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

**a.** x(t) = x(t +T_{0})

**b.** x(n) = x(n+ N)

**c.** x(t) = e^{-αt}

**d.** None of the above

**ANSWER: (a) x(t) = x(t +T _{0})**

**2) Which property of delta function indicates the equality between the area under the product of function with shifted impulse and the value of function located at unit impulse instant?**

**a.** Replication

**b.** Sampling

**c.** Scaling

**d.** Product

**ANSWER: (b) Sampling**

**3) Which among the below specified conditions/cases of discrete time in terms of real constant ‘a’, represents the double-sided decaying exponential signal?**

**a.** a > 1

**b.** 0 < a < 1

**c.** a < -1

**d.** -1 < a < 0

**ANSWER: (d) -1 < a < 0**

**4) Damped sinusoids are _____**

**a.** sinusoid signals multiplied by growing exponentials

**b.** sinusoid signals divided by growing exponentials

**c.** sinusoid signals multiplied by decaying exponentials

**d.** sinusoid signals divided by decaying exponentials

**ANSWER: (c) sinusoid signals multiplied by decaying exponentials**

**5) An amplitude of sinc function that passes through zero at multiple values of an independent variable ‘x’ ______**

**a.** Decreases with an increase in the magnitude of an independent variable (x)

**b.** Increases with an increase in the magnitude of an independent variable (x)

**c.** Always remains constant irrespective of variation in magnitude of ‘x’

**d.** Cannot be defined

**ANSWER: (a) Decreases with an increase in the magnitude of an independent variable (x)**

**6) A system is said to be shift invariant only if______**

**a.** a shift in the input signal also results in the corresponding shift in the output

**b.** a shift in the input signal does not exhibit the corresponding shift in the output

**c.** a shifting level does not vary in an input as well as output

**d.** a shifting at input does not affect the output

**ANSWER: (a) a shift in the input signal also results in the corresponding shift in the output**

**7) Which condition determines the causality of the LTI system in terms of its impulse response?**

**a.** Only if the value of an impulse response is zero for all negative values of time

**b.** Only if the value of an impulse response is unity for all negative values of time

**c.** Only if the value of an impulse response is infinity for all negative values of time

**d.** Only if the value of an impulse response is negative for all negative values of time

**ANSWER: (a) Only if the value of an impulse response is zero for all negative values of time**

**8) 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

**ANSWER: (a) only if bounded input generates unbounded output**

**9) 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)

**a.** 1 & 3

**b.** 2 & 4

**c.** 1, 3 & 4

**d.** 1, 2, 3 & 4

**ANSWER: (d) 1, 2, 3 & 4**

**10) An equalizer used to compensate the distortion in the communication system by faithful recovery of an original signal is nothing but an illustration of _________**

**a.** Static system

**b.** Dynamic system

**c.** Invertible system

**d.** None of the above

**ANSWER: (c) Invertible system**

**11) Which block of the discrete time systems requires memory in order to store the previous input?**

**a.** Adder

**b.** Signal Multiplier

**c.** Unit Delay

**d.** Unit Advance

**ANSWER: (c)Unit Delay**

**12) Which type/s of discrete-time system do/does not exhibit the necessity of any feedback?**

**a.** Recursive Systems

**b.** Non-recursive Systems

**c.** Both a & b

**d.** None of the above

**ANSWER: (b) Non-recursive Systems**

**13) Which among the following belongs to the category of non-recursive systems?**

**a.** Causal FIR Systems

**b.** Non-causal FIR Systems

**c.** Causal IIR Systems

**d.** Non-causal IIR Systems

**ANSWER: (a) Causal FIR Systems**

**14) Recursive Systems are basically characterized by the dependency of its output on _______**

**a.** Present input

**b.** Past input

**c.** Previous outputs

**d.** All of the above

**ANSWER: (d) All of the above**

**15) What does the term y(-1) indicate especially in an equation that represents the behaviour 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

**ANSWER: (a) initial condition of the system**

**16) Which type of system response to its input represents the zero value of its initial condition?**

**a.** Zero state response

**b.** Zero input response

**c.** Total response

**d.** Natural response

**ANSWER: (a) Zero state response**

**17) Which is/are the essential condition/s to get satisfied for a recursive system to be linear?**

**a.** Zero state response should be linear

**b.** Principle of Superposition should be applicable to zero input response

**c.** Total Response of the system should be addition of zero state & zero input responses

**d.** All of the above

**ANSWER: (d) All of the above**

**18) Which among the following operations is/are not involved /associated with the computation process of linear convolution?**

**a.** Folding Operation

**b.** Shifting Operation

**c.** Multiplication Operation

**d.** Integration Operation

**ANSWER: (d) Integration Operation**

**19) A LTI system is said to be initially relaxed system only if ____**

**a.** Zero input produces zero output

**b.** Zero input produces non-zero output

**c.** Zero input produces an output equal to unity

**d.** None of the above

**ANSWER:(a) Zero input produces zero output**

**20) What are the number of samples present in an impulse response called as?**

**a.** string

**b.** array

**c.** length

**d.** element

**ANSWER: (c) length**

**21) Which are the only waves that correspond/ support the measurement of phase angle in the line spectra?**

**a.** Sine waves

**b.** Cosine waves

**c.** Triangular waves

**d.** Square waves

**ANSWER: (b) Cosine waves**

**22) Double-sided phase & amplitude spectra _____**

**a.** Possess an odd & even symmetry respectively

**b.** Possess an even & odd symmetry respectively

**c.** Both possess an odd symmetry

**d.** Both possess an even symmetry

**ANSWER: (a) Possess an odd & even symmetry respectively**

**23) What does the first term ‘a _{0}‘ in the below stated expression of a line spectrum indicate?**

x(t) = a_{0} + a_{1} cos w_{0} t + a_{2} cos2 w_{0}t +……+ b_{1} sin w_{0} t + b_{2 }sin w_{0} t + …..

**a.** DC component

**b.** Fundamental component

**c.** Second harmonic component

**d.** All of the above

**ANSWER: (a) DC component**

**24) Which kind of frequency spectrum/spectra is/are obtained from the line spectrum of a continuous signal on the basis of Polar Fourier Series Method?**

**a.** Continuous in nature

**b.** Discrete in nature

**c.** Sampled in nature

**d.** All of the above

**ANSWER: (b) Discrete in nature**

**25) Which type/s of Fourier Series allow/s to represent the negative frequencies by plotting the double-sided spectrum for the analysis of periodic signals?**

**a.** Trigonometric Fourier Series

**b.** Polar Fourier Series

**c.** Exponential Fourier Series

**d.** All of the above

**ANSWER: (c) Exponential Fourier Series**

**26) What does the signalling rate in the digital communication system imply?**

**a.** Number of digital pulses transmitted per second

**b.** Number of digital pulses transmitted per minute

**c.** Number of digital pulses received per second

**d.** Number of digital pulses received per minute

**ANSWER: (a)Number of digital pulses transmitted per second**

**27) As the signalling rate increases, _______**

**a.** Width of each pulse increases

**b.** Width of each pulse decreases

**c.** Width of each pulse remains unaffected

**d.** None of the above

**ANSWER: (b)Width of each pulse decreases**

**28) Which phenomenon occurs due to an increase in the channel bandwidth during the transmission of narrow pulses in order to avoid any intervention of signal distortion?**

**a.** Compression in time domain

**b.** Expansion in time domain

**c.** Compression in frequency domain

**d.** Expansion in frequency domain

**ANSWER: (d)Expansion in frequency domain**

**29) Why are the negative & positive phase shifts introduced for positive & negative frequencies respectively in amplitude and phase spectra?**

**a.** To change the symmetry of the phase spectrum

**b.** To maintain the symmetry of the phase spectrum

**c.** Both a & b

**d.** None of the above

**ANSWER: (b) To maintain the symmetry of the phase spectrum**

**30) Duality Theorem / Property of Fourier Transform states that _________**

**a.** Shape of signal in time domain & shape of spectrum can be interchangeable

**b.** Shape of signal in frequency domain & shape of spectrum can be interchangeable

**c.** Shape of signal in time domain & shape of spectrum can never be interchangeable

**d.** Shape of signal in time domain & shape of spectrum can never be interchangeable

**ANSWER: (a) Shape of signal in time domain & shape of spectrum can be interchangeable**

**31) Which property of fourier transform gives rise to an additional phase shift of -2π ft _{d} for the generated time delay in the communication system without affecting an amplitude spectrum?**

**a.** Time Scaling

**b.** Linearity

**c.** Time Shifting

**d.** Duality

**ANSWER: (c) Time Shifting**

**32) Which among the below assertions is precise in accordance to the effect of time scaling?**

A : Inverse relationship exists between the time and frequency domain representation of signal

B : A signal must be necessarily limited in time as well as frequency domains

**a.** A is true & B is false

**b.** A is false & B is true

**c.** Both A & B are true

**d.** Both A & B are false

**ANSWER: (a)A is true & B is false**

**33) Which is/are the mandatory condition/s to get satisfied by the transfer function for the purpose of distortionless transmission?**

**a.** Amplitude Response should be constant for all frequencies

**b.** Phase should be linear with frequency passing through zero

**c.** Both a & b

**d.** None of the above

**ANSWER: (c)Both a & b**

**34) What is/are the crucial purposes of using the Fourier Transform while analyzing any elementary signals at different frequencies?**

**a.** Transformation from time domain to frequency domain

**b.** Plotting of amplitude & phase spectrum

**c.** Both a & b

**d.** None of the above

**ANSWER: (c)Both a & b**

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

**a.** 0 to 2π

**b.** -π to +π

**c.** Both a & b

**d.** None of the above

**ANSWER: (c)Both a & b**

**36) Which among the following assertions represents a necessary condition for the existence of Fourier Transform of discrete time signal (DTFT)?**

**a.** Discrete Time Signal should be absolutely summable

**b.** Discrete Time Signal should be absolutely multipliable

**c.** Discrete Time Signal should be absolutely integrable

**d.** Discrete Time Signal should be absolutely differentiable

**ANSWER: (a)Discrete Time Signal should be absolutely summable**

**37) What is the nature of Fourier representation of a discrete & aperiodic signal?**

**a.** Continuous & periodic

**b.** Discrete & aperiodic

**c.** Continuous & aperiodic

**d.** Discrete & periodic

**ANSWER: (a) Continuous & periodic**

**38) Which property of periodic signal in DTFS gets completely clarified / identified by the equation x (n – n _{0})?**

**a.** Conjugation

**b.** Time Shifting

**c.** Frequency Shifting

**d.** Time Reversal

**ANSWER: (b) Time Shifting**

**39) 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

**ANSWER: (a) A & B**

**40) Where is the ROC defined or specified for the signals containing causal as well as anti-causal terms?**

**a.** Greater than the largest pole

**b.** Less than the smallest pole

**c.** Between two poles

**d.** Cannot be defined

**ANSWER: (c) Between two poles**

**41) What should be the value of laplace transform for the time-domain signal equation e ^{-at} cos ωt.u(t)?**

**a.** 1 / s + a with ROC σ > – a

**b.** ω / (s + a) ^{2} + ω^{2} with ROC σ > – a

**c.** s + a / (s + a)^{2} + ω^{2} with ROC σ > – a

**d.** Aω / s^{2} + ω^{2} with ROC σ > 0

**ANSWER: (c) s + a / (s + a) ^{2} + ω^{2} with ROC σ > – a**

**42) According to the time-shifting property of Laplace Transform, shifting the signal in time 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

**ANSWER: (b) Multiplication by e ^{-st0} in the frequency domain**

**43) 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: (b) Ramp Function shifted by an amount equal to step**

**44) Unilateral Laplace Transform is applicable for the determination of linear constant coefficient differential equations with ________**

**a.** Zero initial condition

**b.** Non-zero initial condition

**c.** Zero final condition

**d.** Non-zero final condition

**ANSWER: (b) Non-zero initial condition**

**45) 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: (c) On both sides of ROC**

**46) 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: (a) Simple multiplication in complex frequency domain**

**47) 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

**ANSWER: (c) Green’s function**

**48) 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 left-half of S-plane

**b.** Only if all the poles of system transfer function lie in right-half of S-plane

**c.** Only if all the poles of system transfer function lie at the centre of S-plane

**d.** None of the above

**ANSWER: (a) Only if all the poles of system transfer function lie in left-half of S-plane**

**49) 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: (a) Amplitude of one signal plotted against the amplitude of another signal**

**50) 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: (a) Parseval’s Theorem**

**51) 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 one-fourth power of its amplitude spectrum

**d.** Estimating the area exactly half as that of its amplitude spectrum

**ANSWER: (b) Estimating the area under the square of its amplitude spectrum**

**52) 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: (a) Distribution of energy or power**

**53) Which among the below mentioned transform pairs is/are formed between the auto-correlation function and the energy spectral density, in accordance to the property of Energy Spectral Density (ESD)?**

**a.** Laplace Transform

**b.** Z-Transform

**c.** Fourier Transform

**d.** All of the above

**ANSWER: (c) Fourier Transform**

**54) The ESD of a real valued energy signal is always _________**

**a.** An even (symmetric) function of frequency

**b.** An odd (non-symmetric) function of frequency

**c.** A function that is odd and half-wave symmetric

**d.** None of the above

**ANSWER: (a) An even (symmetric) function of frequency**

**55) 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

**ANSWER: (c) A & D**

**56) Which function has a provision of determining the similarity between the signal and its delayed version?**

**a.** Auto-correlation Function

**b.** Cross-correlation Function

**c.** Both a & b

**d.** None of the above

**ANSWER: (a) Auto-correlation Function**

**57) Which property is exhibited by the auto-correlation function of a complex valued signal?**

**a.** Commutative property

**b.** Distributive property

**c.** Conjugate property

**d.** Associative property

**ANSWER: (c) Conjugate property**

**58) Where does the maximum value of auto-correlation function of a power signal occur?**

**a.** At origin

**b.** At extremities

**c.** At unity

**d.** At infinity

**ANSWER: (a) At origin**

**59) 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

**ANSWER: (b) Sure event**

**60) 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

**ANSWER: (c) Both a & b**

**61) 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: (c) Does not contain any common sample point**

**62) 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:(b) P (G) = 1 – P (G)**

**63) 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: (c) Conditional probability becomes equal to the elementary probability**

**64) 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: (b) Not equal to zero**

**65) 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: (c) Both A & B are true but B is a reason for A**

**66) The Joint Cumulative Density Function (CDF) _____**

**a.** Is a non-negative function

**b.** Is a non-decreasing function of x & y planes

**c.** Is always a continuous function in xy plane

**d.** All of the above

**ANSWER: (d) All of the above**

**67) 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

**ANSWER: (c) Equal to ‘1’**

**68) 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: (b) Only if random variables exhibit statistical independency**

**69) 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: (c) Poisson distribution**

**70) 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

**ANSWER: (c) Both a & b**

**71) What would happen if the value of term [(m-x) / (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: (b) Complementary error function goes on decreasing**

**72) 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

**ANSWER: (a) Binomial**