# Signals & Systems - GATE practice papers - Electronics & Communication

1)   What is the obligatory sequence that need to be performed or executed in time shifting ,scaling and time reversal operational processes under the category of continuous time signals? (Marks : 02)
- Published on 19 Oct 15

a. Time Shifting, Time Scaling & Time Reversal
b. Time Scaling, Time Reversal & Time Shifting
c. Time Shifting, Time Reversal & Time Scaling
d. Time Reversal, Time Scaling & Time Shifting
 Answer  Explanation ANSWER: Time Shifting, Time Scaling & Time Reversal Explanation: In accordance to the properties of continuous time signals, when the stages of time shifting, scaling and reversal are to be performed,then it is always obligatory to initially perform time shifting, and then scaling and the reversal. This is so because scaling can only be done after shifting the time signal. Time shifting property does not affect the amplitude of signal but it shows a slightly delayed version of original signal. Eventually, once the signal undergoes time scaling, it can further undergo the time reversal phase, where the exact reflection of the time-scaled signal is generated about Y-axis.

2)   Consider the following assertions:

A: x(t) or x[n] is assumed to be an energy signal if and only if 0>E>∞ and P=1
B: x(t) or x[n] is assumed to be a power signal only if 0>P> ∞ and E=1
C: x(t) or x[n] is assumed to be a power signal only if 0 < P < ∞ and E= ∞
D: x(t) or x[n] is assumed to be an energy signal if and only if 0
Which among them are correct in accordance to energy and power signals?
(Marks : 02)

- Published on 19 Oct 15

a. A & B
b. C & D
c. A & C
d. B & D
 Answer  Explanation ANSWER: C & D Explanation: According to the property of energy and power signals, a signal is said to be an energy signal only when the value of normalized energy lies within zero and infinity i.e. normalized energy should be greater than zero but less than infinity. Similarly, Power signals lie within the same range of zero and infinity. This implies that , a signal is known as a power signal only if the value of normalized average power is greater than zero but less than infinity. Signals which do not satisfy any of these properties are generally known as neither energy signals nor power signals.

3)   Y1 : It is not mandatory for every signal to be even or odd
Y2 : : Any signal which is neither even nor odd can be expressed as the difference of even and odd signals
(Marks : 02)

- Published on 19 Oct 15

a. Y1 only
b. Y2 only
c. Both Y1 & Y2 are correct but Y2 is not a reason for Y1
d. Both Y1 & Y2 are correct but Y2 is definitely a reason of Y1
 Answer  Explanation ANSWER: Y1 only Explanation: The statement Y1 is only precise because every signal should not be necessarily even or odd. It can also belong to some other category of signals. Also, the signal which is neither odd nor even odd is basically expressed as the addition (sum) of even and odd signals.

4)   Which Fourier Dirichlet conditions for transform existence specify the necessity of possessing finite values of the signal at any instant over a finite interval of time (T) ? (Marks : 02)
- Published on 19 Oct 15

a. Single Valued Property
b. Finite-discontinuities
c. Finite Peaks
d. Absolute Integration
 Answer  Explanation ANSWER: Single Valued Property Explanation: The conditions which provide chances to the periodic function to get expanded in a convergent Fourier series , are renowned as Dirichlet Conditions. Thus, the very first Dirichlet condition states that, the signal should have only the finite values over any time instant for a finite interval of time so the signal can be considered to be fourier transformable. This condition implies the single-valued property that does not change or tend to increase over the infinite time intervals.

5)   Which among the below specified notations exhibit an odd signal? (Marks : 01)
- Published on 19 Oct 15

a. x(-t) = -x(t) & x[-n] = -x[n]
b. x(-t) = x(t) & x[-n] = x[n]
c. x(-t) = -x(-t) & x[-n] = -x[-n]
d. x(t) = x(-t) & x[n] = x[-n]
 Answer  Explanation ANSWER: x(-t) = -x(t) & x[-n] = -x[n] Explanation: The necessary condition of an odd signal is that it must be zero at t=o or n=o . Thus, it can be expressed as x(-t) = -x(t) & x[-n] = -x[n]. This implies that negative value of time instants are equal to the negativity of an entire term in an odd signal, while the negative value of time instants are equal to the positive values of an entire term in an even signal. However, sin t is an odd signal while cos t is an even signal

6)   Any signal that exhibits symmetry on Y-axis is called as _______ (Marks : 01)
- Published on 19 Oct 15

a. odd signal
b. even signal
c. periodic signal
d. exponential signal
 Answer  Explanation ANSWER: even signal Explanation: A signal can be said to be symmetric on Y-axis only when the symmetrical nature of curve obtained from the signal exhibits two equal portions of the curve exactly similar to each other over the Y-axis. Since this kind of symmetry is shown by the signal has even (equal) form of distributions in terms of curve portions,amplitudes & time instants, they are generally referred as 'Even Signals'

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