1) What should be the value of laplace transform for the timedomain signal equation eat cos ωt.u(t)?
a. 1 / s + a with ROC σ > – a
b. ω / (s + a) 2 + ω2 with ROC σ > – a
c. s + a / (s + a)2 + ω2 with ROC σ > – a
d. Aω / s2 + ω2 with ROC σ > 0

ANSWER: s + a / (s + a)2 + ω2 with ROC σ > – a


2) According to
the timeshifting property of Laplace Transform, shifting the signal in
time domain corresponds to the ______
a. Multiplication by est0 in the time domain
b. Multiplication by est0 in the frequency domain
c. Multiplication by est0 in the time domain
d. Multiplication by est0 in the frequency domain

ANSWER: Multiplication by est0 in the frequency domain


3) Which result is generated/ obtained by the addition of a step to a ramp function?
a. Step Function shifted by an amount equal to ramp
b. Ramp Function shifted by an amount equal to step
c. Ramp function of zero slope
d. Step function of zero slope

ANSWER: Ramp Function shifted by an amount equal to step


4) Unilateral
Laplace Transform is applicable for the determination of linear constant
coefficient differential equations with ________
a. Zero initial condition
b. Nonzero initial condition
c. Zero final condition
d. Nonzero final condition

ANSWER: Nonzero initial condition


5) What should
be location of poles corresponding to ROC for bilateral Inverse Laplace
Transform especially for determining the nature of time domain signal?
a. On L.H.S of ROC
b. On R.H.S of ROC
c. On both sides of ROC
d. None of the above

ANSWER: On both sides of ROC


6) 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

ANSWER: Simple multiplication in complex frequency domain


7) An impulse
response of the system at initially rest condition is basically a
response to its input & hence also regarded as,
a. Black’s function
b. Red’s function
c. Green’s function
d. None of the above

8) When is the
system said to be causal as well as stable in accordance to pole/zero of
ROC specified by system transfer function?
a. Only if all the poles of system transfer function lie in lefthalf of Splane
b. Only if all the poles of system transfer function lie in righthalf of Splane
c. Only if all the poles of system transfer function lie at the centre of Splane
d. None of the above

ANSWER: Only if all the poles of system transfer function lie in lefthalf of Splane


9) Correlogram is a graph of ______
a. Amplitude of one signal plotted against the amplitude of another signal
b. Frequency of one signal plotted against the frequency of another signal
c. Amplitude of one signal plotted against the frequency of another signal
d. Frequency of one signal plotted against the time period of another signal

ANSWER: Amplitude of one signal plotted against the amplitude of another signal


10) Which
theorem states that the total average power of a periodic signal is
equal to the sum of average powers of the individual fourier
coefficients?
a. Parseval’s Theorem
b. Rayleigh’s Theorem
c. Both a & b
d. None of the above

ANSWER: Parseval’s Theorem


11) According to Rayleigh’s theorem, it becomes possible to determine the energy of a signal by________
a. Estimating the area under the square root of its amplitude spectrum
b. Estimating the area under the square of its amplitude spectrum
c. Estimating the area under the onefourth power of its amplitude spectrum
d. Estimating the area exactly half as that of its amplitude spectrum

ANSWER: Estimating the area under the square of its amplitude spectrum


12) What would be the value of normalized energy for the causal exponential pulse shown below?
a. 8α
b. 1 / 8α
c. 1 / 8α
d. 8α

13) What does the spectral density function of any signal specify?
a. Distribution of energy or power
b. Consumption of energy or power
c. Conservation of energy or power
d. Generation of energy or power

ANSWER: Distribution of energy or power


14) Which among
the below mentioned transform pairs is/are formed between the
autocorrelation function and the energy spectral density, in accordance
to the property of Energy Spectral Density (ESD)?
a. Laplace Transform
b. ZTransform
c. Fourier Transform
d. All of the above

ANSWER: Fourier Transform


15) The ESD of a real valued energy signal is always _________
a. An even (symmetric) function of frequency
b. An odd (nonsymmetric) function of frequency
c. A function that is odd and halfwave symmetric
d. None of the above

ANSWER: An even (symmetric) function of frequency


16) Which among the below mentioned assertions is /are correct? a. Greater the value of correlation function, higher is the similarity level between two signals b. Greater the value of correlation function, lower is the similarity level between two signals c. Lesser the value of correlation function, higher is the similarity level between two signals d. Lesser the value of correlation function, lower is the similarity level between two signals
a. Only C
b. Only B
c. A & D
d. B & C

17) Which function has a provision of determining the similarity between the signal and its delayed version?
a. Autocorrelation Function
b. Crosscorrelation Function
c. Both a & b
d. None of the above

ANSWER: Autocorrelation Function


18) Which property is exhibited by the autocorrelation function of a complex valued signal?
a. Commutative property
b. Distributive property
c. Conjugate property
d. Associative property

ANSWER: Conjugate property


19) Where does the maximum value of autocorrelation function of a power signal occur?
a. At origin
b. At extremities
c. At unity
d. At infinity

20) What does the set comprising all possible outcomes of an experiment known as?
a. Null event
b. Sure event
c. Elementary event
d. None of the above

21) What does an each outcome in the sample space regarded as?
a. Sample point
b. Element
c. Both a & b
d. None of the above

22) Mutually Exclusive events ________
a. Contain all sample points
b. Contain all common sample points
c. Does not contain any common sample point
d. Does not contain any sample point

ANSWER: Does not contain any common sample point


23) What would
be the probability of an event ‘G’ if G denotes its complement,
according to the axioms of probability?
a. P (G) = 1 / P (G)
b. P (G) = 1 – P (G)
c. P (G) = 1 + P (G)
d. P (G) = 1 * P (G)

ANSWER: P (G) = 1 – P (G)


24) What would happen if the two events are statistically independent?
a. Conditional probability becomes less than the elementary probability
b. Conditional probability becomes more than the elementary probability
c. Conditional probability becomes equal to the elementary probability
d. Conditional as well as elementary probabilities will exhibit no change

ANSWER: Conditional probability becomes equal to the elementary probability


25) What would be the joint probability of statistically independent events that occur simultaneously?
a. Zero
b. Not equal to zero
c. Infinite
d. None of the above

ANSWER: Not equal to zero


26) Consider the assertions given below A : CDF is a monotonously increasing function B : PDF is a derivative of CDF & is always positive Which among them is correct according to the properties of PDF?
a. A is true & B is false
b. A is false & B is true
c. Both A & B are true but B is a reason for A
d. Both A & B are false since B is not a reason for A

ANSWER: Both A & B are true but B is a reason for A


27) The Joint Cumulative Density Function (CDF) _____
a. Is a nonnegative function
b. Is a nondecreasing function of x & y planes
c. Is always a continuous function in xy plane
d. All of the above

28) What is the value of an area under the conditional PDF?
a. Greater than ‘0’ but less than ‘1’
b. Greater than ‘1’
c. Equal to ‘1’
d. Infinite

29) When do the conditional density functions get converted into the marginally density functions?
a. Only if random variables exhibit statistical dependency
b. Only if random variables exhibit statistical independency
c. Only if random variables exhibit deviation from its mean value
d. None of the above

ANSWER: Only if random variables exhibit statistical independency


30) Which among the below mentioned standard PDFs is/are applicable to discrete random variables?
a. Gaussian distribution
b. Rayleigh distribution
c. Poisson distribution
d. All of the above

ANSWER: Poisson distribution


31) A random variable belongs to the category of a uniform PDF only when ______
a. It occurs in a finite range
b. It is likely to possess zero value outside the finite range
c. Both a & b
d. None of the above

32) What would happen if the value of term [(mx) / (σ √2)] increases in the expression of Guassian CDF?
a. Complementary error function also goes on increasing
b. Complementary error function goes on decreasing
c. Complementary error function remains constant or unchanged
d. Cannot predict

ANSWER: Complementary error function goes on decreasing


33) Which type
of standard PDFs has/ have an ability to describe an integer valued
random variable concerning to the repeated trials carried /conducted in
an experiment?
a. Binomial
b. Uniform
c. Both a & b
d. None of the above
