GATE EC 2015 Set 2 — Question 15
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+1 / -0.33MediumFourier SeriesContinuous-Time SignalsSignals & Systems
Signals & Systems → Continuous-Time Signals → Fourier Series
Last updated
Question
The magnitude and phase of the complex Fourier series coefficients of a periodic signal are shown in the figure. Choose the correct statement from the four choices given. Notation: is the set of complex numbers, is the set of purely real numbers, and is the set of purely imaginary numbers.
Correct answer
(A) x(t) ∈ R
Solution
From the provided plots of the complex Fourier series coefficients :
1.Magnitude Plot: is an even function of , i.e., .
2.Phase Plot: is also an even function of , i.e., . Specifically, the phase is either or for all , which means all coefficients are purely real.
Combining these two observations, we have . Since all are real, . Therefore, the condition is satisfied (). This is the necessary and sufficient condition for the periodic signal to be purely real. Thus, .Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE EC question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Continuous-Time Signals
2026 Set 1 Q13The Laplace Transform of the signal is given by which of the following…2026 Set 1 Q15Two analog signals and ( in second), are sampled at a rate Hz,…2026 Set 1 Q16The response of a discrete time system obeys the following relation:…2026 Set 1 Q37The continuous time signal is real, periodic with period and satisfies the Dirichlet…2026 Set 1 Q43Consider a real signal , , such that for , …