Q.1 What is the definition of a continuous-time signal?
A signal that changes value only at discrete times
A signal that changes value continuously over time
A signal that has a finite number of distinct amplitude levels
A signal that is constant over time
Explanation - A continuous-time signal is one whose value is defined for every instant in time, as opposed to discrete-time signals which are defined only at specific sample points.
Correct answer is: A signal that changes value continuously over time
Q.2 Which of the following is a basic example of a continuous-time signal?
A digital clock display
A sine wave with frequency 5 Hz
A list of sampled audio samples
A sequence of integers
Explanation - A sine wave is a continuous-time signal because it is defined for all real time values, unlike sampled data or discrete sequences.
Correct answer is: A sine wave with frequency 5 Hz
Q.3 The unit impulse function δ(t) has what property?
It is zero for all t except at t=0 where it is infinite
It is constant for all t
It is periodic with period 1 second
It has zero area under the curve
Explanation - δ(t) is defined such that it is zero everywhere except at t=0 where it is theoretically infinite, but its integral over all time equals 1.
Correct answer is: It is zero for all t except at t=0 where it is infinite
Q.4 Which transform is most commonly used to analyze frequency content of continuous-time signals?
Z-transform
Discrete Fourier Transform (DFT)
Fourier Transform (FT)
Laplace Transform
Explanation - The Fourier Transform decomposes a continuous-time signal into its constituent sinusoidal frequencies.
Correct answer is: Fourier Transform (FT)
Q.5 The Laplace Transform of a signal x(t) is X(s). What does s represent?
Time variable
Complex frequency variable
Amplitude of the signal
Sampling rate
Explanation - In the Laplace Transform, s is a complex number (s = σ + jω) that represents complex frequency, allowing analysis of growth/decay and oscillation.
Correct answer is: Complex frequency variable
Q.6 Which of the following is a property of linear time-invariant (LTI) systems?
The system response depends on the absolute time of input
The system output is always a constant
Convolution with the input equals the output
The system is always non-causal
Explanation - For LTI systems, the output y(t) is the convolution of the input x(t) with the system's impulse response h(t).
Correct answer is: Convolution with the input equals the output
Q.7 If x(t) = e^{-at}u(t) with a>0, what is its Laplace Transform X(s)?
1/(s + a)
1/(s - a)
(s + a)
(s - a)
Explanation - The Laplace Transform of e^{-at}u(t) is 1/(s + a) for Re{s} > -a.
Correct answer is: 1/(s + a)
Q.8 Which equation represents the convolution integral for continuous-time signals?
y(t) = ∫_{-∞}^{∞} x(τ) h(t-τ) dτ
y(t) = x(t) * h(t)
y(t) = x(t) + h(t)
y(t) = x(t) - h(t)
Explanation - Convolution of two continuous-time signals x(t) and h(t) is defined as the integral over all time of their product after time reversal and shifting.
Correct answer is: y(t) = ∫_{-∞}^{∞} x(τ) h(t-τ) dτ
Q.9 What is the main advantage of using the Laplace Transform over the Fourier Transform?
It can handle non-periodic signals only
It can represent both growth and decay in signals
It is only defined for real frequencies
It requires discrete sampling
Explanation - The Laplace Transform’s s-domain allows representation of exponential growth/decay (through its real part) and oscillatory components (through its imaginary part).
Correct answer is: It can represent both growth and decay in signals
Q.10 Which of the following signals has a finite energy but infinite power?
Continuous sinusoid
Finite-duration pulse
Unit step function
White noise
Explanation - A continuous sinusoid is periodic, has infinite energy over infinite time, but its average power is finite. However, if we consider finite energy signals, a finite-duration pulse has finite energy and zero average power over infinite time.
Correct answer is: Continuous sinusoid
Q.11 What condition must an LTI system satisfy to be considered causal?
Its impulse response h(t) = 0 for t < 0
Its impulse response h(t) = 0 for t > 0
It must be linear
It must be time-invariant
Explanation - Causality requires that the system's output at any time depends only on present and past inputs, meaning the impulse response must be zero for negative time.
Correct answer is: Its impulse response h(t) = 0 for t < 0
Q.12 Which of the following is NOT a stability criterion for continuous-time LTI systems?
All poles must lie in the left-half of the s-plane
Impulse response must be absolutely integrable
Poles must be located on the imaginary axis
Poles must have negative real parts
Explanation - Poles on the imaginary axis lead to marginal stability; absolute integrability of h(t) is required for stability.
Correct answer is: Poles must be located on the imaginary axis
Q.13 For a continuous-time system with transfer function H(s) = (s + 1)/(s^2 + 2s + 2), what is its step response at t=0+?
0
1
1/2
∞
Explanation - A causal system with a finite transfer function has zero output at t=0+ because the impulse response starts at zero due to the numerator’s s-term.
Correct answer is: 0
Q.14 Which transform is used to solve differential equations with initial conditions?
Laplace Transform
Fourier Transform
Z-Transform
Wavelet Transform
Explanation - The Laplace Transform handles initial conditions naturally and is ideal for solving linear differential equations.
Correct answer is: Laplace Transform
Q.15 What is the impulse response of a first-order RC low-pass filter described by differential equation dy/dt + (1/RC)y = (1/RC)x(t)?
h(t) = e^{-t/(RC)}u(t)
h(t) = (1/RC) e^{-t/(RC)}u(t)
h(t) = u(t)
h(t) = δ(t)
Explanation - Solving the differential equation with a unit impulse input yields the exponential decay scaled by (1/RC).
Correct answer is: h(t) = (1/RC) e^{-t/(RC)}u(t)
Q.16 Which property of the Fourier Transform states that time scaling corresponds to frequency scaling?
Linearity
Time Shifting
Time Scaling
Frequency Inversion
Explanation - If x(at) is time-scaled, its Fourier Transform becomes (1/|a|)X(ω/a), demonstrating the reciprocal relationship between time and frequency scaling.
Correct answer is: Time Scaling
Q.17 Which of the following is the definition of the continuous-time Fourier Transform pair for x(t) and X(ω)?
X(ω) = ∫ x(t) e^{-jωt} dt; x(t) = (1/2π)∫ X(ω) e^{jωt} dω
X(ω) = ∑ x[n] e^{-jωn}; x(n) = (1/2π)∑ X(ω) e^{jωn}
X(s) = ∫ x(t) e^{-st} dt; x(t) = (1/2πj)∮ X(s) e^{st} ds
X(f) = ∫ x(t) e^{-j2πft} dt; x(t) = ∫ X(f) e^{j2πft} df
Explanation - This is the standard pair for continuous-time Fourier Transform using angular frequency ω.
Correct answer is: X(ω) = ∫ x(t) e^{-jωt} dt; x(t) = (1/2π)∫ X(ω) e^{jωt} dω
Q.18 Which condition ensures that a continuous-time signal x(t) is bandlimited?
Its Fourier Transform X(ω) is non-zero only for |ω| < ω_c
Its Laplace Transform X(s) has no poles
Its impulse response h(t) decays exponentially
Its time integral is finite
Explanation - A signal is bandlimited if its frequency spectrum is zero outside a finite bandwidth ω_c.
Correct answer is: Its Fourier Transform X(ω) is non-zero only for |ω| < ω_c
Q.19 What is the effect of multiplying a continuous-time signal x(t) by a sinusoid cos(ω₀t) in the time domain?
It shifts the signal in time
It shifts the signal in frequency
It changes the amplitude only
It creates a delay
Explanation - Multiplication by a sinusoid corresponds to frequency shifting (modulation), creating sidebands at ω ± ω₀.
Correct answer is: It shifts the signal in frequency
Q.20 Which of the following describes the Dirichlet kernel in Fourier series?
Kernel used for convolution in time domain
Kernel used to approximate a periodic function
Kernel that describes frequency resolution of DFT
Kernel for low-pass filtering
Explanation - The Dirichlet kernel arises in Fourier series and is used in the partial sum representation of periodic signals.
Correct answer is: Kernel used to approximate a periodic function
Q.21 In the Laplace domain, the term s in the transfer function H(s) = 1/(s+1) corresponds to what in the time domain?
A derivative operator
An integral operator
A delay
A gain
Explanation - Multiplication by s in the s-domain corresponds to differentiation in the time domain.
Correct answer is: A derivative operator
Q.22 Which property of LTI systems allows the use of frequency response to predict output for a sinusoidal input?
Linearity
Time-Invariance
Causality
Stability
Explanation - Time-invariance ensures that the system's response to a sinusoid is simply a scaled and phase-shifted sinusoid at the same frequency.
Correct answer is: Time-Invariance
Q.23 What is the convolution property of the Fourier Transform?
Convolution in time corresponds to multiplication in frequency
Convolution in time corresponds to division in frequency
Convolution in time corresponds to addition in frequency
Convolution in time is unrelated to frequency
Explanation - The Fourier Transform of the convolution of two signals equals the product of their individual Fourier Transforms.
Correct answer is: Convolution in time corresponds to multiplication in frequency
Q.24 What is the result of applying an ideal low-pass filter with cutoff frequency ω_c to a signal whose spectrum is limited to |ω| < 2ω_c?
The signal remains unchanged
The signal is attenuated at all frequencies
Only frequencies above ω_c are removed
The signal becomes high-pass
Explanation - Since the signal’s spectrum lies entirely within the filter’s passband (|ω| < ω_c), the filter passes it unchanged.
Correct answer is: The signal remains unchanged
Q.25 Which of the following is an example of a continuous-time, band-limited signal?
A square wave with infinite harmonics
A sine wave with frequency 1 kHz
White noise
A step function
Explanation - A single-frequency sinusoid has a spectrum consisting of two delta functions at ±1 kHz, thus it is band-limited.
Correct answer is: A sine wave with frequency 1 kHz
Q.26 Which expression represents the impulse response of a second-order system with transfer function H(s) = ω_n^2/(s^2 + 2ζω_n s + ω_n^2)?
h(t) = e^{-ζω_n t} sin(ω_d t) u(t)
h(t) = e^{-ζω_n t} cos(ω_d t) u(t)
h(t) = δ(t)
h(t) = u(t)
Explanation - The impulse response of a second-order system has an exponentially decaying sinusoid with damped natural frequency ω_d.
Correct answer is: h(t) = e^{-ζω_n t} sin(ω_d t) u(t)
Q.27 For a continuous-time system described by y(t) = ∫ h(τ) x(t-τ)dτ, what does h(τ) represent?
The system's frequency response
The input signal
The system's impulse response
The output signal
Explanation - In convolution, h(τ) is the impulse response that characterizes the system’s behavior.
Correct answer is: The system's impulse response
Q.28 Which condition on the transfer function H(s) ensures the system is BIBO stable?
All poles are in the right-half s-plane
All poles lie on the imaginary axis
All poles are in the left-half s-plane
All poles are at the origin
Explanation - BIBO stability requires that the impulse response be absolutely integrable, which is true if all poles have negative real parts.
Correct answer is: All poles are in the left-half s-plane
Q.29 What is the relationship between the Laplace Transform of a derivative d/dt x(t) and X(s)?
s X(s) - x(0-)
X(s) / s
s X(s) + x(0-)
X(s) - s x(0-)
Explanation - The Laplace Transform of a derivative introduces an initial condition term x(0-) due to integration by parts.
Correct answer is: s X(s) - x(0-)
Q.30 Which of the following is NOT a type of continuous-time filter?
Low-pass filter
Band-pass filter
High-pass filter
Discrete filter
Explanation - Discrete filters operate on sampled signals, whereas the other three are continuous-time filter types.
Correct answer is: Discrete filter
Q.31 When designing a continuous-time RC circuit as a differentiator, which condition must be satisfied regarding the signal frequency relative to the cutoff frequency?
Signal frequency >> cutoff frequency
Signal frequency << cutoff frequency
Signal frequency ≈ cutoff frequency
Signal frequency is irrelevant
Explanation - For differentiation behavior, the signal frequency should be much lower than the cutoff so that the RC network behaves as a differentiator.
Correct answer is: Signal frequency << cutoff frequency
Q.32 Which theorem allows us to find the Fourier Transform of a time-reversed signal x(-t)?
Time reversal property
Frequency shift property
Convolution theorem
Sampling theorem
Explanation - The time reversal property states that the Fourier Transform of x(-t) is X(-ω).
Correct answer is: Time reversal property
Q.33 Which of the following best describes a continuous-time Gaussian pulse?
Amplitude is constant for all time
Amplitude decays exponentially
Amplitude follows a Gaussian shape with infinite support
Amplitude is zero except at discrete points
Explanation - A Gaussian pulse has a bell-shaped envelope extending infinitely, but its amplitude rapidly approaches zero.
Correct answer is: Amplitude follows a Gaussian shape with infinite support
Q.34 The unit step function u(t) satisfies which differential equation?
du/dt = δ(t)
du/dt = u(t)
du/dt = 0
du/dt = 1
Explanation - The derivative of the step function is the unit impulse δ(t).
Correct answer is: du/dt = δ(t)
Q.35 The Fourier Transform of a rectangular pulse of width T centered at t=0 is:
T sinc(ωT/2)
T δ(ω)
1/ω
T e^{-jωT/2}
Explanation - The Fourier Transform of a rectangular pulse results in a sinc function scaled by its width T.
Correct answer is: T sinc(ωT/2)
Q.36 Which of the following is a property of the Fourier Transform regarding scaling?
Scaling in time results in scaling in frequency by the same factor
Scaling in time results in scaling in frequency by the reciprocal factor
Scaling in time does not affect the frequency domain
Scaling in time inverts the frequency spectrum
Explanation - Time scaling by a factor a leads to frequency scaling by 1/a and amplitude scaling by 1/|a|.
Correct answer is: Scaling in time results in scaling in frequency by the reciprocal factor
Q.37 Which expression correctly represents the Laplace Transform of a decaying exponential e^{-at}u(t) for a>0?
1/(s+a)
1/(s-a)
(s+a)
s+a
Explanation - The Laplace Transform of e^{-at}u(t) is 1/(s + a) for Re{s} > -a.
Correct answer is: 1/(s+a)
Q.38 What is the primary difference between continuous-time and discrete-time convolution integrals?
Continuous uses sum, discrete uses integral
Continuous uses integral, discrete uses sum
Continuous uses product, discrete uses difference
No difference
Explanation - In continuous time convolution is an integral over τ, while in discrete time it is a summation over k.
Correct answer is: Continuous uses integral, discrete uses sum
Q.39 Which of the following is a necessary condition for a continuous-time signal to be considered bandlimited to ω_c?
Its Fourier Transform is zero for |ω| > ω_c
Its Laplace Transform has poles only at s = jω_c
Its time-domain representation is finite in duration
Its impulse response decays faster than 1/t
Explanation - Bandlimited means the spectral content is confined to frequencies within ±ω_c.
Correct answer is: Its Fourier Transform is zero for |ω| > ω_c
Q.40 The Fourier Transform pair X(ω) = δ(ω - ω₀) + δ(ω + ω₀) corresponds to which time-domain signal?
x(t) = cos(ω₀ t)
x(t) = sin(ω₀ t)
x(t) = e^{jω₀ t}
x(t) = u(t)
Explanation - A pair of delta functions at ±ω₀ in frequency corresponds to a real cosine in time.
Correct answer is: x(t) = cos(ω₀ t)
Q.41 Which of the following best describes the impulse response of a lossless transmission line?
Zero for all t
A delta function delayed by the propagation time
An exponential decay
A periodic sinusoid
Explanation - A lossless line propagates impulses with no attenuation, simply delaying them by the line's propagation time.
Correct answer is: A delta function delayed by the propagation time
Q.42 In continuous-time signal processing, what is meant by a 'stable' system?
It always outputs zero
Its impulse response is absolutely integrable
Its transfer function has poles on the imaginary axis
Its input and output have the same energy
Explanation - A stable system yields finite outputs for any bounded input, which requires the integral of |h(t)| to be finite.
Correct answer is: Its impulse response is absolutely integrable
Q.43 Which transform is used to solve initial value problems for linear differential equations in continuous-time systems?
Discrete Fourier Transform
Laplace Transform
Z-Transform
Wavelet Transform
Explanation - The Laplace Transform incorporates initial conditions and is ideal for solving differential equations.
Correct answer is: Laplace Transform
Q.44 For a continuous-time LTI system with transfer function H(s) = (s+3)/(s^2 + 2s + 5), how many poles does it have?
1
2
3
0
Explanation - Denominator has a quadratic polynomial, implying two poles in the s-plane.
Correct answer is: 2
Q.45 The Nyquist-Shannon sampling theorem states that a bandlimited continuous-time signal can be:
Reconstructed perfectly from samples taken at any rate
Reconstructed perfectly from samples taken at a rate twice the bandwidth
Reconstructed perfectly from samples taken at half the bandwidth
Not reconstructible from any sampling rate
Explanation - The theorem requires sampling at at least twice the maximum frequency (Nyquist rate) to avoid aliasing.
Correct answer is: Reconstructed perfectly from samples taken at a rate twice the bandwidth
Q.46 Which of the following signals has zero mean over any symmetric interval?
Constant signal
Sine wave
Square wave
Exponential decay
Explanation - A sine wave integrates to zero over a full period due to its symmetric positive and negative parts.
Correct answer is: Sine wave
Q.47 Which property of the Fourier Transform states that a time delay of T in x(t) results in a phase shift in X(ω)?
Time shift property
Frequency shift property
Convolution property
Sampling property
Explanation - Time shifting by T multiplies the spectrum by e^{-jωT}, which is a phase shift.
Correct answer is: Time shift property
Q.48 In the context of continuous-time filtering, what is the purpose of a Butterworth filter?
Provide a sharp cutoff with ripple in passband
Provide a flat passband and maximally flat amplitude response
Create an all-pass filter
Introduce a stopband ripple
Explanation - Butterworth filters are designed to have a flat magnitude response in the passband with no ripples.
Correct answer is: Provide a flat passband and maximally flat amplitude response
Q.49 The Fourier Transform of a periodic signal can be represented as a sum of what?
Continuous spectrum
Discrete impulses (Dirac comb)
Gaussian functions
Sinusoidal functions
Explanation - A periodic signal's spectrum consists of discrete delta functions at harmonically spaced frequencies.
Correct answer is: Discrete impulses (Dirac comb)
Q.50 Which of the following is NOT a type of continuous-time filter?
Low-pass filter
High-pass filter
Band-stop filter
Digital filter
Explanation - Digital filters operate on discrete-time signals, whereas low-pass, high-pass, and band-stop are continuous-time filter categories.
Correct answer is: Digital filter
Q.51 What is the effect of multiplying a continuous-time signal by a constant scalar A?
It shifts the signal in time
It scales the amplitude by A
It changes the frequency
It introduces a delay
Explanation - Multiplication by a scalar only changes the signal's amplitude, not its timing or frequency content.
Correct answer is: It scales the amplitude by A
Q.52 Which property of the Fourier Transform relates to the energy of a signal?
Parseval's theorem
Time-shifting property
Frequency scaling property
Convolution theorem
Explanation - Parseval's theorem equates the total energy in time domain with the total energy in frequency domain.
Correct answer is: Parseval's theorem
Q.53 The Fourier Transform of a Gaussian function is also a Gaussian. What does this imply about Gaussian functions?
They are only defined in time domain
They are self-similar under Fourier transform
They cannot be bandlimited
They have infinite support in frequency
Explanation - A Gaussian remains a Gaussian after Fourier transformation, indicating its minimal time-frequency spread.
Correct answer is: They are self-similar under Fourier transform
Q.54 Which of the following signals is NOT bandlimited?
Sine wave
Rectangular pulse
Ideal impulse δ(t)
Cosine wave
Explanation - δ(t) has an infinite spectrum (constant magnitude across all frequencies), so it is not bandlimited.
Correct answer is: Ideal impulse δ(t)
Q.55 What does the convolution theorem state for continuous-time signals?
Convolution in time corresponds to multiplication in frequency
Convolution in frequency corresponds to multiplication in time
Convolution in time corresponds to addition in frequency
Convolution in frequency corresponds to division in time
Explanation - The theorem allows simplifying convolution integrals to simple multiplications in the frequency domain.
Correct answer is: Convolution in time corresponds to multiplication in frequency
Q.56 Which of the following best describes the effect of a time shift of t₀ on a continuous-time signal's Fourier Transform?
X(ω) is multiplied by e^{-jωt₀}
X(ω) is multiplied by e^{jωt₀}
X(ω) is shifted by t₀ in frequency
X(ω) is shifted by t₀ in time
Explanation - A time delay introduces a linear phase shift in the frequency domain.
Correct answer is: X(ω) is multiplied by e^{-jωt₀}
Q.57 The impulse response of a continuous-time system with transfer function H(s) = 1/(s+1) is:
h(t) = e^{-t}u(t)
h(t) = e^{t}u(t)
h(t) = δ(t)
h(t) = u(t)
Explanation - The inverse Laplace Transform of 1/(s+1) yields e^{-t}u(t).
Correct answer is: h(t) = e^{-t}u(t)
Q.58 Which of the following signals is strictly bandlimited to ±5 kHz?
A sine wave of 4 kHz
A square wave with fundamental 4 kHz
A Gaussian pulse
White noise
Explanation - A pure sinusoid at 4 kHz has frequency content only at ±4 kHz, within ±5 kHz.
Correct answer is: A sine wave of 4 kHz
Q.59 The magnitude response of a first-order RC low-pass filter is:
|H(jω)| = 1/√(1+(ωRC)²)
|H(jω)| = √(1+(ωRC)²)
|H(jω)| = (ωRC)/√(1+(ωRC)²)
|H(jω)| = 0
Explanation - The standard magnitude response for a first-order low-pass filter decreases with frequency.
Correct answer is: |H(jω)| = 1/√(1+(ωRC)²)
Q.60 Which condition ensures that a continuous-time system is causal?
h(t) = 0 for t > 0
h(t) = 0 for t < 0
H(s) has poles only in the right-half plane
H(s) has zeros only in the left-half plane
Explanation - Causality requires the impulse response to be zero for negative time values.
Correct answer is: h(t) = 0 for t < 0
Q.61 The Laplace Transform of the derivative dx/dt is:
sX(s) - x(0)
X(s) + s x(0)
sX(s) + x(0)
X(s) - s x(0)
Explanation - The Laplace transform of a derivative introduces an initial condition term.
Correct answer is: sX(s) - x(0)
Q.62 Which of the following signals is NOT a stable LTI system's impulse response?
h(t) = e^{-t}u(t)
h(t) = e^{t}u(-t)
h(t) = u(t)
h(t) = 0
Explanation - An exponentially growing function for t < 0 results in an impulse response that is not absolutely integrable.
Correct answer is: h(t) = e^{t}u(-t)
Q.63 Which of the following best describes the frequency response of an ideal bandpass filter with center frequency f₀ and bandwidth B?
All frequencies are attenuated equally
Only frequencies exactly at f₀ are passed
Frequencies within ±B/2 around f₀ are passed
Frequencies outside the range f₀ ± B/2 are passed
Explanation - An ideal bandpass filter allows a finite band of frequencies centered at f₀.
Correct answer is: Frequencies within ±B/2 around f₀ are passed
Q.64 Which of the following signals has an energy of 1 Joule when integrated over all time?
x(t) = δ(t)
x(t) = u(t)
x(t) = e^{-t}u(t)
x(t) = sin(t)
Explanation - The unit impulse has a total energy of 1 due to the property ∫δ(t)² dt = 1.
Correct answer is: x(t) = δ(t)
Q.65 The Laplace Transform of the unit step function u(t) is:
1/s
s
δ(s)
0
Explanation - The Laplace Transform of u(t) yields 1/s, valid for Re{s} > 0.
Correct answer is: 1/s
Q.66 Which of the following is true about the Fourier Transform of a real and even function?
It is imaginary and odd
It is real and even
It is zero
It is complex and odd
Explanation - Real, even time-domain signals produce real, even frequency spectra.
Correct answer is: It is real and even
Q.67 What is the effect of a time reversal operation on the Fourier Transform of a signal?
X(ω) becomes X(-ω)
X(ω) becomes -X(ω)
X(ω) is unchanged
X(ω) becomes e^{jωt}X(ω)
Explanation - Time reversal flips the sign of the frequency variable in the spectrum.
Correct answer is: X(ω) becomes X(-ω)
Q.68 Which of the following is a property of the Fourier Transform concerning scaling in frequency?
Scaling in frequency scales amplitude by the same factor
Scaling in frequency scales amplitude by the reciprocal of the scaling factor
Scaling in frequency has no effect on amplitude
Scaling in frequency inverts the time-domain signal
Explanation - If X(aω) is the scaled spectrum, the time-domain signal scales by 1/|a|.
Correct answer is: Scaling in frequency scales amplitude by the reciprocal of the scaling factor
Q.69 Which transform is particularly useful for solving linear differential equations with boundary conditions?
Fourier Transform
Laplace Transform
Z-Transform
Hilbert Transform
Explanation - Laplace Transform handles initial conditions naturally and converts differential equations to algebraic ones.
Correct answer is: Laplace Transform
Q.70 For a continuous-time LTI system, which of the following best describes the relationship between the system's frequency response H(jω) and its impulse response h(t)?
H(jω) is the derivative of h(t)
H(jω) is the Fourier Transform of h(t)
H(jω) is the Laplace Transform of h(t)
H(jω) is the inverse Laplace Transform of h(t)
Explanation - The system's frequency response is obtained by Fourier transforming the impulse response.
Correct answer is: H(jω) is the Fourier Transform of h(t)
Q.71 The Fourier Transform of a periodic rectangular pulse train with period T and duty cycle 50% is:
A Dirac comb of impulses with amplitude 1/T
A sinc function
A Gaussian function
A step function
Explanation - A periodic rectangular pulse train transforms to a Dirac comb in the frequency domain.
Correct answer is: A Dirac comb of impulses with amplitude 1/T
Q.72 Which of the following continuous-time signals is NOT energy-limited (i.e., has infinite energy)?
A sinusoidal signal of finite amplitude
A decaying exponential e^{-t}u(t)
A finite-duration pulse
A step function u(t)
Explanation - The step function maintains a nonzero constant value for infinite time, yielding infinite energy.
Correct answer is: A step function u(t)
Q.73 Which property of the Laplace Transform allows it to handle both exponential growth and oscillatory behavior?
Complex variable s
Linearity
Time-shifting
Convolution
Explanation - The real part of s represents exponential growth/decay, while the imaginary part represents oscillations.
Correct answer is: Complex variable s
Q.74 What is the inverse Laplace Transform of 1/(s^2 + ω₀²)?
sin(ω₀t)/ω₀
cos(ω₀t)
e^{-ω₀t}u(t)
t
Explanation - The standard Laplace pair gives sin(ω₀t)/ω₀ for that denominator.
Correct answer is: sin(ω₀t)/ω₀
Q.75 Which of the following signals has a magnitude spectrum that is a sinc function?
A continuous sine wave
A rectangular pulse
An impulse train
A Gaussian pulse
Explanation - The Fourier Transform of a rectangular time-domain pulse yields a sinc frequency-domain shape.
Correct answer is: A rectangular pulse
Q.76 The Laplace Transform of the product x(t)h(t) corresponds to which operation in the s-domain?
Addition of X(s) and H(s)
Convolution of X(s) and H(s)
Multiplication of X(s) and H(s)
Differentiation of X(s) times H(s)
Explanation - Multiplication in time domain corresponds to convolution in s-domain for Laplace transforms.
Correct answer is: Multiplication of X(s) and H(s)
Q.77 Which of the following best describes a continuous-time system that is both causal and stable?
All poles in the right-half plane
All poles on the imaginary axis
All poles in the left-half plane
Poles anywhere as long as zeros are finite
Explanation - Poles in the left-half plane ensure that the impulse response is absolutely integrable and zero for t<0.
Correct answer is: All poles in the left-half plane
Q.78 In continuous-time signal processing, what is the relationship between the convolution integral and the system's impulse response?
Convolution integral equals the sum of the signals
Convolution integral gives the output as the product of signals
Convolution integral gives the output as the integral of the product of input and delayed impulse response
Convolution integral is irrelevant to impulse response
Explanation - Output y(t) = ∫ x(τ)h(t-τ)dτ shows the system's linear superposition property.
Correct answer is: Convolution integral gives the output as the integral of the product of input and delayed impulse response
Q.79 Which of the following is a correct statement about the Fourier Transform of a real, odd function?
It is real and odd
It is imaginary and odd
It is real and even
It is zero
Explanation - Real, odd time-domain signals produce purely imaginary, odd frequency spectra.
Correct answer is: It is imaginary and odd
Q.80 The frequency response of an ideal low-pass filter with cutoff frequency ω_c is:
1 for |ω| ≤ ω_c, 0 otherwise
0 for |ω| ≤ ω_c, 1 otherwise
|ω|/ω_c for |ω| ≤ ω_c
ω_c/|ω| for |ω| > ω_c
Explanation - An ideal low-pass filter passes frequencies within the cutoff and attenuates all others.
Correct answer is: 1 for |ω| ≤ ω_c, 0 otherwise
Q.81 Which of the following signals is NOT an example of a continuous-time periodic signal?
x(t) = sin(2πt)
x(t) = e^{t}u(t)
x(t) = cos(5t)
x(t) = rect(t)
Explanation - Exponential growth is not periodic; the other signals repeat over time.
Correct answer is: x(t) = e^{t}u(t)
Q.82 Which of the following transforms is commonly used for analyzing continuous-time signals in the complex frequency domain?
Z-Transform
Fourier Transform
Laplace Transform
Wavelet Transform
Explanation - The Laplace Transform maps signals into the complex s-plane, enabling analysis of system poles and stability.
Correct answer is: Laplace Transform
Q.83 Which of the following is the correct definition of the unit impulse function δ(t)?
δ(t) = 0 for t ≠ 0, ∞ for t = 0
δ(t) = 1 for all t
δ(t) = e^{-t}u(t)
δ(t) = sin(t)/t
Explanation - δ(t) is zero everywhere except at zero where it is infinite, but its integral equals 1.
Correct answer is: δ(t) = 0 for t ≠ 0, ∞ for t = 0
Q.84 Which of the following best describes a continuous-time LTI system's stability condition in terms of its frequency response H(jω)?
H(jω) must be zero for all ω
H(jω) must have finite magnitude for all ω
H(jω) must be purely imaginary
H(jω) must be real and positive
Explanation - A stable system has a bounded frequency response; it cannot have infinite magnitude at any frequency.
Correct answer is: H(jω) must have finite magnitude for all ω
Q.85 The convolution of a continuous-time signal x(t) with a delta function δ(t - t₀) results in:
A time delay of x(t) by t₀
A time advance of x(t) by t₀
The derivative of x(t)
The integral of x(t)
Explanation - Convolving with δ(t - t₀) shifts the signal by t₀.
Correct answer is: A time delay of x(t) by t₀
Q.86 Which of the following signals is energy-limited but not power-limited?
Sinusoidal signal
Finite-duration rectangular pulse
Continuous exponential growth
White Gaussian noise
Explanation - A finite-duration pulse has finite energy but zero average power over infinite time.
Correct answer is: Finite-duration rectangular pulse
Q.87 The Fourier Transform of a real-valued time-domain signal exhibits which symmetry property?
Symmetric in magnitude, antisymmetric in phase
Antisymmetric in magnitude, symmetric in phase
Symmetric in both magnitude and phase
Antisymmetric in both magnitude and phase
Explanation - Real signals have even magnitude spectra and odd phase spectra.
Correct answer is: Symmetric in magnitude, antisymmetric in phase
Q.88 What is the main difference between the Fourier Transform and the Laplace Transform?
Fourier Transform is only for discrete signals
Laplace Transform can represent system stability through poles
Fourier Transform uses a complex variable s
Laplace Transform cannot handle initial conditions
Explanation - The Laplace Transform maps system poles in the s-plane, providing stability insight; the Fourier Transform does not consider poles in the same way.
Correct answer is: Laplace Transform can represent system stability through poles
Q.89 Which of the following statements is true about a continuous-time system that is time-invariant?
The impulse response changes over time
Shifting the input by t₀ shifts the output by t₀
The system is always causal
The system's frequency response is zero
Explanation - Time-invariance implies that a time shift in the input leads to an identical shift in the output.
Correct answer is: Shifting the input by t₀ shifts the output by t₀
Q.90 Which of the following best describes the relationship between the Laplace Transform of a derivative and the original transform?
Multiplication by s in the s-domain
Division by s in the s-domain
Addition of s in the s-domain
Subtraction of s in the s-domain
Explanation - The Laplace Transform of dx/dt is sX(s) minus the initial value, reflecting the derivative property.
Correct answer is: Multiplication by s in the s-domain
Q.91 Which of the following signals has a Fourier Transform that is a pure impulse?
Constant signal
Delta function
Step function
Rectangular pulse
Explanation - The Fourier Transform of δ(t) is a constant (1) across all frequencies, which can be regarded as an impulse in the frequency domain.
Correct answer is: Delta function
Q.92 Which of the following conditions ensures that a continuous-time system is BIBO stable?
All poles are on the imaginary axis
Impulse response is absolutely integrable
All poles are in the right-half plane
All zeros are in the left-half plane
Explanation - BIBO stability requires that the impulse response be absolutely integrable.
Correct answer is: Impulse response is absolutely integrable
Q.93 The Fourier Transform of the product of two signals corresponds to what operation in the frequency domain?
Multiplication
Convolution
Differentiation
Integration
Explanation - Multiplying two time-domain signals results in convolution of their Fourier Transforms.
Correct answer is: Convolution
Q.94 Which of the following best describes the effect of a low-pass filter on a high-frequency sinusoid?
It amplifies the sinusoid
It passes the sinusoid unchanged
It attenuates the sinusoid
It reverses the phase of the sinusoid
Explanation - A low-pass filter allows low frequencies to pass while attenuating frequencies above its cutoff.
Correct answer is: It attenuates the sinusoid
Q.95 Which of the following continuous-time signals has a Fourier Transform that is also a sinc function?
A Gaussian pulse
A rectangular pulse
A sinusoid
An impulse train
Explanation - The Fourier Transform of a rectangular time-domain pulse yields a sinc-shaped frequency spectrum.
Correct answer is: A rectangular pulse
Q.96 The Laplace Transform of the function e^{-a t}u(t) for a>0 is:
1/(s + a)
1/(s - a)
(s + a)
(s - a)
Explanation - This is a standard Laplace Transform pair for a decaying exponential multiplied by the unit step.
Correct answer is: 1/(s + a)
Q.97 Which of the following best describes the relationship between time reversal and Fourier Transform?
Time reversal adds a phase shift
Time reversal multiplies the Fourier Transform by e^{-jωt}
Time reversal results in a frequency-domain reversal, X(-ω)
Time reversal has no effect on the Fourier Transform
Explanation - Reversing a signal in time flips its frequency spectrum about the origin.
Correct answer is: Time reversal results in a frequency-domain reversal, X(-ω)
Q.98 Which of the following statements is true about the Fourier Transform of a real, even signal?
It is purely imaginary
It is purely real and even
It is purely real and odd
It is purely imaginary and odd
Explanation - A real, even time-domain signal produces a real, even spectrum.
Correct answer is: It is purely real and even
Q.99 Which of the following signals has a finite energy but infinite power?
A sinusoid
A unit step function
An exponential decay e^{-t}u(t)
A finite-duration pulse
Explanation - A sinusoid extends indefinitely, giving infinite energy but finite average power.
Correct answer is: A sinusoid
Q.100 Which of the following statements correctly describes the impulse response of a differentiator circuit?
h(t) = δ(t)
h(t) = u(t)
h(t) = e^{-t}u(t)
h(t) = 0
Explanation - An ideal differentiator has an impulse response that is the derivative of δ(t), which for ideal systems is represented as δ(t) in simplified models.
Correct answer is: h(t) = δ(t)
Q.101 The Laplace Transform of the unit step function u(t) is:
1/s
s
δ(s)
0
Explanation - The Laplace Transform of u(t) yields 1/s, defined for Re{s} > 0.
Correct answer is: 1/s
Q.102 Which of the following continuous-time signals is bandlimited to 10 Hz?
x(t) = cos(5t)
x(t) = sin(15t)
x(t) = e^{-t}u(t)
x(t) = δ(t)
Explanation - The cosine at 5 Hz has frequency components only at ±5 Hz, which is below 10 Hz.
Correct answer is: x(t) = cos(5t)
Q.103 The frequency response of a first-order high-pass filter with transfer function H(s) = s/(s + a) has magnitude:
1/√(1 + (a/ω)²)
√(1 + (a/ω)²)
a/√(a² + ω²)
ω/√(a² + ω²)
Explanation - The magnitude of H(jω) is |jω|/√(a² + ω²) = ω/√(a² + ω²).
Correct answer is: ω/√(a² + ω²)
Q.104 Which of the following statements is true regarding the Laplace Transform of a causal signal?
All poles are in the right-half s-plane
All poles are on the imaginary axis
All poles are in the left-half s-plane
Poles can be anywhere
Explanation - Causality requires that the Laplace Transform converges in the right-half plane, meaning poles lie in the left-half.
Correct answer is: All poles are in the left-half s-plane
Q.105 Which of the following transforms is specifically used for converting a continuous-time signal into its frequency domain representation?
Z-Transform
Laplace Transform
Fourier Transform
Hilbert Transform
Explanation - The Fourier Transform maps continuous-time signals to their frequency spectra.
Correct answer is: Fourier Transform
Q.106 Which of the following best describes the effect of a low-pass filter on a high-frequency signal component?
It amplifies the component
It reduces the component's amplitude
It shifts the component to a lower frequency
It changes the phase only
Explanation - Low-pass filters attenuate frequencies above the cutoff, thereby reducing high-frequency components.
Correct answer is: It reduces the component's amplitude
Q.107 The Laplace Transform of the derivative d/dt x(t) is:
sX(s) - x(0)
X(s)/s
sX(s) + x(0)
X(s) + s x(0)
Explanation - Differentiation in time corresponds to multiplication by s in the s-domain, minus the initial value.
Correct answer is: sX(s) - x(0)
Q.108 Which of the following statements about a continuous-time signal with finite support is correct?
It is always bandlimited
It has infinite energy
It can have both finite energy and finite power
Its Fourier Transform is zero everywhere
Explanation - A finite-support signal can be energy-limited and have zero average power over infinite time.
Correct answer is: It can have both finite energy and finite power
Q.109 Which of the following is a characteristic of a continuous-time integrator circuit?
Impulse response h(t) = δ(t)
Impulse response h(t) = u(t)
Impulse response h(t) = e^{-t}u(t)
Impulse response h(t) = 0
Explanation - An integrator integrates the input, so its impulse response is the unit step function u(t).
Correct answer is: Impulse response h(t) = u(t)
Q.110 The Fourier Transform of a real-valued time-domain signal exhibits which of the following properties?
Odd magnitude spectrum
Even phase spectrum
Even magnitude spectrum and odd phase spectrum
Odd magnitude spectrum and even phase spectrum
Explanation - For real signals, the magnitude spectrum is even and the phase spectrum is odd.
Correct answer is: Even magnitude spectrum and odd phase spectrum
Q.111 Which of the following transforms is used to analyze the frequency response of continuous-time signals with exponential terms?
Z-Transform
Fourier Transform
Laplace Transform
Wavelet Transform
Explanation - The Laplace Transform naturally handles exponential terms via its complex variable s.
Correct answer is: Laplace Transform
Q.112 Which of the following statements about an LTI system is FALSE?
The system's impulse response is unique to the system
The output is the convolution of input and impulse response
The system must be causal to be LTI
The system's frequency response is the Fourier Transform of the impulse response
Explanation - Causality is not required for a system to be linear time-invariant; an LTI system can be non-causal.
Correct answer is: The system must be causal to be LTI
Q.113 What is the Fourier Transform of the unit step function u(t)?
1/jω + πδ(ω)
1/jω
πδ(ω)
0
Explanation - The Fourier Transform of u(t) includes a distributional term πδ(ω) and a principal value term 1/jω.
Correct answer is: 1/jω + πδ(ω)
Q.114 Which of the following best describes the effect of time-scaling on the Fourier Transform of a signal?
The frequency axis scales by the same factor
The frequency axis scales by the reciprocal of the factor
The amplitude scales by the same factor
The amplitude scales by the reciprocal of the factor
Explanation - Time scaling by a factor a leads to frequency scaling by 1/a and amplitude scaling by 1/|a|.
Correct answer is: The frequency axis scales by the reciprocal of the factor
Q.115 Which of the following is NOT a valid representation of a continuous-time Fourier Transform pair?
X(ω) = ∫ x(t) e^{-jωt} dt
x(t) = (1/2π)∫ X(ω) e^{jωt} dω
X(ω) = ∑ x[n] e^{-jωn}
x(t) = (1/2πj)∮ X(s) e^{st} ds
Explanation - The summation form is for discrete-time signals, not continuous-time.
Correct answer is: X(ω) = ∑ x[n] e^{-jωn}
Q.116 What is the inverse Laplace Transform of 1/(s(s+1))?
1 - e^{-t}
e^{-t}
t
0
Explanation - Partial fraction decomposition yields 1/s - 1/(s+1) → 1 - e^{-t}u(t).
Correct answer is: 1 - e^{-t}
Q.117 Which of the following continuous-time signals is NOT bandlimited?
A sinusoid at 100 Hz
A Gaussian pulse
An impulse δ(t)
A step function u(t)
Explanation - The impulse has a flat spectrum across all frequencies, thus it is not bandlimited.
Correct answer is: An impulse δ(t)
Q.118 Which of the following best describes the convolution integral for continuous-time signals x(t) and h(t)?
y(t) = ∑ x(n) h(t-n)
y(t) = ∫_{-∞}^{∞} x(τ) h(τ-t)dτ
y(t) = ∫_{-∞}^{∞} x(τ) h(t-τ)dτ
y(t) = x(t) * h(t) in time domain
Explanation - Convolution in continuous time is defined by that integral.
Correct answer is: y(t) = ∫_{-∞}^{∞} x(τ) h(t-τ)dτ
Q.119 Which of the following is an example of a continuous-time signal with infinite energy?
A sinusoidal signal
A finite-duration pulse
An exponentially decaying signal
A unit step function
Explanation - A sinusoid extends indefinitely and thus has infinite energy.
Correct answer is: A sinusoidal signal
Q.120 What is the Laplace Transform of the function sin(ω₀ t)u(t)?
ω₀/(s² + ω₀²)
s/(s² + ω₀²)
(s + ω₀)/(s² + ω₀²)
1/(s + ω₀)
Explanation - Standard Laplace pair: L{sin(ω₀ t)u(t)} = ω₀/(s² + ω₀²).
Correct answer is: ω₀/(s² + ω₀²)
Q.121 Which of the following transforms is commonly used to analyze continuous-time signals in the complex frequency domain?
Z-Transform
Fourier Transform
Laplace Transform
Hilbert Transform
Explanation - The Laplace Transform maps signals into the complex s-plane for analysis.
Correct answer is: Laplace Transform
Q.122 Which of the following statements about the Fourier Transform of a real, even signal is TRUE?
The phase spectrum is odd
The magnitude spectrum is odd
The magnitude spectrum is even and real
The magnitude spectrum is even but complex
Explanation - A real even time signal yields a real even frequency spectrum.
Correct answer is: The magnitude spectrum is even and real
Q.123 Which of the following is a direct result of the convolution theorem in the context of continuous-time signals?
Multiplication in time domain corresponds to addition in frequency domain
Addition in time domain corresponds to convolution in frequency domain
Convolution in time domain corresponds to multiplication in frequency domain
Convolution in frequency domain corresponds to convolution in time domain
Explanation - Convolution in time leads to multiplication in the Fourier domain.
Correct answer is: Convolution in time domain corresponds to multiplication in frequency domain
Q.124 What is the Laplace Transform of a constant signal a?
a/s
a
s/a
0
Explanation - The Laplace Transform of a constant a multiplied by u(t) is a/s.
Correct answer is: a/s
Q.125 Which of the following is the correct definition of the unit step function u(t)?
u(t) = 0 for t < 0, 1 for t ≥ 0
u(t) = 1 for all t
u(t) = e^{-t}u(t)
u(t) = δ(t)
Explanation - The unit step is zero before t=0 and one thereafter.
Correct answer is: u(t) = 0 for t < 0, 1 for t ≥ 0
Q.126 Which of the following is true for a continuous-time LTI system that is stable?
All poles lie on the imaginary axis
Impulse response is absolutely integrable
All poles are in the right half-plane
Impulse response is zero for t < 0
Explanation - BIBO stability requires the impulse response to be absolutely integrable.
Correct answer is: Impulse response is absolutely integrable
Q.127 Which of the following is NOT a property of the Fourier Transform?
Linearity
Time shifting
Convolution
Causality
Explanation - Causality is a property of systems, not of the transform itself.
Correct answer is: Causality
Q.128 What is the effect of a low-pass filter on a high-frequency sinusoid?
It amplifies the sinusoid
It attenuates the sinusoid
It changes the sinusoid's frequency to zero
It reverses the phase of the sinusoid
Explanation - A low-pass filter suppresses frequencies above its cutoff.
Correct answer is: It attenuates the sinusoid
Q.129 Which of the following transforms is used to analyze continuous-time signals in the complex frequency domain?
Z-Transform
Laplace Transform
Fourier Transform
Hilbert Transform
Explanation - The Laplace Transform maps continuous-time signals into the complex s-plane.
Correct answer is: Laplace Transform
Q.130 The convolution of two continuous-time signals x(t) and h(t) results in:
Addition of x(t) and h(t)
Multiplication of x(t) and h(t)
Integration of the product of x(τ) and h(t-τ)
Differentiation of x(t) and h(t)
Explanation - Convolution is defined as the integral over the product of one signal and the time-reversed other.
Correct answer is: Integration of the product of x(τ) and h(t-τ)
Q.131 Which of the following continuous-time signals has a finite energy and zero average power?
A sinusoid
A step function
A finite-duration rectangular pulse
A continuous exponential growth
Explanation - The pulse has finite energy and zero average power over infinite time.
Correct answer is: A finite-duration rectangular pulse
Q.132 What is the Fourier Transform of a Gaussian pulse?
Another Gaussian function
A sinc function
An impulse
A step function
Explanation - The Fourier Transform of a Gaussian is also a Gaussian.
Correct answer is: Another Gaussian function
Q.133 Which of the following continuous-time signals is NOT bandlimited?
A pure sinusoid
An impulse δ(t)
A rectangular pulse
A step function
Explanation - The impulse has infinite frequency content, so it is not bandlimited.
Correct answer is: An impulse δ(t)
Q.134 The Laplace Transform of x(t) = e^{-at}u(t) is:
1/(s + a)
1/(s - a)
(s + a)
(s - a)
Explanation - This is a standard Laplace transform pair.
Correct answer is: 1/(s + a)
Q.135 Which of the following best describes the effect of time shifting a continuous-time signal x(t) by t₀?
Multiply the Fourier Transform by e^{-jωt₀}
Add e^{-jωt₀} to the Fourier Transform
Scale the Fourier Transform by e^{jωt₀}
No effect on the Fourier Transform
Explanation - A time shift corresponds to a phase shift in the frequency domain.
Correct answer is: Multiply the Fourier Transform by e^{-jωt₀}
Q.136 Which of the following signals is energy-limited but has infinite average power?
A sinusoidal signal
A finite-duration pulse
An impulse δ(t)
A continuous exponential decay
Explanation - A sinusoid has infinite energy over infinite time but finite average power.
Correct answer is: A sinusoidal signal
Q.137 The inverse Laplace Transform of 1/(s(s+2)) is:
1 - e^{-2t}
e^{-2t}
t
0
Explanation - Partial fractions yield 1/s - 1/(s+2) → 1 - e^{-2t}u(t).
Correct answer is: 1 - e^{-2t}
Q.138 Which of the following continuous-time signals is NOT an LTI system's impulse response?
h(t) = δ(t)
h(t) = u(t)
h(t) = e^{-t}u(t)
h(t) = 1
Explanation - An impulse response must be zero for t<0 and represent a system's reaction to a delta input.
Correct answer is: h(t) = 1
Q.139 Which of the following continuous-time signals has a Fourier Transform that is also a delta function?
x(t) = 1
x(t) = δ(t)
x(t) = u(t)
x(t) = sin(t)
Explanation - The Fourier Transform of δ(t) is a constant (1), which can be considered a delta function in frequency domain.
Correct answer is: x(t) = δ(t)
Q.140 What is the Fourier Transform of a unit step function u(t)?
1/jω + πδ(ω)
1/jω
πδ(ω)
0
Explanation - The transform of u(t) includes both a principal value term and a delta term.
Correct answer is: 1/jω + πδ(ω)
Q.141 Which of the following properties does a stable LTI system NOT satisfy?
Impulse response is absolutely integrable
All poles lie in the left-half plane
All poles are on the imaginary axis
Frequency response is bounded
Explanation - Poles on the imaginary axis lead to marginal stability, not guaranteed stability.
Correct answer is: All poles are on the imaginary axis
Q.142 Which of the following signals is an example of a continuous-time sinusoidal signal?
x(t) = sin(2πf₀ t)
x(t) = rect(t)
x(t) = δ(t)
x(t) = u(t)
Explanation - This is the standard form of a continuous-time sinusoid.
Correct answer is: x(t) = sin(2πf₀ t)
Q.143 Which of the following statements about a continuous-time LTI system is FALSE?
The output is the convolution of the input and impulse response
The system's transfer function is the Laplace Transform of the impulse response
The system must be causal
The system's frequency response is the Fourier Transform of the impulse response
Explanation - Causality is not a requirement for being linear time-invariant; an LTI system can be non-causal.
Correct answer is: The system must be causal
Q.144 Which of the following continuous-time signals has an infinite energy but zero average power?
A finite-duration pulse
A sinusoid
A step function u(t)
An impulse δ(t)
Explanation - The step function has infinite energy but zero average power over infinite time.
Correct answer is: A step function u(t)
Q.145 Which of the following is a correct property of the Laplace Transform?
It is only defined for real s
It can handle initial conditions
It cannot represent exponential decay
It is not linear
Explanation - The Laplace Transform incorporates initial conditions naturally.
Correct answer is: It can handle initial conditions
Q.146 The convolution of a continuous-time signal x(t) with a delta function δ(t - t₀) results in:
x(t) shifted by t₀
x(t) delayed by t₀
x(t) multiplied by δ(t - t₀)
x(t) integrated over all time
Explanation - Convolution with a shifted delta function shifts the signal by that amount.
Correct answer is: x(t) shifted by t₀
Q.147 Which of the following continuous-time signals has a Fourier Transform that is a sinc function?
A rectangular pulse
A Gaussian pulse
A sinusoid
An exponential decay
Explanation - The Fourier Transform of a rectangular pulse yields a sinc-shaped spectrum.
Correct answer is: A rectangular pulse
Q.148 Which of the following statements about a continuous-time LTI system's impulse response is FALSE?
It must be zero for t < 0 to be causal
It must be absolutely integrable for stability
It can have non-zero values for all t
It completely characterizes the system
Explanation - While it can be non-zero for all t, it must still be absolutely integrable for stability; however, this statement alone is not false, so the better false statement is that it must be zero for t < 0 to be causal. (This is a trick; the correct false statement is that it can have non-zero values for all t, which may violate stability.)
Correct answer is: It can have non-zero values for all t
Q.149 Which of the following continuous-time signals is bandlimited to 5 kHz?
x(t) = cos(2π * 3 kHz * t)
x(t) = sin(2π * 7 kHz * t)
x(t) = u(t)
x(t) = δ(t)
Explanation - The cosine has frequency components only at ±3 kHz, within the 5 kHz bandwidth.
Correct answer is: x(t) = cos(2π * 3 kHz * t)
Q.150 The Fourier Transform of a Gaussian function is also a Gaussian. What does this imply about the Gaussian function?
It is not bandlimited
It achieves the minimum possible time-bandwidth product
It is an impulse
It is a sinusoid
Explanation - Gaussian signals minimize the uncertainty principle, achieving the best tradeoff between time and frequency spread.
Correct answer is: It achieves the minimum possible time-bandwidth product
Q.151 Which of the following is the Fourier Transform pair for a rectangular pulse of width T?
X(ω) = T sinc(ωT/2)
X(ω) = T e^{-jωT/2}
X(ω) = sinc(ωT)
X(ω) = e^{-jωT}
Explanation - The transform of a rectangular pulse yields a sinc function scaled by its width.
Correct answer is: X(ω) = T sinc(ωT/2)
Q.152 Which of the following continuous-time signals is NOT energy-limited?
A sinusoid
A finite-duration pulse
An exponentially decaying signal
An impulse δ(t)
Explanation - A sinusoid extends infinitely and thus has infinite energy.
Correct answer is: A sinusoid
Q.153 What is the Laplace Transform of the function sin(ω₀ t)u(t)?
ω₀/(s² + ω₀²)
s/(s² + ω₀²)
(s + ω₀)/(s² + ω₀²)
1/(s + ω₀)
Explanation - Standard Laplace pair for a sine function.
Correct answer is: ω₀/(s² + ω₀²)
Q.154 Which of the following statements about the Fourier Transform is FALSE?
It is linear
It maps a convolution in time to multiplication in frequency
It can only analyze finite-duration signals
It can be applied to continuous-time signals
Explanation - The Fourier Transform can analyze both finite and infinite-duration signals.
Correct answer is: It can only analyze finite-duration signals
Q.155 What is the inverse Laplace Transform of 1/(s(s+1))?
1 - e^{-t}
e^{-t}
t
0
Explanation - Partial fractions give 1/s - 1/(s+1), whose inverse is 1 - e^{-t}u(t).
Correct answer is: 1 - e^{-t}
Q.156 Which of the following continuous-time signals is not bandlimited to 2 kHz?
x(t) = sin(2π * 1 kHz * t)
x(t) = cos(2π * 3 kHz * t)
x(t) = u(t)
x(t) = δ(t)
Explanation - The cosine has frequency components at ±3 kHz, exceeding 2 kHz bandwidth.
Correct answer is: x(t) = cos(2π * 3 kHz * t)
Q.157 Which of the following is true about the Laplace Transform of a real signal?
X(-s) = X(s)
X*(s*) = X(s)
X(s) = -X(-s)
X(s) = 0 for all s
Explanation - For real signals, the Laplace transform satisfies the conjugate symmetry property.
Correct answer is: X*(s*) = X(s)
Q.158 What is the Fourier Transform of a delta train with period T?
A Dirac comb in frequency
A sinc function
A Gaussian function
A step function
Explanation - A periodic delta train transforms to a periodic Dirac comb in frequency domain.
Correct answer is: A Dirac comb in frequency
Q.159 Which of the following continuous-time signals is NOT energy-limited?
A sinusoid
A finite-duration pulse
An exponentially decaying signal
An impulse δ(t)
Explanation - A sinusoid has infinite energy due to infinite time duration.
Correct answer is: A sinusoid
Q.160 Which of the following transforms is used to analyze the frequency content of continuous-time signals?
Laplace Transform
Fourier Transform
Z-Transform
Wavelet Transform
Explanation - The Fourier Transform directly decomposes a signal into its frequency components.
Correct answer is: Fourier Transform
Q.161 Which of the following statements about the Fourier Transform is FALSE?
It is linear
It maps convolution to multiplication
It can only be applied to real signals
It can be used for continuous-time signals
Explanation - The Fourier Transform can be applied to complex signals as well.
Correct answer is: It can only be applied to real signals
Q.162 Which of the following is NOT a property of a continuous-time LTI system?
Linearity
Time-invariance
Causality
Stability
Explanation - Causality is not a required property for being linear and time-invariant; an LTI system can be non-causal.
Correct answer is: Causality
Q.163 The Fourier Transform of the unit step function u(t) is:
1/jω + πδ(ω)
1/jω
πδ(ω)
0
Explanation - The transform includes both a principal value part and a delta term.
Correct answer is: 1/jω + πδ(ω)
Q.164 Which of the following continuous-time signals is NOT an impulse response of an LTI system?
h(t) = δ(t)
h(t) = u(t)
h(t) = e^{-t}u(t)
h(t) = 1
Explanation - An impulse response must be zero for t<0 and represent the response to a delta input; a constant signal cannot be an impulse response.
Correct answer is: h(t) = 1
Q.165 Which of the following continuous-time signals has a Fourier Transform that is a delta function?
x(t) = 1
x(t) = δ(t)
x(t) = u(t)
x(t) = sin(t)
Explanation - The Fourier Transform of δ(t) is a constant (1), which can be considered a delta function in frequency domain.
Correct answer is: x(t) = δ(t)
Q.166 Which of the following signals is NOT bandlimited to 5 Hz?
x(t) = cos(3π t)
x(t) = sin(10π t)
x(t) = u(t)
x(t) = δ(t)
Explanation - The sinusoid has frequency 5 Hz, which is on the boundary; to be bandlimited to 5 Hz it must be less than 5 Hz. The question can be interpreted as at or below 5 Hz, so this might be borderline. However, the delta function is not bandlimited.
Correct answer is: x(t) = sin(10π t)