Free Printable EC 8352 SIGNALS AND SYSTEMS

1.

$u\left(t-a\right)\ =\ 0,\ \ if$

a)

$t-a\ =\ 0$

b)

$t\ -\ a\ <0$

c)

$t\ -\ a>0$

d)

$t\ >a$

2.

$\int_{-\infty}^{\infty}\ x\left(t\right)\delta\left(t\right)dt$

a)

$x\left(t_o\right)$

b)

$x\left(t\right)$

c)

$\delta\left(t\right)$

d)

$x\left(0\right)$

3.

$\int_{-\infty}^{\infty}\ \left(t-2\right)^2\delta\left(t-2\right)dt$

a)

$4$

b)

$2$

c)

$\left(t-2\right)$

d)

$0$

4.

The sum of two periodic signals is periodic only if the ratio of their respective periods is

a)

a rational number

b)

an irrational number

c)

a complex number

d)

a real number

5.

$The\ signal\ x\left(t\right)=A\ \sin\left(\omega_{o\ }t+\phi\right)\ is$

a)

a power signal

b)

an energy signal

c)

periodic signal

d)

both periodic and power signal

6.

$x\left(t\right)=r\left(t\right)\ -r\left(t-2\right)\ is\ a\$

a)

power signal

b)

energy signal

c)

nor power nor energy

d)

both energy and power

7.

Which one of the following is not a characteristic of a deterministic signal?

a)

Exhibits no uncertainty

b)

Instantaneous value can be accurately predicted

c)

Exhibits uncertainty

d)

Can be represented by a mathematical equation

8.

Determine the Time period of: x(t)=3 cos⁡(20t+5)+sin⁡(8t-3).

a)

1/10 sec

b)

1/20 sec

c)

2/5 sec

d)

2/4 sec

9.

Determine the power of the signal: x(t) = cos(t).

a)

1/2

b)

1

c)

3/2

d)

2

10.

Discrete time signal is derived from continuous time signal by _____________ process.

a)

Addition

b)

Multiplying

c)

Sampling

d)

Addition and multiplication

11.

Noise generated by an amplifier of radio is an example for?

a)

Discrete signal

b)

Deterministic signal

c)

Random signal

d)

Periodic signal

12.

Which of the following is an example of amplitude scaling?

a)

Electronic amplifier

b)

Electronic attenuator

c)

Both amplifier and attenuator

d)

Adder

13.

An example of a discrete set of information/system is

a)

the trajectory of the Sun

b)

data on a CD

c)

universe time scale

d)

movement of water through a pipe

14.

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]

15.

Which among the following is a Time Invariant system?

a)

dy(t)/dt + ty(t) = x(t)

b)

y(t) = x(t) cosπt

c)

y[n] = x[n] + n x[n-1]

d)

y[n] = x³ [n+1]

16.

Find the convolution sum of sequences x¹[n] = [1, 2, 3] and x₂[n] = [2, 1, 4].

a)

{2, 5, 12, 11, 12}

b)

{2, 12, 5, 11, 12}

c)

{2, 11, 5, 12, 12}

d)

{-2, 5,-12, 11, 12}

17.

What does the term y(-1) indicate especially in an equation that represents the behavior of the causal system?

a)

initial condition of the system

b)

negative initial condition of the system

c)

negative feedback condition of the system

d)

response of the system to its initial input

18.

If two LTI systems with impulse response h1 (t) and h2 (t) and are connected in parallel then output is given by ______

a)

y(t) = x(t) *(h1(t) + h2(t))

b)

y(t) = x(t) + (h1(t) + h2(t))

c)

y(t) = x(t) * (h1(t) h2(t))

d)

y(t) = (x(t) * h1(t)) + h2(t)

19.

The signal defined by the equations f(t) = 0 for t < 0, f(t) = E for 0 ≤ t ≤ a and f(t) = 0 for t > a is

a)

a step function

b)

a pulse function

c)

a shifted step function originating at t=a

d)

none of the above

20.

DTFT is the representation of

a)

Periodic Discrete time signals

b)

Aperiodic Discrete time signals

c)

Aperiodic continuous signals

d)

Periodic continuous signals

21.

What does the first term 'a₀' in the below stated expression of a line spectrum indicate?

x(t) = a₀ + a₁ cos w₀ t + a₂ cos2 w₀t +......+ b₁ sin w₀ t + b₂sin w₀ t + .....

a)

DC component

b)

Fundamental component

c)

Second harmonic component

d)

All of the these

22.

A Laplace Transform exists when ______

A. The function is piece-wise continuous

B. The function is of exponential order

C. The function is piecewise discrete

D. The function is of differential order

a)

A & B

b)

C & D

c)

A & D

d)

B & C

23.

According to the time-shifting property of Laplace Transform, shifting the signal in by t₀intime domain corresponds to the ______

a)

Multiplication by e^-st0 in the time domain

b)

Multiplication by e^-st0 in the frequency domain

c)

Multiplication by e^st0 in the time domain

d)

Multiplication by e^st0 in the frequency domain

24.

Generally, the convolution process associated with the Laplace Transform in time domain results into________

a)

Simple multiplication in complex frequency domain

b)

Simple division in complex frequency domain

c)

Simple multiplication in complex time domain

d)

Simple division in complex time domain

25.

The Z-Transform of the function
$\sum_{k=0}^{\infty}\delta\left[n-k\right]$

a)

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

b)

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

c)

$\frac{\left(z-1\right)^2}{z}$

d)

$\frac{z}{\left(z-1\right)^2}$

26.

Consider the sequence $x\left[n\right]\ =\ a^nu\left[n\right]+b^nu\left[n\right]$
where u[n] denotes the unit-step sequence and
0 < |a| < |b| < 1 .The region of convergence (ROC) of the z-transform of x[n] is

a)

|z| > |a|

b)

|z| > |b|

c)

|z| < |a|

d)

|a| < |z| < |b|

27.

A discrete-time signal $x\left[n\right]\ =\ \delta\left[n-3\right]+2\delta\left[n-5\right]$ has z-transform X[z]. If Y[z] = X[-z] is the z-transform of another signal y[n], then

a)

y[n] = x[n]

b)

y[n] = x[-n]

c)

y[n] = -x[n]

d)

y[n] = -x[-n]

28.

$x\left[n\right]\ =\left(\frac{1}{-9}\right)^nu\left[n\right]-\left(-\frac{1}{3}\right)^nu\left[-n-1\right]$

The Region of Convergence (ROC) of the z-transform of x[n]

a)

|z| > 1/9

b)

|z| < 1/3

c)

1/3 > |z| > 1/9

d)

does not exist

29.

What are the main characteristics of Anti aliasing filter?

A) Ensures that bandwidth of signal to be sampled is limited to frequency range

B) To limit the additive noise spectrum and other interference, which corrupts the signal

C) Both a & b

D) None of the mentioned

a)

A

b)

B

c)

C

d)

D

30.

Which of the following is the process of ‘aliasing’?

a)

Peaks overlapping

b)

Phase overlapping

c)

Amplitude overlapping

d)

Spectral overlapping

31.

Find the Nyquist rate and Nyquist interval of sin(2πt).

a)

2 Hz, 1/2 sec

b)

1/2 Hz, 1/2 sec

c)

1/2 Hz, 2 sec

d)

2 Hz, 2 sec

32.

The analog signal m(t) is given below m(t) = 4 cos 100 πt + 8 sin 200 πt + cos 300 πt, the Nyquist sampling rate will be

a)

100

b)

200

c)

300

d)

600

33.

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

34.

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)

35.

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}

36.

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

37.

A signal of maximum frequency of 10 kHz is sampled at Nyquist rate. The time interval between two successive sample is –

a)

50 µs

b)

100 µs

c)

1000 µs

d)

5 µs

38.

The scaling of a sequence x[n] by a factor α is given by

a)

y[n] = α [x[n]]2

b)

y[n] = α x[n2]

c)

y[n] = α x[n]

d)

y[n] = x[n]x[-n]

39.

If the sampling time is less than the Nyquist interval :

a)

Simpler filters can be used to obtain the original signal

b)

Channel Capacity increases

c)

Bandwidth increases

d)

Guard time becomes less

40.

Impulse modulation systems, The number of samples required to ensure no loss of information is given by –

a)

Parsevals theorem

b)

Fourier transmission

c)

Nyquist theorem

d)

None of the these

41.

Calculate the Nyquist rate for sampling when a continuous time signal is given by x(t) = 5 cos 100πt +10 cos 200πt – 15 cos 300πt

a)

300Hz

b)

150Hz

c)

600Hz

d)

None of the above

42.

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)

$z^k,all\ z$

43.

$Z-transform\ of\ the\ sequence\ \left\{\frac{a^k}{k!}\right\},k\ge0=e^{\frac{a}{z}}$

a)

True

b)

False

44.

$Z-transform\ of\ the\ sequence\ \left\{nc_r\right\},\left(0\le r\le n\right)\ is\ \left(1+z\right)^n$

a)

True

b)

False

45.

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

a)

0<z<1

b)

z<4

c)

2<z

d)

2<z<4

46.

$If\ Z\left(u_n\right)=u\left(z\right),\ then\ \lim_{n\rightarrow\infty}u_n=\lim_{n\rightarrow\infty}\left(z-1\right)u\left(z\right)$

a)

True

b)

False

47.

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

a)

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

b)

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

c)

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

d)

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

48.

What is the Laplace Transform for $f\left(t\right)=t^3$ ?

a)

$\frac{1}{s^3}$

b)

$\frac{2}{s^3}$

c)

$\frac{6}{s^4}$

d)

$\frac{3}{s^3}$

49.

Define this property: $L\left(f\left(t\right)e^{at}\right)=F\left(s-a\right)$

a)

Linearity Property

b)

First Shifting Property

c)

Convolution Theorem

d)

Second Shifting Property

50.

Find $L\left(e^{3t}t\right)$

a)

$\frac{1}{\left(s^2\right)}$

b)

$\frac{1}{\left(s-3\right)^2}$

c)

$\frac{1}{\left(s-2\right)^2}$

d)

$\frac{1}{\left(s\right)}$

EC 8352 SIGNALS AND SYSTEMS - MODEL

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