Test: Signals & Systems - 2


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20 Questions MCQ Test GATE ECE (Electronics) 2023 Mock Test Series | Test: Signals & Systems - 2

Test: Signals & Systems - 2 for Electronics and Communication Engineering (ECE) 2023 is part of GATE ECE (Electronics) 2023 Mock Test Series preparation. The Test: Signals & Systems - 2 questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: Signals & Systems - 2 MCQs are made for Electronics and Communication Engineering (ECE) 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Signals & Systems - 2 below.
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Test: Signals & Systems - 2 - Question 1

If relation between input x[n] and output y[n] of a system is given by y[n] - 1/2 y[n -1] = x[n]

then the system is

Detailed Solution for Test: Signals & Systems - 2 - Question 1

Simply lake Z transform from both sides:

Then H(z)

it is right of the right - most pole

Test: Signals & Systems - 2 - Question 2

lf x[n] = - u[-n -1] + (1 /2)n u[-n -1] then ROC of signal is:

Detailed Solution for Test: Signals & Systems - 2 - Question 2

Overall ROC is IZI < 1 /2

Test: Signals & Systems - 2 - Question 3

Consider, discrete time signal x[n] = (1 /3)n u[n] If signal y[n] is defined as y[n] = x[—n], —∞< n < ∞ then value of   equals to

Detailed Solution for Test: Signals & Systems - 2 - Question 3

Now

Put

Test: Signals & Systems - 2 - Question 4

If signal x(t) and h(t) shown in figure are convolved to yield y(t).

   

Detailed Solution for Test: Signals & Systems - 2 - Question 4

Simply use difference and sum between points.

Test: Signals & Systems - 2 - Question 5

Given that g (t) g (t) = t exp (—t) u(t) then value of g(t) is

Detailed Solution for Test: Signals & Systems - 2 - Question 5

Test: Signals & Systems - 2 - Question 6

If u(t) r(t) denotes unit step and unit ramp respectively then u(t)  r(t) denotes their convolution, then function u(t + 1) r(t — 2) is given by.

Detailed Solution for Test: Signals & Systems - 2 - Question 6

y(t) = u(t) r(t)

Y(s) = 1/s3

Test: Signals & Systems - 2 - Question 7

If wave form is given only for I period then

 

Q. Waveform x (t) is

 

Test: Signals & Systems - 2 - Question 8

If wave form is given only for I period then

 

Q. Fourier series representation on of x (t) will be.

 

Detailed Solution for Test: Signals & Systems - 2 - Question 8

it is an odd function with half symmetry.

Test: Signals & Systems - 2 - Question 9

If complex Fourier- series coefficient Ck is given as Ck = (— 1/2)|k| then value of x(t) is:

Test: Signals & Systems - 2 - Question 10

Which statements are true about Fourier transform?

  1. If x(t) is real then X(jω) is complex conjugate symmetric.
  2. If x(t) is imaginary then X(jω) is complex conjugate anti-symmetric
  3. If x(t) is even then X(jω) is also even.
Test: Signals & Systems - 2 - Question 11

Check status of linearity of given functions.

I .   x1(t) = x(t) .cost

2.  x2(t) = cos(x(t)).t

Detailed Solution for Test: Signals & Systems - 2 - Question 11

x2(t) = t cos (x (t)

if x(t) = 0   ⇒  x2(t) = t

So x2(t) is non - linear

Test: Signals & Systems - 2 - Question 12

If Fourier transform of x(t) is X(ω) then Fourier transform of 

Detailed Solution for Test: Signals & Systems - 2 - Question 12

Test: Signals & Systems - 2 - Question 13

0.5 If Z-Transform X(z) of a sequence x[n] is given by .It is given that R.O.C. of X (z) includes unit circle then

Q. Value of x[0] is

Detailed Solution for Test: Signals & Systems - 2 - Question 13

Test: Signals & Systems - 2 - Question 14

0.5 If Z-Transform X(z) of a sequence x[n] is given by .It is given that R.O.C. of X (z)includes unit circle then

Q. In above system if x[n] is causal then value of x[0] is

Detailed Solution for Test: Signals & Systems - 2 - Question 14

 if it includes, unit - circle then, Iz| < 2

x[n] = - (0.5) 2n u(-n-1)

x[0] = 0

if it is causal then

Test: Signals & Systems - 2 - Question 15

 If frequency response of a causal & stable linear Time Invariant system is  , then value of phase delay and group delay are.

Detailed Solution for Test: Signals & Systems - 2 - Question 15

Test: Signals & Systems - 2 - Question 16

Which among the following are the stable discrete time systems?

1. y(n) = x(4n)
2. y(n) = x(-n)
3. y(n) = ax (n) + 8 
4. y(n) = cos x(n)

*Answer can only contain numeric values
Test: Signals & Systems - 2 - Question 17

For given Fourier — series coefficients for real signals Co = 1, C1 = — 2, C2 = — 1 then power of this signal is _______


Test: Signals & Systems - 2 - Question 18

What is inverse Fourier transform of  

Detailed Solution for Test: Signals & Systems - 2 - Question 18

Test: Signals & Systems - 2 - Question 19

Which statement is true about y[n] = x[n] . cos (ωo n)

*Answer can only contain numeric values
Test: Signals & Systems - 2 - Question 20

For given signal s(t), shown below what is slope of matched filter output during interval 1 ≤ t ≤ 2 is 


Detailed Solution for Test: Signals & Systems - 2 - Question 20

h(t) =    = s(2

y(t) = NW h(t )

Just draw y(t) and then calculate slope of y(t)

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