Which of the following is not a continuous-time signal? A) Sinusoidal signal
B) Unit step signal
C) Impulse signal
D) Rectangular pulse Answer: C
The Laplace transform of a unit impulse δ(t) is: A) 1
B) 0
C) ∞
D) Cannot be determined Answer: A
The property of a signal that determines whether it is odd or even is: A) Symmetry
B) Periodicity
C) Linearity
D) Causality Answer: A
A system that depends only on the current and past inputs is: A) Causal
B) Non-causal
C) Anti-causal
D) Acausal Answer: A
Which of the following is a linear time-invariant (LTI) system property? A) Memory
B) Time-varying
C) Causal
D) Superposition Answer: D
The convolution of two signals in time domain corresponds to which operation in Laplace domain? A) Addition
B) Multiplication
C) Differentiation
D) Integration Answer: B
Which of the following signals is periodic? A) e^(-t)
B) t
C) sin(t)
D) δ(t) Answer: C
The Fourier series of a periodic signal expresses it as a sum of: A) Cosine functions
B) Sine functions
C) Exponentials
D) Both sine and cosine functions Answer: D
The transfer function H(s) of a system is used to analyze its: A) Input-output behavior
B) Frequency response
C) Phase response
D) All of the above Answer: D
The region of convergence (ROC) of the Laplace transform is determined by the: A) Magnitude of the poles
B) Magnitude of the zeros
C) Exponential growth of the signal
D) None of the above Answer: A
Which property is NOT associated with a causal system? A) Stability
B) Memory
C) Predictability
D) Non-zero initial conditions Answer: B
The Laplace transform of a ramp signal t*u(t) is: A) 1/s^2
B) 1/s^3
C) 1/s^2 + 1/s
D) 1/s^2 – 1/s Answer: C
The property of a system that ensures its output depends only on present and future inputs is: A) Linearity
B) Time-invariance
C) Causality
D) Memory Answer: C
The Fourier transform of a real and even signal is: A) Real and even
B) Real and odd
C) Complex and even
D) Complex and odd Answer: A
The Laplace transform of a derivative of a signal x(t) with respect to time is: A) sX(s)
B) X(s)/s
C) -X(s)
D) X'(s) Answer: B
The frequency response of a system is defined as the: A) Ratio of output to input in the time domain
B) Ratio of output to input in the frequency domain
C) Impulse response of the system
D) None of the above Answer: B
The Fourier transform of a Gaussian function in time domain is another Gaussian function in: A) Time domain
B) Frequency domain
C) Both
D) Neither Answer: B
Which of the following properties is true for the impulse response of a system? A) It is always causal
B) It is always stable
C) It is a characteristic of the system
D) It is always linear Answer: C
The Laplace transform of the convolution of two functions x(t) and y(t) is: A) X(s)Y(s)
B) X(s)/Y(s)
C) X(s) + Y(s)
D) X(s)Y(s)/2 Answer: A
Which of the following signals is not time-limited? A) e^(-t)
B) t*u(t)
C) sin(t)
D) δ(t) Answer: A
The region in the s-plane where the Laplace transform converges is called the: A) Stability region
B) Causality region
C) Region of convergence (ROC)
D) Frequency response region Answer: C
The Fourier transform of a rectangular pulse of duration T in time domain is: A) sinc(fT)
B) T sinc(fT)
C) sin(fT)/fT
D) cos(fT)/fT Answer: B
A system is said to be BIBO stable if: A) It has bounded input and bounded output
B) It is causal and stable
C) Its impulse response decays to zero
D) Its frequency response is constant Answer: A
Which of the following is a continuous-time, periodic signal? A) e^(-t)
B) u(t)
C) sin(t)
D) δ(t) Answer: C
The Laplace transform of a unit step signal u(t) is: A) 1/s
B) 1/(s+1)
C) 1/s^2
D) 1/(s-1) Answer: A
The Fourier series of a function represents it as a sum of: A) Complex exponentials
B) Real exponentials
C) Sinusoids and cosinusoids
D) Cosine functions only Answer: C
A system is said to be linear if it satisfies the principle of: A) Additivity
B) Homogeneity
C) Superposition
D) All of the above Answer: D
Which of the following is a time-domain characterization of a signal? A) Transfer function
B) Impulse response
C) Frequency response
D) Laplace transform Answer: B
The Fourier transform of a delta function δ(t) is: A) 1
B) δ(f)
C) 2πδ(f)
D) 1/2π Answer: A
Which property of a system implies that if the input is zero for t < 0, then the output is also zero for t < 0? A) Memory
B) Causality
C) Linearity
D) Time-invariance Answer: B
The Laplace transform of the product of two signals x(t) and y(t) is: A) X(s)/Y(s)
B) X(s)Y(s)
C) X(s) + Y(s)
D) X(s)Y(s)/2 Answer: B
The Nyquist sampling theorem states that: A) The sampling rate must be at least twice the highest frequency component of the signal
B) The sampling rate must be at least half the highest frequency component of the signal
C) The sampling rate must be exactly equal to the highest frequency component of the signal
D) The sampling rate must be exactly double the highest frequency component of the signal Answer: A
The Laplace transform of an exponential decay signal e^(-at) is: A) 1/(s+a)
B) 1/(s-a)
C) a/(s+a)
D) a/(s-a) Answer: A
Which property is true for the Fourier transform of a periodic signal? A) It is periodic
B) It is aperiodic
C) It is bounded
D) It is always real Answer: A
The Laplace transform of a sine function sin(ωt) is: A) ω/(s^2 + ω^2)
B) s/(s^2 + ω^2)
C) s/(s^2 – ω^2)
D) ω/(s^2 – ω^2) Answer: A
The system property that describes the ability of the system to return to its initial state after an input is removed is: A) Linearity
B) Time-invariance
C) Memory
D) Stability Answer: D
The Fourier transform of a complex exponential e^(jwt) is a: A) Sine function
B) Cosine function
C) Complex exponential
D) Real exponential Answer: C
Which of the following signals is not energy-limited? A) Sinusoidal signal
B) Rectangular pulse
C) Exponential decay
D) Impulse signal Answer: A
The Z-transform is used to analyze: A) Continuous-time signals
B) Discrete-time signals
C) Periodic signals
D) Non-linear signals Answer: B
The Laplace transform of the derivative of a signal x(t) with respect to time t is: A) sX(s)
B) X(s)/s
C) X(s)
D) -X(s) Answer: A
A system is said to be time-invariant if: A) Its output depends only on current input
B) Its response does not change with time
C) Its output depends linearly on input
D) Its response is unchanged by a time shift in input Answer: D
The inverse Laplace transform is used to convert: A) A function in the s-domain to time-domain
B) A function in the frequency domain to time-domain
C) A function in the z-domain to time-domain
D) A function in the Laplace domain to time-domain Answer: A
Which property distinguishes between even and odd signals? A) Linearity
B) Symmetry
C) Time-invariance
D) Causality Answer: B
The Dirac delta function δ(t) is defined as: A) 1 for t = 0, 0 otherwise
B) 0 for t = 0, 1 otherwise
C) ∞ for t = 0, 0 otherwise
D) 0 for all t Answer: A
The Laplace transform of a constant signal x(t) = K is: A) K
B) 1/K
C) K/s
D) Ks Answer: C
The system property that implies the output depends on future values of the input is: A) Causality
B) Memory
C) Linearity
D) Time-invariance Answer: B
The Laplace transform of a unit impulse δ(t – a) is: A) 1
B) e^(-as)
C) e^(as)
D) δ(s – a) Answer: C
Which of the following is a time-domain characterization of a system? A) Transfer function
B) Impulse response
C) Frequency response
D) Z-transform Answer: B
A system is said to be stable if: A) Its impulse response is bounded
B) Its output does not go to infinity for bounded input
C) It has no memory
D) Its transfer function is well-defined Answer: B
The Fourier transform of a constant signal is: A) A delta function
B) Zero
C) An impulse
D) Not defined Answer: A