Ultimate Signal Processing Engineering
Practice Exam 2026 Questions for Mastery
and Certification
1. Which of the following is a time-invariant system?
A. y(t) = t·x(t)
B. y(t) = x(t - 3)
C. y(t) = x(t) + t
D. y(t) = sin(t)·x(t)
Rationale: A system is time-invariant if a time shift in input results in
the same time shift in output. Only y(t) = x(t - 3) satisfies this.
2. The Fourier Transform of a delta function δ(t) is:
A. 0
B. t
C. cos(t)
D. 1
Rationale: δ(t) contains all frequencies equally, so its Fourier
Transform is 1 across all frequencies.
3. Which of the following signals is periodic?
,A. x(t) = e^(-t)
B. x(t) = sin(2πt)
C. x(t) = t
D. x(t) = ln(t)
Rationale: A periodic signal repeats after a fixed interval. sin(2πt)
repeats every 1 second.
4. The convolution of two signals in time domain corresponds to what
in frequency domain?
A. Division
B. Subtraction
C. Multiplication
D. Addition
Rationale: Convolution in time domain is equivalent to multiplication
in frequency domain according to the Convolution Theorem.
5. Which of these is the Z-transform of x*n+ = δ*n+?
A. z
B. 1/z
C. 1
D. 0
Rationale: The Z-transform of δ*n+ is 1 because δ*n+ = 1 at n = 0 and 0
elsewhere.
,6. A linear system satisfies which property?
A. y(t) = x(t)^2
B. Superposition (additivity and homogeneity)
C. y(t) = sin(x(t))
D. y(t) = |x(t)|
Rationale: Linearity requires that the system output for a sum of
inputs equals the sum of outputs and scaling of input scales the
output.
7. Which of the following is a low-pass filter characteristic?
A. Passes high frequencies
B. Passes low frequencies
C. Attenuates low frequencies only
D. Rejects DC component
Rationale: A low-pass filter allows frequencies below a cutoff to pass
and attenuates higher frequencies.
8. The sampling theorem states that a continuous signal can be
reconstructed from its samples if:
A. Fs < 2·Fmax
B. Fs ≥ 2·Fmax
C. Fs = Fmax/2
D. Fs = Fmax^2
, Rationale: Nyquist-Shannon sampling theorem requires the sampling
frequency Fs to be at least twice the maximum frequency Fmax.
9. The Fourier series represents a signal in terms of:
A. Exponential decay functions
B. Sinusoids
C. Step functions
D. Delta functions
Rationale: Fourier series decomposes a periodic signal into a sum of
sine and cosine functions (or complex exponentials).
10. Which of the following is true about the Laplace Transform region
of convergence (ROC)?
A. ROC is always the entire s-plane
B. ROC depends on the sampling rate
C. ROC depends on the signal type and its growth
D. ROC is only for causal signals
Rationale: ROC is determined by the properties of the signal (causal,
stable, growing) and ensures convergence of the Laplace integral.
11. What is the inverse Z-transform of X(z) = z/(z-0.5)?
A. 0.5^n
B. (0.5)^n u[n]
Practice Exam 2026 Questions for Mastery
and Certification
1. Which of the following is a time-invariant system?
A. y(t) = t·x(t)
B. y(t) = x(t - 3)
C. y(t) = x(t) + t
D. y(t) = sin(t)·x(t)
Rationale: A system is time-invariant if a time shift in input results in
the same time shift in output. Only y(t) = x(t - 3) satisfies this.
2. The Fourier Transform of a delta function δ(t) is:
A. 0
B. t
C. cos(t)
D. 1
Rationale: δ(t) contains all frequencies equally, so its Fourier
Transform is 1 across all frequencies.
3. Which of the following signals is periodic?
,A. x(t) = e^(-t)
B. x(t) = sin(2πt)
C. x(t) = t
D. x(t) = ln(t)
Rationale: A periodic signal repeats after a fixed interval. sin(2πt)
repeats every 1 second.
4. The convolution of two signals in time domain corresponds to what
in frequency domain?
A. Division
B. Subtraction
C. Multiplication
D. Addition
Rationale: Convolution in time domain is equivalent to multiplication
in frequency domain according to the Convolution Theorem.
5. Which of these is the Z-transform of x*n+ = δ*n+?
A. z
B. 1/z
C. 1
D. 0
Rationale: The Z-transform of δ*n+ is 1 because δ*n+ = 1 at n = 0 and 0
elsewhere.
,6. A linear system satisfies which property?
A. y(t) = x(t)^2
B. Superposition (additivity and homogeneity)
C. y(t) = sin(x(t))
D. y(t) = |x(t)|
Rationale: Linearity requires that the system output for a sum of
inputs equals the sum of outputs and scaling of input scales the
output.
7. Which of the following is a low-pass filter characteristic?
A. Passes high frequencies
B. Passes low frequencies
C. Attenuates low frequencies only
D. Rejects DC component
Rationale: A low-pass filter allows frequencies below a cutoff to pass
and attenuates higher frequencies.
8. The sampling theorem states that a continuous signal can be
reconstructed from its samples if:
A. Fs < 2·Fmax
B. Fs ≥ 2·Fmax
C. Fs = Fmax/2
D. Fs = Fmax^2
, Rationale: Nyquist-Shannon sampling theorem requires the sampling
frequency Fs to be at least twice the maximum frequency Fmax.
9. The Fourier series represents a signal in terms of:
A. Exponential decay functions
B. Sinusoids
C. Step functions
D. Delta functions
Rationale: Fourier series decomposes a periodic signal into a sum of
sine and cosine functions (or complex exponentials).
10. Which of the following is true about the Laplace Transform region
of convergence (ROC)?
A. ROC is always the entire s-plane
B. ROC depends on the sampling rate
C. ROC depends on the signal type and its growth
D. ROC is only for causal signals
Rationale: ROC is determined by the properties of the signal (causal,
stable, growing) and ensures convergence of the Laplace integral.
11. What is the inverse Z-transform of X(z) = z/(z-0.5)?
A. 0.5^n
B. (0.5)^n u[n]
