 2 are correct

c)

1 and 3 are correct

d)

All the four are correct

23.

The fourier transform is also called the analysis of discrete time signal x(n)

a)

True

b)

False

24.

The Fourier Transform of a signal is also called

a)

Frequency Spectrum

b)

Phase Spectrum

c)

Signal Spectrum

d)

None of the Above

25.

The Fourier Transform of a discrete time signal is periodic with period 2 $\pi$

a)

True

b)

False

26.

The overlap of frequency spectrum is called

a)

Band Of frequency

b)

Aliasing

c)

Sampling

d)

None of the Above

27.

Due to Aliasing the information shifts from one band of frequency to another band of frequency

a)

True

b)

False

28.

The Fourier series representation can be obtained only for______ Discrete time signals.

a)

Periodic

b)

Nonperiodic

c)

Both periodic and non periodic

d)

None

29.

The Fourier transform technique can be applied to ______ discrete time signals.

a)

Periodic

b)

Non Periodic

c)

Both Periodic and Non periodic

d)

NOne

30.

The z – transform of a system is 𝐻(𝑧) = 𝑧 /𝑧 − 0.2 If the ROC is |𝑧| < 0.2, then the impulse response of the system is

a)

(a) (0.2)^ 𝑛 𝑢[𝑛]

b)

(b) (0.2)^2 𝑢[−𝑛 − 1]

c)

(c) −(0.2) ^2 𝑢[𝑛]

d)

(d)−(0.2)^ 𝑛 𝑢[−𝑛 − 1]

31.

According to Time shifting property of z -transform, if X(z) is the z -transform of x(n) then n what is transform of x(n-k)?

a)

Z^k X(Z)

b)

Z^-k X(Z)

c)

X(Z-k)

d)

X(Z+k)

32.

A real valued signal x(n) is called as anti-symmetric if

a)

a) x(n)=x(-n)

b)

b) x(n)=-x(-n)

c)

c) x(n)=-x(n)

d)

d) None of the mentioned

33.

Consider the z – transform 𝑋(𝑧) = 5𝑧 ² + 4𝑧 −1 + 3; 0 < |𝑧| < ∞. The inverse z – transform 𝑥[𝑛] is

a)

(a) 5𝛿[𝑛 + 2] + 3𝛿[𝑛] + 4𝛿[𝑛 − 1]

b)

(b)5𝛿[𝑛 − 2] + 3𝛿[𝑛] + 4𝛿[𝑛 + 1]

c)

(c) 5𝑢[𝑛 + 2] + 3 𝑢[𝑛] + 4 𝑢[𝑛 − 1]

d)

(d)5𝑢[𝑛 − 2] + 3 𝑢[𝑛] + 4 𝑢[𝑛 + 1]

34.

Two discrete time systems with impulse responses ℎ1 [𝑛] = 𝛿[𝑛 − 1] and ℎ2 [𝑛] = 𝛿[𝑛 − 2] are connected in cascade. The overall impulse response of the cascaded system is

a)

(a) 𝛿[𝑛 − 1] + 𝛿[𝑛 − 2]

b)

(b)𝛿[𝑛 − 4]

c)

(c) 𝛿[𝑛 − 3]

d)

(d)𝛿[𝑛 − 1] 𝛿[𝑛 − 2]

35.

The region of convergence of the Z-Transform of the signal 2 ^n u(n) − 3^n u(−n − 1) is

a)

(a). ӏzӏ>1

b)

(b). ӏzӏ<1

c)

(c). 2<ӏzӏ<3

d)

(d). Does not exist

36.

The unilateral Z-Transform of sequence x[n] = {1,2,2,1} is

a)

1+2z+2z^2+z^3

b)

z^3+2z^2+2z+1/z

c)

1+2z^-1+2z^-2+z^-3

d)

None of the above

37.

Out of the three transforms viz. Z-transform, Laplace transform and Fourier transform

a)

A.all three are used in continuous time domain

b)

B.all three are used in both continuous time domain and discrete time domain

c)

C.Z transform is used in continuous time domain while Laplace and Fourier transforms are used in discrete time domain

d)

D.Z transform is used is discrete time domain while Laplace and Fourier transforms are used in continuous time domain

38.

A system is stable if ROC

a)

A.include the unit circle

b)

B.exclude the unit circle

c)

C.Lies on the circle

d)

D. Entire plane

39.

What is the set of all values of z for which X(z) attains a finite value?

a)

a) Region of convergence

b)

b) Radius of divergence

c)

c) Feasible solution

d)

d) None of the mentioned

40.

What is the ROC of the system function H(z) if the discrete time LTI system is BIBO stable?

a)

Entire Z plane except at z=0

b)

Entire Z plane except at z=infinity

c)

contains unit circle

d)

none

41.

if z{x1(n)}= X1(z) and z{x2(n)}= X2(z) ,then z{x1(n)* x2(n)} is given ny

a)

X1(z).X2(z^-1)

b)

X1(z).X2(z)

c)

X1(z^-1).X2(z)

d)

X1(z).X2(-z)

42.

Continuous signal can be converted to discrete signal by the process of

(a)

43.

The z-transform of a signal X(n) whose definition is given by X(z)=

\sum_{n=0}^{\infty}x\left(n\right)z^{-n}

is known as

a)

Unilateral Z-transform

b)

Bilateral Z-transform

c)

Rational Z-transform

d)

None of the above

44.

For what kind of signals one sided Z-transfrom is unique

a)

All signals

b)

Anti-causal signal

c)

Causal signal

d)

None of the above

45.

Z-transform is linear

a)

True

b)

False

46.

The Z-transform of

\delta\left(n+k\right)>0

is

a)

$z^{-k,\ }z\ne0$

b)

$z^k,z\ne0$

c)

$z^{-k},\ all\ z$

d)

$z^k,all\ z$

47.

Z-transform of the sequence $\left\{2^k\right\},k\ge0\ is\ \frac{z}{z-2}$

a)

True

b)

False

48.

$The\ value\ of\ the\ Radius\ of\ convergence\ of\ f\left(n\right)=2^n,n<0\ is$

a)

0< $\left|z\right|$ <1

b)

-2< $\left|z\right|$

c)

$\left|z\right|$ <2

d)

z-plane

49.

$The\ ROC\ of\ u\left(n\right)=4^n,for\ n<0;2^n,for\ n\ge0\ is$

a)

0<z<1

b)

z<4

c)

2<z

d)

2<z<4

50.

$The\ Inverse\ Z-transform\ of\frac{z}{\left(z+1\right)^2}is$

a)

$\left(-1\right)^{n+1}$

b)

$n\left(-1\right)^{n-1}$

c)

$\left(-1\right)^{n-1}$

d)

$n\left(-1\right)^{n+1}$

EC 8352 SS IAT#3

Total questions: 50

Worksheet time: 34mins

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