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Signals and Systems
Signals

Practice questions from Signals.

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Q#1 Signals GATE EE 2025 (Set 1) MCQ +1 mark -0.33 marks

Consider a continuous-time signal

 

where  is the continuous-time unit step function. Let  be the continuous time unit impulse function. The value of  is

-9

9

3

-3

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Q#2 Signals GATE EE 2025 (Set 1) NAT +1 mark -0 marks

A continuous time periodic signal x(t)  is

 

If  is the period of , then  __________ (round off to the nearest integer).

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Q#3 Signals GATE EE 2024 (Set 1) MCQ +2 marks -0.66 marks

The input  and the output  of a system are related as

 

nonlinear.

linear and time-invariant.

linear but not time-invariant.

noncausal.

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Q#4 Signals GATE EE 2024 (Set 1) MCQ +2 marks -0.66 marks

Consider the discrete-time systems  and  defined as follows:                                       

 

 

Which one of the following statements is true?

 and  are BIBO stable.

 and  are not BIBO stable.

 is BIBO stable but  is not BIBO stable.

 is not BIBO stable but  is BIBO stable.

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Q#5 Signals GATE EE 2024 (Set 1) NAT +2 marks -0 marks

If the energy of a continuous-time signal  is  and the energy of the signal  is , then  is ________ (rounded off to 1 decimal place).

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Q#6 Signals GATE EE 2023 (Set 1) NAT +2 marks -0 marks

The period of the discrete-time signal  described by the equation below is  __________ (Round off to the nearest integer).

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Q#7 Signals GATE EE 2020 (Set 1) MCQ +1 mark -0.33 marks

 and  are, respectively, the rms and average values of x(t) = x(t — T) , and similarly,  and  are, respectively, the rms and average values of . k,T are independent of t . Which of the following is true?

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Q#8 Signals GATE EE 2018 (Set 1) MCQ +2 marks -0.66 marks

Consider the two continuous-time signals defined below:  

These signals are sampled with a sampling period of T=0.25 seconds to obtain discrete-time signalsand , respectively. Which one of the following statements is true?

The energy of  is greater than the energy of.

The energy of  is greater than the energy of.

 and  have equal energies.

Neither nor is a finite-energy signal.

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Q#9 Signals GATE EE 2018 (Set 1) MCQ +2 marks -0.66 marks

The signal energy of the continuous-time signal

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Q#10 Signals GATE EE 2017 (Set 2) NAT +1 mark -0 marks

The mean square value of the given periodic waveform f(t) is ______

Z:\PY\EE\Redreaw figure\Signal & System\updated\Signal & system\135-17.jpg

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Q#11 Signals GATE EE 2016 (Set 1) MCQ +1 mark -0.33 marks

The value of , where  is the Dirac delta function, is

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Q#12 Signals GATE EE 2015 (Set 1) NAT +1 mark -0 marks

A moving average function is given by . If the input u is a sinusoidal signal of frequency, then in steady state, the output y will lag u (in degree) by___________.

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Q#13 Signals GATE EE 2014 (Set 1) MCQ +2 marks -0.66 marks

The function shown in the figure can be represented as

14.jpg

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Q#14 Signals GATE EE 2013 (Set 1) MCQ +2 marks -0.66 marks

The impulse response of a continuous time system is given by h(t)=δ(t-1)+δ(t-3). The value of the step response at t=2 is

0

1

2

3

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Q#15 Signals GATE EE 2011 (Set 1) MCQ +2 marks -0.66 marks

A zero mean random signal is uniformly distributed between limits –a and +a and its mean square value is equal to its variance. Then the RMS value of the signal is

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Q#16 Signals GATE EE 2010 (Set 1) MCQ +1 mark -0.33 marks

The period of the signal  is

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Q#17 Signals GATE EE 2008 (Set 1) MCQ +2 marks -0.66 marks

Given a sequence x(n], to generate the sequence, which one of the following procedures would be correct?

First delay x[n] by 3 samples to generate , then pick every  samples of  to generate , and then finally time reverse  to obtain y[n].

First advance x[n] by 3 samples to generate , then pick every  samples of  to generate , and then finally time reverse  to obtain y[n]

First pick every fourth sample of x[n] to generate , time reverse  to obtain , and finally advance  by 3 samples to obtain y[n]

First pick every fourth sample of x[n] to generate , time reverse  to obtain , and finally delay  by 3 samples to obtain y[n]

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Q#18 Signals GATE EE 2006 (Set 1) MCQ +1 mark -0.33 marks

Which of the following is true

A finite signal is always bounded

A bounded signal always possesses finite energy

A bounded signal is always zero outside the interval  for some

None

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Q#19 Signals GATE EE 2005 (Set 1) MCQ +2 marks -0.66 marks

For the triangular waveform shown in Figure, the RMS value of the voltage is equal to

Q33.jpg

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Q#20 Signals GATE EE 2004 (Set 1) MCQ +2 marks -0.66 marks

The RMS value of the periodic waveform given in figure is

Q31.jpg

1.5 A

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Q#21 Signals GATE EE 2002 (Set 1) MCQ +2 marks -0.66 marks

A current impulse, , is forced through a capacitor C. The voltage, , across the capacitor is given by

5t

5u(t) − C

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Q#22 Signals GATE EE 2002 (Set 1) MCQ +1 mark -0.33 marks

What is the RMS value of the voltage waveform shown in Figure?

C:\Users\Ankit\Dropbox\GATE papers\EE papers\Typed\Gate-EE-2002\Figures\Q24.jpg

200 V

100 V

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Q#23 Signals GATE EE 1999 (Set 1) MCQ +1 mark -0.33 marks

The RMS value of a half-wave rectified symmetrical square wave current of 2A is:

1A

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Q#24 Signals GATE EE 1995 (Set 1) MCQ +1 mark -0.33 marks

The RMS value of the periodic waveform S(t), shown in figure is:

D:\1Mayu\Gate-9\JPG\JPG\1995\1995\Q1_1.5.jpg

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Q#25 Signals GATE EE 1994 (Set 1) MCQ +1 mark -0.33 marks

Match the waveforms on the left-hand side with the correct mathematical description listed on the right-hand side.

(a) => (R)
(b) => (U)
(c) => (S)
(d) => (V)

(a) => (P)
(b) => (R)
(c) => (S)
(d) => (T)

(a) => (R)
(b) => (U)
(c) => (S)
(d) => (P)

(a) => (S)
(b) => (T)
(c) => (U)
(d) => (V)

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Q#26 Signals GATE EE 1994 (Set 1) MCQ +1 mark -0.33 marks

The value of the integral   is equal to ______________

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