Practice tests · GATE

GATE signals and systems: 5 practice questions with answers

By the PrepMatic team · Updated 9 Oct 2026 · 4 min read

Signals and Systems is a section in both the GATE EC and EE papers (in EC it sits with networks as "Networks, Signals and Systems"), and its ideas return in control systems and communications. The questions are mostly short property checks plus a few transform calculations, so a clear table of properties beats long derivations. The five original questions below mix convolution, power and energy, system properties and sampling.

What GATE tests in signals and systems

Check your paper's current list on the official syllabus page, because the 2027 syllabi were revised. The standard content is continuous-time and discrete-time signals, LTI systems and convolution, system properties (linearity, time-invariance, causality, stability, memory), Fourier series, the Fourier, Laplace and z-transforms and their regions of convergence, sampling and reconstruction, and the DTFT and DFT.

Typical questions give a signal or an impulse response and ask for a property, a transform value, an output sample or the minimum sampling rate. The real paper has MCQ, MSQ and NAT questions, and MSQ suits property questions well ("select all stable systems"). All five below are MCQ.

Practice questions

Question 1

The sequences x[n] and h[n] are both equal to 1, 2, 1 for n = 0, 1, 2 and zero elsewhere. If y[n] is the convolution of x[n] and h[n], the value of y[2] is:

• A. 4
• B. 5
• C. 6
• D. 8

Question 2

The average power of the signal x(t) = 3 + 4 cos(2πt) + 2 sin(4πt) is:

• A. 13
• B. 21
• C. 29
• D. 19

Question 3

An LTI system has the impulse response h(t) = e^(−2t) u(t) + e^(t) u(−t), where u(t) is the unit step. The system is:

• A. causal and stable
• B. non-causal and stable
• C. causal and unstable
• D. non-causal and unstable

Question 4

The signal x(t) = 2 cos(200πt) cos(600πt) is sampled uniformly. The minimum sampling rate that avoids aliasing (the Nyquist rate) is:

• A. 800 Hz
• B. 400 Hz
• C. 600 Hz
• D. 1600 Hz

Question 5

The signal x(t) = e^(−t) u(t) has energy 1/2. The energy of y(t) = x(2t) is:

• A. 1/8
• B. 1/4
• C. 1/2
• D. 1

Answers and explanations

1. C. For finite sequences, y[2] = x[0]h[2] + x[1]h[1] + x[2]h[0] = 1 × 1 + 2 × 2 + 1 × 1 = 6. The full output is 1, 4, 6, 4, 1 for n = 0 to 4. A quick check: the sum of y equals (sum of x) × (sum of h) = 4 × 4 = 16, and 1 + 4 + 6 + 4 + 1 = 16.
2. D. Power adds for components at different frequencies. The DC term gives 3² = 9, a cosine of amplitude A gives A²/2 = 8, and a sine of amplitude 2 gives 4/2 = 2. The total is 9 + 8 + 2 = 19. The cosine (1 Hz) and sine (2 Hz) are orthogonal, so there are no cross terms.
3. B. The system is non-causal because h(t) is non-zero for t < 0 (the e^t u(−t) part). It is stable because h(t) is absolutely integrable: the integral from 0 to infinity of e^(−2t) is 1/2 and the integral from minus infinity to 0 of e^t is 1, so the total is 3/2, which is finite.
4. A. Use 2 cos A cos B = cos(A + B) + cos(A − B). With A = 200πt and B = 600πt, x(t) = cos(800πt) + cos(400πt). These are at 400 Hz and 200 Hz, so the highest frequency is 400 Hz and the Nyquist rate is 2 × 400 = 800 Hz. Option B confuses the highest frequency with the rate.
5. B. Substituting 2t compresses the signal in time by a factor of 2, so the energy halves: y(t) = e^(−2t) u(t), and the energy is the integral from 0 to infinity of e^(−4t), which is 1/4. In general x(at) has energy E / |a|, which here is (1/2) / 2 = 1/4.

How to prepare signals and systems

• Keep a property table for each transform: linearity, time shift, frequency shift, scaling, convolution, differentiation, Parseval's relation, and the common pairs (impulse, step, exponential, rectangular and sinc).
• Practise convolution three ways: direct sum for short sequences, graphical method for continuous signals, and transform multiplication. Check results with the sum rule from Question 1.
• Be exact about ROCs. In the Laplace and z-transforms, the region of convergence decides causality and stability. Practise reading both from a pole-zero plot.
• Memorise stability and causality tests: stable if h is absolutely summable or integrable (poles inside the unit circle or in the left half-plane for causal systems), causal if h(t) = 0 for t < 0.
• For sampling, find the highest frequency in the signal first. Products of sinusoids add frequencies, as in Question 4, and are a frequent trick.
• Learn the DFT and the FFT's structure for EC, and Fourier series conditions and the Gibbs phenomenon for both papers.

The next topics in the signal chain are control systems and communications. Laplace transform practice is in differential equations. The GATE ECE preparation guide and GATE electrical preparation guide show where this section sits in each plan.

Take the full topic test on PrepMatic

PrepMatic's topic tests run about 15 questions in 30 minutes, which is a good pace for property and transform questions. The free assessment shows your weakest subjects first.

← All practice tests