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Signals & Systems MCQs

Practice Signals & Systems MCQs from fundamental concepts through intermediate, advanced and application-oriented questions. Each page contains up to 100 questions with answers and explanations where available.

Question 1

Signals & SystemsSampling

According to the sampling theorem, a band-limited signal should be sampled at a rate of at least?

AHalf the highest signal frequency
BEqual to the highest signal frequency
CTwice the highest signal frequency
DFour times the lowest signal frequency

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Correct Answer: C. Twice the highest signal frequency

Explanation: For ideal reconstruction, the sampling frequency must be at least twice the highest frequency component of the band-limited signal.

Reference: Nyquist sampling theorem

Question 2

Signals & SystemsSignal Fundamentals

A signal that is defined for every value of continuous time t is called a?

AContinuous-time signal
BDiscrete-time signal
CBinary code only
DQuantized sequence only

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Correct Answer: A. Continuous-time signal

Explanation: A continuous-time signal x(t) is defined over a continuous range of the independent variable t.

Reference: Standard signals and systems: signal fundamentals

Question 3

Signals & SystemsSignal Transformations

Which operation represents a time delay of 3 seconds applied to x(t)?

Ax(t+3)
Bx(t-3)
Cx(3t)
Dx(t/3)

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Correct Answer: B. x(t-3)

Explanation: Replacing t by t-3 shifts the signal to the right by 3 seconds, representing a delay.

Reference: Standard signals and systems: signal transformations

Question 4

Signals & SystemsSignal Fundamentals

A discrete-time signal is commonly represented as?

Ax(t) only
Bx[n]
CX(s) only
DV/Hz

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Correct Answer: B. x[n]

Explanation: A discrete-time signal is represented as a sequence x[n], where n is an integer index.

Reference: Standard signals and systems: signal fundamentals

Question 5

Signals & SystemsSignal Transformations

The signal x(2t) is, relative to x(t),?

ATime-expanded by 2
BTime-compressed by 2
CDelayed by 2 s
DAmplitude-scaled by 2 only

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Correct Answer: B. Time-compressed by 2

Explanation: Replacing t by 2t compresses the time axis by a factor of 2.

Reference: Standard signals and systems: signal transformations

Question 6

Signals & SystemsElementary Signals

The continuous-time unit step u(t) is conventionally equal to 1 for?

At<0
Bt>0
CAll t only when differentiated
DNo value of t

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Correct Answer: B. t>0

Explanation: Under the usual convention, u(t)=0 for t0; the value exactly at t=0 depends on convention.

Reference: Standard signals and systems: elementary signals

Question 7

Signals & SystemsElementary Signals

The continuous-time unit impulse delta(t) has unit?

AAmplitude at all times
BArea
CPeriod
DAverage power

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Correct Answer: B. Area

Explanation: The Dirac impulse is characterized by zero value away from t=0 and unit area over an interval containing the origin.

Reference: Standard signals and systems: elementary signals

Question 8

Signals & SystemsElementary Signals

The derivative of the continuous-time unit step u(t) is?

Au(t)
Bdelta(t)
Ct u(t)
D1 for all t

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Correct Answer: B. delta(t)

Explanation: In the generalized-function sense, d[u(t)]/dt = delta(t).

Reference: Standard signals and systems: elementary signals

Question 9

Signals & SystemsElementary Signals

The integral of delta(t) from minus infinity to t is?

Au(t)
Bdelta(t)
Ct
D0 for every t

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Correct Answer: A. u(t)

Explanation: Integrating the unit impulse from -infinity up to t produces the unit-step function.

Reference: Standard signals and systems: elementary signals

Question 10

Signals & SystemsElementary Signals

For any continuous signal x(t), the sifting property gives integral x(t)delta(t-t0)dt over all time equal to?

A0
Bx(0) only
Cx(t0)
Ddelta(t0)

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Correct Answer: C. x(t0)

Explanation: The shifted impulse samples the signal at its location: ∫x(t)delta(t-t0)dt=x(t0).

Reference: Standard signals and systems: elementary signals

Question 11

Signals & SystemsPeriodic Signals

A continuous-time sinusoid x(t)=cos(100pi t) has frequency?

A25 Hz
B50 Hz
C100 Hz
D200 Hz

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Correct Answer: B. 50 Hz

Explanation: Comparing cos(2pi f t) with cos(100pi t), 2pi f=100pi, so f=50 Hz.

Reference: Standard signals and systems: periodic signals

Question 12

Signals & SystemsPeriodic Signals

The fundamental period of x(t)=cos(20pi t) is?

A0.01 s
B0.05 s
C0.1 s
D0.2 s

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Correct Answer: C. 0.1 s

Explanation: Here omega=20pi rad/s, so f=10 Hz and T=1/f=0.1 s.

Reference: Standard signals and systems: periodic signals

Question 13

Signals & SystemsPeriodic Signals

A continuous-time sinusoidal signal is periodic when its angular frequency is?

ANonzero; every single continuous-time sinusoid with fixed nonzero frequency is periodic
BAn integer only
CLess than 1 rad/s only
DExactly pi rad/s only

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Correct Answer: A. Nonzero; every single continuous-time sinusoid with fixed nonzero frequency is periodic

Explanation: A single continuous-time sinusoid cos(omega0 t+phi) with fixed nonzero omega0 has period 2pi/|omega0|.

Reference: Standard signals and systems: periodic signals

Question 14

Signals & SystemsPeriodic Signals

A discrete-time sinusoid x[n]=cos(omega0 n) is periodic only if?

Aomega0/(2pi) is rational
Bomega0/(2pi) is irrational
Comega0=1 always
DIts amplitude is less than one

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Correct Answer: A. omega0/(2pi) is rational

Explanation: A discrete-time sinusoid is periodic if there exist integers N>0 and k such that omega0 N=2pi k, equivalently omega0/(2pi) is rational.

Reference: Standard signals and systems: periodic signals

Question 15

Signals & SystemsPeriodic Signals

The sequence x[n]=cos(pi n/2) has fundamental period?

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Correct Answer: B. 4

Explanation: The smallest positive N satisfying (pi/2)N=2pi k is N=4.

Reference: Standard signals and systems: periodic signals

Question 16

Signals & SystemsSignal Classification

A signal x(t) is even if it satisfies?

Ax(-t)=x(t)
Bx(-t)=-x(t)
Cx(t+T)=0
Dx(t)=delta(t) only

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Correct Answer: A. x(-t)=x(t)

Explanation: An even signal is symmetric about the vertical axis and obeys x(-t)=x(t).

Reference: Standard signals and systems: signal classification

Question 17

Signals & SystemsSignal Classification

A signal x(t) is odd if it satisfies?

Ax(-t)=x(t)
Bx(-t)=-x(t)
Cx(t)=1 for all t
Dx(t)=x(t-1)

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Correct Answer: B. x(-t)=-x(t)

Explanation: An odd signal has origin symmetry and obeys x(-t)=-x(t).

Reference: Standard signals and systems: signal classification

Question 18

Signals & SystemsSignal Classification

Any signal x(t) can be decomposed into even and odd parts. Its even part is?

A[x(t)+x(-t)]/2
B[x(t)-x(-t)]/2
Cx(t)+x(-t)
D2x(t)

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Correct Answer: A. [x(t)+x(-t)]/2

Explanation: The even component is xe(t)=1/2[x(t)+x(-t)].

Reference: Standard signals and systems: signal classification

Question 19

Signals & SystemsSignal Classification

The odd part of a signal x(t) is?

A[x(t)+x(-t)]/2
B[x(t)-x(-t)]/2
Cx(-t) only
Dx(t)/2 only

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Correct Answer: B. [x(t)-x(-t)]/2

Explanation: The odd component is xo(t)=1/2[x(t)-x(-t)].

Reference: Standard signals and systems: signal classification

Question 20

Signals & SystemsSignal Transformations

The signal x(t/2) is, relative to x(t),?

ATime-compressed by 2
BTime-expanded by 2
CTime-reversed
DDifferentiated

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Correct Answer: B. Time-expanded by 2

Explanation: Replacing t by t/2 expands the time axis by a factor of 2.

Reference: Standard signals and systems: signal transformations

Question 21

Signals & SystemsSignal Transformations

The transformation x(-t) represents?

AAmplitude inversion
BTime reversal
CTime delay
DIntegration

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Correct Answer: B. Time reversal

Explanation: Changing t to -t reflects the signal about t=0, which is time reversal.

Reference: Standard signals and systems: signal transformations

Question 22

Signals & SystemsEnergy & Power Signals

A finite-energy signal has energy E that is?

AFinite and nonzero, with zero average power
BInfinite with finite average power
CAlways equal to one
DZero for every nonzero signal

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Correct Answer: A. Finite and nonzero, with zero average power

Explanation: For the usual energy/power classification, an energy signal has 0<E<infinity and average power equal to zero.

Reference: Standard signals and systems: energy & power signals

Question 23

Signals & SystemsEnergy & Power Signals

A nonzero periodic signal with finite average power is generally classified as a?

APower signal
BEnergy signal with finite nonzero energy
CNeither under all conditions
DImpulse only

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Correct Answer: A. Power signal

Explanation: A typical nonzero periodic signal has infinite total energy but finite nonzero average power, so it is a power signal.

Reference: Standard signals and systems: energy & power signals

Question 24

Signals & SystemsEnergy & Power Signals

The total energy of x(t)=e^(-t)u(t) is?

A1/4
B1/2
C1
D2

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Correct Answer: B. 1/2

Explanation: E=∫0^infinity |e^-t|^2 dt=∫0^infinity e^-2t dt=1/2.

Reference: Standard signals and systems: energy & power signals

Question 25

Signals & SystemsSystem Properties

A system is linear if it satisfies the principle of?

ASuperposition
BAliasing
CQuantization
DModulation only

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Correct Answer: A. Superposition

Explanation: Linearity requires additivity and homogeneity, together expressed by the superposition principle.

Reference: Standard signals and systems: system properties

Question 26

Signals & SystemsSystem Properties

A system is time-invariant if?

AA time shift of the input produces the same time shift of the output
BIts output never changes with time
CIt has no memory under all conditions
DIts input must be periodic

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Correct Answer: A. A time shift of the input produces the same time shift of the output

Explanation: For a time-invariant system, delaying the input by t0 delays the corresponding output by the same amount without otherwise changing it.

Reference: Standard signals and systems: system properties

Question 27

Signals & SystemsConvolution

Continuous-time convolution is?

AIntegral x(tau)h(t-tau)d tau over all tau
BIntegral x(t)h(t)dt only
Cx(t)+h(t)
Dx(t)/h(t)

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Correct Answer: A. Integral x(tau)h(t-tau)d tau over all tau

Explanation: Continuous-time convolution integrates x(tau)h(t-tau) over all tau.

Reference: Standard signals and systems: convolution

Question 28

Signals & SystemsConvolution

Which is a property of convolution?

Ax*h=h*x
Bx*h=x-h
CIt is never associative
DIt requires x=h

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Correct Answer: A. x*h=h*x

Explanation: Convolution is commutative.

Reference: Standard signals and systems: convolution

Question 29

Signals & SystemsConvolution

Convolution with the unit impulse gives?

A0
Bx(t)
C1
Ddx(t)/dt

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Correct Answer: B. x(t)

Explanation: The unit impulse is the identity for convolution.

Reference: Standard signals and systems: convolution

Question 30

Signals & SystemsConvolution

x(t)*delta(t-t0) equals?

Ax(t+t0)
Bx(t-t0)
Cdelta(t)
Dx(t0) only

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Correct Answer: B. x(t-t0)

Explanation: A shifted impulse shifts the convolved signal by the same amount.

Reference: Standard signals and systems: convolution

Question 31

Signals & SystemsConvolution

If x(t)=u(t) and h(t)=u(t), their convolution is?

Au(t)
Bt u(t)
Cdelta(t)
De^(-t)u(t)

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Correct Answer: B. t u(t)

Explanation: The overlap integral has length t for t>=0, giving t u(t).

Reference: Standard signals and systems: convolution

Question 32

Signals & SystemsConvolution

If x(t)=e^(-t)u(t) and h(t)=delta(t), the output is?

Ae^(-t)u(t)
Bdelta(t)
Cu(t)
De^t u(t)

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Correct Answer: A. e^(-t)u(t)

Explanation: Convolution with delta leaves the signal unchanged.

Reference: Standard signals and systems: convolution

Question 33

Signals & SystemsDiscrete-Time LTI

Discrete-time convolution uses?

AA summation over an integer index
BOnly a continuous integral
CMatrix inversion always
DDifferentiation only

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Correct Answer: A. A summation over an integer index

Explanation: y[n]=sum x[k]h[n-k].

Reference: Standard signals and systems: discrete-time lti

Question 34

Signals & SystemsDiscrete-Time LTI

Discrete-time LTI BIBO stability requires?

ASum of |h[n]| over all n is finite
Bh[n]=n
Ch[n] periodic
Dh[0]=0

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Correct Answer: A. Sum of |h[n]| over all n is finite

Explanation: The impulse response must be absolutely summable.

Reference: Standard signals and systems: discrete-time lti

Question 35

Signals & SystemsDiscrete-Time LTI

For a causal discrete-time LTI system, h[n] must be zero for?

An<0
Bn>0
Cn=0
DAll positive even n

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Correct Answer: A. n<0

Explanation: Causality requires h[n]=0 for negative n.

Reference: Standard signals and systems: discrete-time lti

Question 36

Signals & SystemsSystem Properties

A system is causal if its output at any time depends only on?

AFuture input values
BPresent and past input values
CFuture output values only
DThe input at t=infinity

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Correct Answer: B. Present and past input values

Explanation: A causal system cannot depend on future input values; its output may depend on present and past inputs.

Reference: Standard signals and systems: system properties

Question 37

Signals & SystemsFourier Series

Fourier series is primarily used to represent?

APeriodic signals
BOnly nonperiodic impulses
COnly random noise
DDC circuits only

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Correct Answer: A. Periodic signals

Explanation: Fourier series represents periodic signals using harmonically related components.

Reference: Standard signals and systems: fourier series

Question 38

Signals & SystemsSystem Properties

Which system is memoryless?

Ay(t)=x(t-2)
By(t)=x(t)+x(t-1)
Cy(t)=3x(t)
Dy(t)=integral from -infinity to t of x(tau)d tau

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Correct Answer: C. y(t)=3x(t)

Explanation: A memoryless system output at time t depends only on the input at that same time.

Reference: Standard signals and systems: system properties

Question 39

Signals & SystemsFourier Series

For period T0, fundamental angular frequency is?

AT0/(2pi)
B2pi/T0
C1/T0^2
Dpi T0

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Correct Answer: B. 2pi/T0

Explanation: omega0=2pi/T0.

Reference: Standard signals and systems: fourier series

Question 40

Signals & SystemsSystem Properties

The continuous-time system y(t)=x(t-1) is?

ANoncausal
BCausal with memory
CMemoryless and causal
DUnstable for every input

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Correct Answer: B. Causal with memory

Explanation: It depends on a past input value, so it is causal and has memory.

Reference: Standard signals and systems: system properties

Question 41

Signals & SystemsFourier Series

A periodic signal has period 2 ms. Its fundamental frequency is?

A50 Hz
B500 Hz
C2 kHz
D5 kHz

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Correct Answer: B. 500 Hz

Explanation: f0=1/0.002=500 Hz.

Reference: Standard signals and systems: fourier series

Question 42

Signals & SystemsSystem Properties

A system is BIBO stable if every bounded input produces?

AA bounded output
BAn unbounded output
CZero output only
DA periodic output only

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Correct Answer: A. A bounded output

Explanation: BIBO means bounded-input bounded-output stability.

Reference: Standard signals and systems: system properties

Question 43

Signals & SystemsFourier Series

Fourier-series harmonic frequencies are?

AInteger multiples of the fundamental
BAlways irrational multiples
CAlways lower than fundamental
DIndependent of fundamental

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Correct Answer: A. Integer multiples of the fundamental

Explanation: The kth harmonic is k times the fundamental frequency.

Reference: Standard signals and systems: fourier series

Question 44

Signals & SystemsLTI Systems

For a continuous-time LTI system, BIBO stability requires?

AIntegral of |h(t)| over all time is finite
Bh(t) must be periodic
Ch(t) must be odd
DIntegral of h(t) must always be zero

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Correct Answer: A. Integral of |h(t)| over all time is finite

Explanation: A continuous-time LTI system is BIBO stable if its impulse response is absolutely integrable.

Reference: Standard signals and systems: lti systems

Question 45

Signals & SystemsLTI Systems

For a causal continuous-time LTI system, h(t) must be zero for?

At>0
Bt<0
Ct=1 only
DAll t

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Correct Answer: B. t<0

Explanation: Causality requires h(t)=0 for t<0.

Reference: Standard signals and systems: lti systems

Question 46

Signals & SystemsConvolution

The output of an LTI system is obtained from x(t) and h(t) by?

AMultiplication only
BConvolution
CDifferentiation only
DTime reversal only

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Correct Answer: B. Convolution

Explanation: For an LTI system, y(t)=x(t)*h(t).

Reference: Standard signals and systems: convolution

Question 47

Signals & SystemsFourier Series

A standard symmetric 50% duty-cycle square wave contains?

AOnly odd harmonics
BOnly even harmonics
CNo harmonics
DOnly second harmonic

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Correct Answer: A. Only odd harmonics

Explanation: Its even harmonics vanish due to symmetry.

Reference: Standard signals and systems: fourier series

Question 48

Signals & SystemsLTI Frequency Response

If an LTI system is excited by e^(j omega t), the response is the same exponential multiplied by?

AH(j omega)
BSampling period only
CZero always
Domega squared always

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Correct Answer: A. H(j omega)

Explanation: Complex exponentials are eigenfunctions of LTI systems; output is H(jomega)e^(jomega t).

Reference: Standard signals and systems: lti frequency response

Question 49

Signals & SystemsFourier Series

For a real even periodic signal, the trigonometric Fourier series contains primarily?

ACosine terms
BSine terms only
CNo harmonics
DComplex frequencies only

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Correct Answer: A. Cosine terms

Explanation: Even symmetry eliminates sine coefficients, apart from a possible DC term.

Reference: Standard signals and systems: fourier series

Question 50

Signals & SystemsFourier Series

For a real odd periodic signal, the trigonometric Fourier series contains primarily?

ACosine terms and DC
BSine terms
COnly DC
DNo frequency components

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Correct Answer: B. Sine terms

Explanation: Odd symmetry eliminates cosine and DC terms, leaving sine terms.

Reference: Standard signals and systems: fourier series

Question 51

Signals & SystemsFourier Series

Parseval’s relation connects average power with?

ASquared magnitudes of Fourier-series coefficients
BOnly maximum amplitude
COnly fundamental period
DDerivative at t=0

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Correct Answer: A. Squared magnitudes of Fourier-series coefficients

Explanation: Parseval expresses signal power through the squared Fourier coefficient magnitudes.

Reference: Standard signals and systems: fourier series

Question 52

Signals & SystemsLaplace Transform

A causal rational continuous-time LTI system is BIBO stable if all its poles lie?

AStrictly in the left half of the s-plane
BStrictly in the right half-plane
COnly on the jω-axis
DAt the origin only

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Correct Answer: A. Strictly in the left half of the s-plane

Explanation: For a causal rational system, BIBO stability requires the jω-axis to lie in the ROC, which means all poles must be strictly in the left half-plane.

Reference: Standard signals and systems: laplace transform

Question 53

Signals & SystemsZ-Transform

The bilateral Z-transform of x[n] is defined as?

AΣ x[n]z^(-n) over all integer n
BΣ x[n]z^n for n=0 only
Cx[n]/z
Ddx[n]/dn

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Correct Answer: A. Σ x[n]z^(-n) over all integer n

Explanation: The bilateral Z-transform is X(z)=Σ from n=-∞ to ∞ x[n]z^(-n).

Reference: Standard signals and systems: z-transform

Question 54

Signals & SystemsFourier Transform

The continuous-time Fourier transform X(jω) of x(t) is defined as?

A∫x(t)e^(-jωt)dt over all time
B∫x(t)e^(jωt)dt from 0 to 1
Cx(t)e^(-jωt)
Ddx(t)/dt

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Correct Answer: A. ∫x(t)e^(-jωt)dt over all time

Explanation: The CTFT analysis equation is X(jω)=∫ from -∞ to ∞ x(t)e^(-jωt)dt.

Reference: Standard signals and systems: fourier transform

Question 55

Signals & SystemsFourier Transform

The Fourier transform of the unit impulse delta(t) is?

A0
B1
Cjω
D2πdelta(ω) only

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Correct Answer: B. 1

Explanation: Using the CTFT definition, ∫delta(t)e^(-jωt)dt=1.

Reference: Standard signals and systems: fourier transform

Question 56

Signals & SystemsFourier Transform

The Fourier transform of delta(t-t0) is?

Ae^(-jωt0)
Be^(jωt0)
Cdelta(ω-t0)
D1/(jω)

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Correct Answer: A. e^(-jωt0)

Explanation: The shifted impulse property gives delta(t-t0) ↔ e^(-jωt0).

Reference: Standard signals and systems: fourier transform

Question 57

Signals & SystemsFourier Transform

If x(t) ↔ X(jω), then x(t-t0) has Fourier transform?

AX(jω)e^(-jωt0)
BX(jω)e^(jωt0)
CX(j(ω-t0))
Dt0X(jω)

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Correct Answer: A. X(jω)e^(-jωt0)

Explanation: A time delay t0 introduces the linear phase factor e^(-jωt0).

Reference: Standard signals and systems: fourier transform

Question 58

Signals & SystemsFourier Transform

If x(t) ↔ X(jω), multiplication of x(t) by e^(jω0t) produces?

AX(j(ω-ω0))
BX(j(ω+ω0))
Cω0X(jω)
DX(jω)e^(-jω0)

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Correct Answer: A. X(j(ω-ω0))

Explanation: Time-domain modulation by e^(jω0t) shifts the spectrum by +ω0: X(j(ω-ω0)).

Reference: Standard signals and systems: fourier transform

Question 59

Signals & SystemsFourier Transform

Differentiation in time corresponds in the Fourier domain to?

ADivision by jω
BMultiplication by jω
CTime reversal only
DMultiplication by t

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Correct Answer: B. Multiplication by jω

Explanation: If x(t) ↔ X(jω), then dx(t)/dt ↔ jωX(jω), under standard conditions.

Reference: Standard signals and systems: fourier transform

Question 60

Signals & SystemsFourier Transform

Convolution in the time domain corresponds to what operation in the Fourier domain?

AAddition
BMultiplication
CDifferentiation only
DTime reversal

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Correct Answer: B. Multiplication

Explanation: The convolution theorem states x(t)*h(t) ↔ X(jω)H(jω).

Reference: Standard signals and systems: fourier transform

Question 61

Signals & SystemsFourier Transform

Parseval’s relation for the Fourier transform connects signal energy with?

AIntegral of |X(jω)|² in frequency
BOnly X(0)
COnly signal period
DMaximum signal amplitude only

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Correct Answer: A. Integral of |X(jω)|² in frequency

Explanation: Parseval's relation expresses time-domain energy equivalently in terms of the integral of spectral magnitude squared, with the appropriate 1/(2π) factor.

Reference: Standard signals and systems: fourier transform

Question 62

Signals & SystemsLaplace Transform

The bilateral Laplace transform of x(t) is?

A∫x(t)e^(-st)dt over all time
B∫x(t)e^(st)dt from 0 to 1
Cx(t)/s
Ddx(t)/dt only

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Correct Answer: A. ∫x(t)e^(-st)dt over all time

Explanation: The bilateral Laplace transform is X(s)=∫ from -∞ to ∞ x(t)e^(-st)dt.

Reference: Standard signals and systems: laplace transform

Question 63

Signals & SystemsLaplace Transform

The Laplace transform of e^(-at)u(t), with the appropriate ROC, is?

A1/(s-a)
B1/(s+a)
Cs/(s+a)
Da/(s²+a²)

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Correct Answer: B. 1/(s+a)

Explanation: For a right-sided exponential e^(-at)u(t), X(s)=1/(s+a) with ROC Re{s}>-a.

Reference: Standard signals and systems: laplace transform

Question 64

Signals & SystemsLaplace Transform

For x(t)=e^(-2t)u(t), the ROC of its bilateral Laplace transform is?

ARe{s}>-2
BRe{s}<-2
CRe{s}=0 only
DAll s including the pole

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Correct Answer: A. Re{s}>-2

Explanation: A right-sided exponential has ROC to the right of its pole at s=-2.

Reference: Standard signals and systems: laplace transform

Question 65

Signals & SystemsLaplace Transform

For x(t)=-e^(-2t)u(-t), whose transform is 1/(s+2), the ROC is?

ARe{s}>-2
BRe{s}<-2
CRe{s}>2
DAll s

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Correct Answer: B. Re{s}<-2

Explanation: The left-sided version has the same algebraic transform but an ROC to the left of the pole: Re{s}<-2.

Reference: Standard signals and systems: laplace transform

Question 66

Signals & SystemsLaplace Transform

The ROC of a bilateral Laplace transform can contain a pole of X(s)?

AAlways
BNever
COnly for causal signals
DOnly at s=0

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Correct Answer: B. Never

Explanation: The Laplace-transform integral does not converge at a pole, so poles are excluded from the ROC.

Reference: Standard signals and systems: laplace transform

Question 67

Signals & SystemsLaplace Transform

For a causal rational LTI system, the ROC of H(s) lies?

ATo the right of the rightmost pole
BTo the left of the leftmost pole
COnly between every pair of poles
DExactly on the jω-axis

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Correct Answer: A. To the right of the rightmost pole

Explanation: A causal rational impulse response is right-sided, so its ROC is to the right of the rightmost pole.

Reference: Standard signals and systems: laplace transform

Question 68

Signals & SystemsZ-Transform

The Z-transform of a^n u[n] is?

A1/(1-az^-1), ROC |z|>|a|
B1/(1+az^-1), ROC |z|<|a|
Cz-a, all z
Da/(z+1), all z

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Correct Answer: A. 1/(1-az^-1), ROC |z|>|a|

Explanation: For the right-sided sequence a^n u[n], the geometric series gives X(z)=1/(1-az^-1) with ROC |z|>|a|.

Reference: Standard signals and systems: z-transform

Question 69

Signals & SystemsZ-Transform

For a right-sided sequence a^n u[n], the ROC is?

A|z|>|a|
B|z|<|a|
C|z|=|a| only
Dz=a only

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Correct Answer: A. |z|>|a|

Explanation: Convergence of the geometric series requires |az^-1||a|.

Reference: Standard signals and systems: z-transform

Question 70

Signals & SystemsZ-Transform

For a causal rational discrete-time LTI system, the ROC of H(z) is generally?

AOutside the outermost pole
BInside the innermost pole
COnly on the unit circle
DBetween zero and every pole

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Correct Answer: A. Outside the outermost pole

Explanation: A causal rational impulse response is right-sided, so its ROC extends outward from the outermost pole to infinity.

Reference: Standard signals and systems: z-transform

Question 71

Signals & SystemsZ-Transform

A causal rational discrete-time LTI system is BIBO stable when all its poles are?

AStrictly inside the unit circle
BStrictly outside the unit circle
CExactly on the unit circle
DAt z=1 only

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Correct Answer: A. Strictly inside the unit circle

Explanation: For a causal rational system to be stable, the unit circle must lie in the ROC; therefore all poles must lie strictly inside it.

Reference: Standard signals and systems: z-transform

Question 72

Signals & SystemsZ-Transform

The frequency response of a stable discrete-time LTI system can be obtained from H(z) by evaluating it on?

AThe unit circle z=e^(jω)
BThe real axis only
Cz=0 only
Dz=infinity only

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Correct Answer: A. The unit circle z=e^(jω)

Explanation: When the unit circle is in the ROC, H(e^(jω)) is obtained by evaluating H(z) at z=e^(jω).

Reference: Standard signals and systems: z-transform

Question 73

Signals & SystemsSampling

According to the sampling theorem, a signal band-limited to 6 kHz should be sampled at at least?

A3 kHz
B6 kHz
C12 kHz
D36 kHz

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Correct Answer: C. 12 kHz

Explanation: The Nyquist rate is twice the highest signal frequency: fs≥2×6 kHz=12 kHz.

Reference: Standard signals and systems: sampling

Question 74

Signals & SystemsSampling

A sinusoid of frequency 3 kHz is sampled at 8 kHz. Does the sampling rate satisfy the basic Nyquist criterion?

AYes
BNo
COnly if amplitude is zero
DOnly for a DC signal

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Correct Answer: A. Yes

Explanation: The Nyquist rate is 2×3=6 kHz, and 8 kHz exceeds it.

Reference: Standard signals and systems: sampling

Question 75

Signals & SystemsSampling

Ideal reconstruction of a properly sampled band-limited signal is theoretically performed using a?

AIdeal low-pass reconstruction filter
BHigh-pass differentiator only
CRectifier
DLimiter only

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Correct Answer: A. Ideal low-pass reconstruction filter

Explanation: After ideal impulse-train sampling above the Nyquist rate, an ideal low-pass filter can select the original baseband spectral replica.

Reference: Standard signals and systems: sampling

Question 76

Signals & SystemsSampling

A continuous-time signal band-limited to 4 kHz is sampled at 6 kHz. Which phenomenon can occur?

AAliasing
BPerfect reconstruction guaranteed
CNo spectral repetition
DOnly amplitude scaling

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Correct Answer: A. Aliasing

Explanation: Since 6 kHz is below the 8 kHz Nyquist rate, shifted spectra can overlap, causing aliasing.

Reference: Standard signals and systems: sampling

Question 77

Signals & SystemsStability

A causal discrete-time system has poles at z=0.4 and z=0.8. It is BIBO stable?

AYes
BNo
COnly if both poles are negative
DOnly if a pole is at z=1

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Correct Answer: A. Yes

Explanation: For a causal rational DT system, stability requires all poles to lie strictly inside the unit circle; both 0.4 and 0.8 satisfy this.

Reference: Standard signals and systems: stability

Question 78

Signals & SystemsDTFT

If x[n] is delayed by n0 samples, its DTFT is multiplied by?

Ae^(-jωn0)
Be^(jωn0)
Cn0
Djω

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Correct Answer: A. e^(-jωn0)

Explanation: The DTFT time-shift property is x[n-n0] ↔ e^(-jωn0)X(e^(jω)).

Reference: Standard signals and systems: dtft

Question 79

Signals & SystemsStability

A causal discrete-time system has a pole at z=1.2. Its BIBO stability is?

AStable
BUnstable
CMarginally stable in every sense
DIndependent of pole location

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Correct Answer: B. Unstable

Explanation: For a causal rational DT system, a pole outside the unit circle prevents the unit circle from being in the ROC, so it is not BIBO stable.

Reference: Standard signals and systems: stability

Question 80

Signals & SystemsZ-Transform

If h[n]=(0.5)^n u[n], H(z) is?

A1/(1-0.5z^-1)
B1/(1+0.5z^-1)
Cz^-1/0.5
D1-0.5z^-1

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Correct Answer: A. 1/(1-0.5z^-1)

Explanation: The Z-transform of a^n u[n] is 1/(1-az^-1), with |z|>|a|.

Reference: Standard signals and systems: z-transform

Question 81

Signals & SystemsFrequency Response

For h[n]=(0.5)^n u[n], H(e^(jω)) is obtained by replacing z^-1 with?

Ae^(-jω)
Be^(jω)
Cjω
D1/jω

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Correct Answer: A. e^(-jω)

Explanation: On the unit circle z=e^(jω), hence z^-1=e^(-jω).

Reference: Standard signals and systems: frequency response

Question 82

Signals & SystemsFrequency Response

The DC gain of H(z)=1/(1-0.5z^-1) is H(e^(j0)) equal to?

A0.5
B1
C2
D4

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Correct Answer: C. 2

Explanation: At ω=0, e^(-jω)=1, so H=1/(1-0.5)=2.

Reference: Standard signals and systems: frequency response

Question 83

Signals & SystemsFrequency Response

For an LTI system, if x(t)=e^(j3t) and H(j3)=2e^(-jπ/4), the output is?

A2e^(j(3t-π/4))
Be^(j(6t-π/4))
C2e^(-j3t)
De^(j3t)/2

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Correct Answer: A. 2e^(j(3t-π/4))

Explanation: Complex exponentials are eigenfunctions of LTI systems, so y(t)=H(j3)e^(j3t)=2e^(j(3t-π/4)).

Reference: Standard signals and systems: frequency response

Question 84

Signals & SystemsFrequency Response

If an LTI system has H(jω)=0 at ω=100 rad/s, a sinusoidal component exactly at 100 rad/s is ideally?

APassed unchanged
BCompletely rejected
CFrequency doubled
DConverted to DC

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Correct Answer: B. Completely rejected

Explanation: A zero frequency-response magnitude at that frequency means the corresponding sinusoidal steady-state component is suppressed.

Reference: Standard signals and systems: frequency response

Question 85

Signals & SystemsFilters

A continuous-time ideal low-pass filter has cutoff 1 kHz. Which sinusoid is in its ideal passband?

A500 Hz
B2 kHz
C5 kHz
D10 kHz

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Correct Answer: A. 500 Hz

Explanation: An ideal low-pass filter passes frequency components below its 1 kHz cutoff.

Reference: Standard signals and systems: filters

Question 86

Signals & SystemsFilters

An ideal high-pass filter with cutoff 2 kHz ideally rejects which component?

A500 Hz
B3 kHz
C5 kHz
D10 kHz

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Correct Answer: A. 500 Hz

Explanation: An ideal high-pass filter rejects components below the cutoff frequency, including 500 Hz.

Reference: Standard signals and systems: filters

Question 87

Signals & SystemsFilters

A band-pass filter is designed primarily to pass?

AA selected range of frequencies
BOnly DC
CAll frequencies equally
DOnly frequencies below zero

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Correct Answer: A. A selected range of frequencies

Explanation: A band-pass filter passes frequencies within a specified band while attenuating frequencies outside it.

Reference: Standard signals and systems: filters

Question 88

Signals & SystemsSampling

If x(t) has bandwidth 5 kHz, the theoretical Nyquist sampling rate is?

A2.5 kHz
B5 kHz
C10 kHz
D20 kHz

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Correct Answer: C. 10 kHz

Explanation: For a baseband signal band-limited to 5 kHz, the Nyquist rate is 2×5=10 kHz.

Reference: Standard signals and systems: sampling

Question 89

Signals & SystemsSystem Function

For an LTI system with impulse response h(t)=e^(-2t)u(t), the transfer function H(s) is?

A1/(s+2)
B1/(s-2)
Cs/(s+2)
D2/(s^2+4)

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Correct Answer: A. 1/(s+2)

Explanation: The Laplace transform of e^(-2t)u(t) is 1/(s+2), with ROC Re{s}>-2.

Reference: Standard signals and systems: system function

Question 90

Signals & SystemsSampling

A 7 kHz sinusoid sampled at 10 kHz produces an aliased frequency in the baseband of?

A1 kHz
B3 kHz
C5 kHz
D7 kHz

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Correct Answer: B. 3 kHz

Explanation: The sampled sinusoid aliases to |7-10|=3 kHz, which lies below fs/2=5 kHz.

Reference: Standard signals and systems: sampling

Question 91

Signals & SystemsSystem Function

For H(s)=1/(s+4), the impulse response of the causal system is?

Ae^(-4t)u(t)
Be^(4t)u(t)
C4e^(-t)u(t)
Ddelta(t-4)

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Correct Answer: A. e^(-4t)u(t)

Explanation: The inverse Laplace transform of 1/(s+4) with a right-sided ROC is e^(-4t)u(t).

Reference: Standard signals and systems: system function

Question 92

Signals & SystemsSampling

A 9 kHz sinusoid is sampled at 12 kHz. Its principal aliased frequency is?

A2 kHz
B3 kHz
C6 kHz
D9 kHz

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Correct Answer: B. 3 kHz

Explanation: The equivalent baseband frequency is |9-12|=3 kHz, within the 0 to fs/2 range.

Reference: Standard signals and systems: sampling

Question 93

Signals & SystemsSystem Function

A causal system has H(s)=(s+2)/[(s+1)(s+5)]. Its poles are?

A-2 only
B-1 and -5
C1 and 5
D-2 and -5

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Correct Answer: B. -1 and -5

Explanation: Poles are roots of the denominator, hence s=-1 and s=-5.

Reference: Standard signals and systems: system function

Question 94

Signals & SystemsSampling

If a band-limited signal is sampled above its Nyquist rate, ideal reconstruction uses sinc interpolation because the ideal reconstruction filter has a?

ARectangular frequency response
BTriangular time response only
CConstant impulse at every sample
DHigh-pass response

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Correct Answer: A. Rectangular frequency response

Explanation: An ideal brick-wall low-pass filter has a rectangular frequency response and a sinc-shaped impulse response, leading to sinc interpolation.

Reference: Standard signals and systems: sampling

Question 95

Signals & SystemsSystem Function

For H(s)=(s+2)/[(s+1)(s+5)], the finite zero is at?

As=-2
Bs=-1
Cs=-5
Ds=2

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Correct Answer: A. s=-2

Explanation: A finite zero is a root of the numerator, so s+2=0 gives s=-2.

Reference: Standard signals and systems: system function

Question 96

Signals & SystemsDTFT

The discrete-time Fourier transform X(e^(jω)) is periodic in ω with period?

Aπ
B2π
C4π
DIt is not periodic

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Correct Answer: B. 2π

Explanation: The DTFT is periodic in angular frequency with period 2π because e^(-j(ω+2π)n)=e^(-jωn) for integer n.

Reference: Standard signals and systems: dtft

Question 97

Signals & SystemsStability

A causal rational continuous-time system has poles at -2 and +1. It is BIBO stable?

AYes, because one pole is negative
BNo, because a pole lies in the right half-plane
CYes, because it is causal
DAlways stable if rational

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Correct Answer: B. No, because a pole lies in the right half-plane

Explanation: For a causal rational CT system, all poles must lie strictly in the left half-plane for BIBO stability.

Reference: Standard signals and systems: stability

Question 98

Signals & SystemsDTFT

The DTFT of delta[n] is?

A0
B1
Ce^(-jω)
D2πdelta(ω) only

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Correct Answer: B. 1

Explanation: By definition, the only nonzero sequence sample is at n=0, so X(e^(jω))=1.

Reference: Standard signals and systems: dtft

Question 99

Signals & SystemsDTFT

For a real-valued sequence x[n], its DTFT has conjugate symmetry given by?

AX(e^(-jω))=X*(e^(jω))
BX(e^(-jω))=-X*(e^(jω)) always
CX(e^(jω))=0
DX(e^(jω)) is always purely real

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Correct Answer: A. X(e^(-jω))=X*(e^(jω))

Explanation: A real time-domain sequence has a conjugate-symmetric DTFT: X(e^(-jω))=X*(e^(jω)).

Reference: Standard signals and systems: dtft

Question 100

Signals & SystemsLTI Frequency Response

For a stable LTI system, a bounded sinusoidal input produces a steady-state sinusoidal output at?

AThe same frequency
BTwice the input frequency
CZero frequency only
DA random frequency

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Correct Answer: A. The same frequency

Explanation: An LTI system does not create new frequencies from a single sinusoidal input in steady state; it changes only amplitude and phase at that frequency.

Reference: Standard signals and systems: lti frequency response

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