Free Printable Signals & Systems

1.

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

2.

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]

3.

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]

4.

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}

5.

If a function f(t) u(t) is shifted to right side by t₀,then the function can be expressed as

a)

f(t – t₀) u(t)

b)

f(t) u(t –t₀)

c)

f(t – t₀) u(t – t₀)

d)

f(t +t₀) u(t + t₀)

6.

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

7.

Under which conditions does an initially relaxed system become unstable?

a)

only if bounded input generates unbounded output

b)

only if bounded input generates bounded output

c)

only if unbounded input generates unbounded output

d)

only if unbounded input generates bounded output

8.

Which mathematical notation specifies the condition of periodicity for a continuous time signal?

a)

x(t) = x(t +T₀)

b)

x[n] = x[n+ N]

c)

x(t) = e-αt

d)

None of these

9.

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)

10.

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

11.

DFT is applied to

a)

Infinite discrete sequences

b)

Finite discrete sequences

c)

Continuous infinite signals

d)

Continuous finite sequences

12.

DTFT is the representation of

a)

Periodic Discrete time signals

b)

Aperiodic Discrete time signals

c)

Aperiodic continuous signals

d)

Periodic continuous signals

13.

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

14.

What is the possible range of frequency spectrum for discrete time fourier series (DTFS)?

a)

0 to 2π

b)

-2π to +2π

c)

-∞ to +∞

d)

None of the these

15.

Which property of periodic signal in DTFS gets completely clarified / identified by the equation x (n – n0)?

a)

Conjugation

b)

Time Shifting

c)

Frequency Shifting

d)

Time Reversal

16.

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

17.

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

18.

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

19.

Laplace transform is basically an

a)

differential transform

b)

algebraic transform

c)

integral transform

d)

rational transform

20.

Laplace transform if sin(at) u(t) is

a)

$\frac{s}{a^2+s^2}$

b)

$\frac{a}{a^2+s^2}$

c)

$\frac{s^2}{a^2+s^2}$

d)

$\frac{a^2}{a^2+s^2}$

21.

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

a)

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

b)

$z^3+2z^2+2z+\frac{1}{z}$

c)

$1+\frac{2}{z}+\frac{2}{z^2}+\frac{1}{z^3}$

d)

$1+\frac{1}{z}+\frac{2}{z^2}+\frac{2}{z^3}+\frac{1}{z^4}$

22.

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)

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

23.

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|

24.

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]

25.

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

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

26.

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

27.

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

a)

Peaks overlapping

b)

Phase overlapping

c)

Amplitude overlapping

d)

Spectral overlapping

28.

Which of this is not a type of analog modulation

a)

amplitude modulation

b)

frequency modulation

c)

phase modulation

d)

frequency shift keying

29.

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

30.

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

Signals & Systems

Total questions: 30

Worksheet time: 30mins

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