Free Printable DSP Quiz 1

1.

Consider the z-transform X(z) = 5z^2 + 4z^{-1} + 3; 0<|z|<∞. The inverse z-transform x[n]

a)

5δ[n+ 2] + 3δ[n] + 4δ[n−1]

b)

5δ[n−2] + 3δ[n] + 4δ[n+ 1]

c)

5u[n+ 2] + 3u[n] + 4u[n−1]

d)

5u[n−2] + 3u[n] + 4u[n+ 1]

2.

The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence 1, 0, 2, 3 is

a)

[0,−2 + 2j, 2,−2−2j]

b)

[2, 2 + 2j, 6,−2−2j]

c)

[6, 1−3j, 2, 1 + 3j]

d)

[6,−1 + 3j, 0,−1−3j]

3.

The power of a signal x[n] is defined as:

a)

$P=\lim_{N\rightarrow\infty\ }\ \frac{1}{1+2N}\sum_{n=-N}^N\left|x\left(n\right)\right|^2$

b)

$P=\lim_{N\rightarrow\infty}\ \frac{1}{1-2N}\sum_{n=-N}^N\left|x\left[n\right]\right|^2$

c)

$P=\lim_{N\rightarrow0}\ \frac{1}{1-2N}\sum_{n=-N}^N\left|x\left[n\right]\right|^2$

d)

$P=\lim_{N\rightarrow n}\ \frac{1}{2N+1}\sum_{-N}^N\left|x\left[n^2\right]\right|$

4.

Find the Z-transform of x(n)={1,2,3,4,2}. consider x(0)=3

a)

Z²+2Z+3+4Z^-1+Z^-2

b)

Z²+4Z+3+2Z^-1+Z^-2

c)

Z²+2Z+3+4Z^-1+2Z^-2

d)

Z²+2Z+1+Z^-1+Z^-2

5.

x(t)=cos(200Πt) what is the maximum frequency?

a)

50Hz

b)

100Hz

c)

200Hz

d)

400Hz

6.

The given signal x(t)=sin(10∏t) is periodic. what is the period?

a)

1/5 sec

b)

5sec

c)

10sec

d)

1/10sec

7.

What is the angular frequency and unit of f(t)=3sin(50t) ?

a)

50 radian/sec

b)

100 radian/sec

c)

25 radian/sec

d)

None

8.

The interface between an analog signal and a digital processor is

a)

D/A converter

b)

A/D converter

c)

Modulator

d)

Demodulator

9.

Any physical phenomenon that carries some information is

a)

System

b)

Processor

c)

Signal

d)

None

10.

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

a)

a) Radius of convergence

b)

b) Radius of divergence

c)

c) Feasible solution

d)

d) None of the mentioned

11.

causal sequence is also known as

a)

anti causal

b)

right hand sequence

c)

left hand sequence

d)

two sided sequence

12.

Z transform is a mathematical tool which is used for analysis of

a)

linear time variant system

b)

linear time invariant system

c)

linear system

d)

non linear time invariant system

13.

Modulos of z less than 1 is known as

a)

causal sequence

b)

anti causal sequence

c)

two sided sequence

14.

In which type of sequence the ROC will not converge at z=0 and z= infinity

a)

causal sequence

b)

non causal sequence

c)

anti causal sequence

d)

none

15.

In anticausal sequence the samples ranges from zero to _____ value

a)

positive value

b)

negative value

c)

both positive and negative

16.

Two sided sequence is also known as

a)

causal sequence

b)

left hand sequence

c)

non causal sequence

d)

anti causal sequence

17.

given x(z) =

\frac{z}{z-a}

and ROC |z|>1 the sample x(n) will be

a)

$a^nu\left(n\right)$

b)

$-b^nu\left(-n-1\right)$

c)

$-a^nu\left(n\right)$

d)

none

18.

$Given\ x\left(n\right)=\ -b^nu\left(-n-1\right)\ find\ the\ x\left(z\right)\ and\ ROC$

a)

$X\left(Z\right)=\ \frac{Z}{Z-a}\ ,\ ROC\ \left|Z\right|>1$

b)

$X\left(Z\right)=\ \frac{Z}{Z-b},\ ROC\ \left|Z\right|<1$

c)

$X\left(Z\right)\ =\ \frac{Z}{Z-b},\ ROC\ \left|z\right|>1$

d)

$x\left(z\right)\ =\ \frac{z}{z+b},\ ROC\ \left|z\right|<1$

19.

What is the ROC of the z-transform of the signal x(n)= aⁿu(n)+bⁿu(-n-1)?

a)

|a|<|z|<|b|

b)

|a|>|z|>|b|

c)

|a|>|z|<|b|

d)

|a|<|z|>|b|

20.

Find the Z-transform of u(-n).

a)

$\frac{1}{1-z}$

b)

$\frac{1}{1+z}$

c)

$\frac{z}{1-z}$

d)

$\frac{z}{1+z}$

21.

For a right hand sequence, the ROC is entire z-plane.

a)

true

b)

false

22.

x(n) = aⁿ u(n) and x(n) = -aⁿ u(-n-1) have the same X(Z) and ROC.

a)

true

b)

false

23.

Which of the following impulse response h(n) represents a stable LTI system

a)

$2^nu(n)$

b)

$0.2^nu(n)$

c)

$2^nu(n-1)$

d)

Both A & C

24.

y(t) +3=x(t) is a linear system

a)

True

b)

False

25.

$y\left(n\right)=x\left(n\right)+\frac{1}{x\left(n-1\right)}$

Check whether the DT system is linear or not?

a)

Linear system

b)

Non Linear system

26.

$y\left(n\right)=x^2\left(n\right)$

Check the linearity and causality of the given DT system.

a)

Linear & Causal

b)

Non Linear & Causal

c)

Non Linear & Non Causal

d)

Linear & Non Causal

27.

$y\left(n\right)=x\left(n\right)+\frac{1}{x\left(n-1\right)}$

Check whether the DT system is causal or not?

a)

Causal system

b)

Non Causal system

28.

$y\left(n\right)=x\left(n\right)+\frac{1}{x\left(n+1\right)}$

Check whether the DT system is causal or not?

a)

Causal system

b)

Non Causal system

29.

In Z-Transform, z =

a)

$re^{-jw}$

b)

$re^{-w}$

c)

$re^{jw}$

d)

$re^w$

30.

$Z\left\{u(n)\right\}=$

a)

$\frac{z}{z-1};z<1$

b)

$\frac{z}{z-1};z<-1$

c)

$\frac{z}{z-1};z>1$

d)

$\frac{z}{z-1};z=1$

31.

x(n)=[1, 3, 3, 1], h(n)=[1, 5, 5, 1]

perform convolution between x(n) and h(n)

a)

[1, 8, 23, 32, 23, 8, 1 ]

b)

[1, 8, 32, 23, 32, 8, 1]

c)

[8, 1, 32, 32, 32, 1, 8]

d)

[8, 1, 23, 23, 23, 1, 8]

32.

x(n)=[1, 3, 3, 1], h(n)=[1, 5, 5, 1]

perform 4- circular convolution between x(n) and h(n)

a)

[24, 16, 24, 32]

b)

[12, 36, 36, 12]

c)

[24, 24, 16, 32]

d)

[24, 32, 24, 16]

33.

x(n)=[1, 3, 3, 1]

Evaluate 4-DFT of x(n) using FFT

a)

[8, -2+2j, 0, -2-2j]

b)

[8, -2-2j, 0, -2+2j]

c)

[8, 2-2j, 0, 2+2j]

d)

[8, 2+2j, 0, 2-2j]

34.

N-DFT of x(n) =

a)

$\sum_{n=0}^{N-1}x\left(n\right)\ e^{-j\ \frac{2\pi}{N}kn}$

b)

$\sum_{n=0}^Nx\left(n\right)\ e^{-j\ \frac{2\pi}{N}kn}$

c)

$\sum_{n=0}^{N-1}x\left(n\right)\ e^{j\ \frac{2\pi}{N}kn}$

d)

$\sum_{n=0}^{N-1}x\left(n\right)\ e^{-j\ 2\pi kn}$

35.

$W_N=?$

a)

$e^{-\frac{j2\pi}{N}k}$

b)

$e^{j2\pi N}$

c)

$e^{\frac{j2\pi}{N}}$

d)

$e^{-\frac{j2\pi}{N}}$

36.

$W_8^2=?$

a)

$j$

b)

$-j$

c)

$-j^2$

d)

$j^2$

37.

Computation of N-DFT of a sequence requires______ complex multiplications

a)

$N$

b)

$4N^2$

c)

$N^2$

d)

$N-1$

38.

In unit step signal the amplitude of u(t) is equal to

a)

zero

b)

one

c)

infinity

d)

none of the above

39.

The unit ramp function is defined as

a)

r(n)=1 for n>0

b)

r(n)=0 for n>0

c)

r(n)=n for n>0

d)

none

40.

A discrete time signal x(n) is even if it satisfies the condition

a)

x(n) = x(n)

b)

x(-n) = x(n)

c)

x(n) = x(-n)

d)

none of the above

41.

In power signals the power will be _______ and energy will be__________

a)

infinity, constant

b)

constant, zero

c)

zero, constant

d)

constant, infinity

42.

The odd signal is also known as

a)

symmetric signal

b)

anti symmetric signal

c)

both 1 and 2

d)

none

43.

Which of the following signal is obtained on integrating step signal?

a)

ramp signal

b)

impulse signal

c)

parabolic signal

d)

gate signal

44.

_________ is defined as any physical quantity that varies with time, space or any other independent variable

a)

Signal

b)

system

c)

signals & system

d)

none of the above

45.

Power of an energy signal is

a)

Zero

b)

Infinity

c)

Cannot be determined

d)

None of the above

46.

Which one of the following systems is causal?

a)

y(t) = x(t) + x(t-3) + x(t²)

b)

y[n] = x[n+2]

c)

y(t)=x(t-1)+x(t-2)

d)

y[n] = x[2n²]

DSP Quiz 1

Total questions: 46

Worksheet time: 39mins

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