Official PYQ · 2016Set 3 · Q30Continuous-time SignalsMCQ2 marks

GATE EC 2016 Set 3 Q30 — Continuous-time Signals

A signal $2 \cos(\frac{2\pi}{3}t)-\cos(\pi t)$ is the input to an LTI system with the transfer function

$H(s)=e^s+e^{-s}.$

If $C_k$ denotes the $k^{th}$ coefficient in the exponential Fourier series of the output signal, then $C_3$ is equal to

View answer

Answer: B

Worked explanation not available yet.

Free practice · Your answers on this page are not saved.

Published 10 Oct 2026

Report a correction

GATE EC · 2026Continuous-time Signals
Two analog signals $x_{1}(t)$ and $x_{2}(t)(t$ in second $)$ , are sampled at a rate $F_{s}=40 \mathrm{~Hz}$ , where $x_{1}(t)=\cos (20 \pi t), t \geq 0, \text{ and } x_{2}(t)=\cos (100 \pi t), t \geq 0$ The first ten samples (starting from $t=0$ ) are considered for the analysis. Which of the following statements is TRUE?
MCQ · 1 mark
GATE EC · 2026Continuous-time Signals
The continuous time signal $x(t)$ is real, periodic with period $T$ and satisfies the Dirichlet conditions. The Fourier series representation of $x(t)=\sum_{-\infty}^{\infty} a_{n} e^{j\left(\frac{2 \pi n t}{T}\right)}$ and $x(t)$ satisfies the following: $x\left(t-\frac{T}{2}\right)=-x(t)$ . For any integer $m$ , which of the following options is …
MCQ · 2 marks
GATE EC · 2026Continuous-time Signals
Consider a real signal $x(t),-\infty < t < \infty$ , such that $x(t) = 0\quad\text{for}\quad t <0, x(t) =2 \quad\text{for} \quad0 \leq t < 1\quad \text{and}\quad x(t) = 0\quad \text{for} \quad t \geq 1$ . Let $E[x(t)]=\int_{-\infty}^{\infty}[x(t)]^{2} d t$ . Which of the following options correctly represents the ratio, …
MCQ · 2 marks
GATE EC · 2026Continuous-time Signals
Consider a real baseband signal $x(t)=e^{-2 t}$ , for $t$ (in seconds) $\geq 0$ . If $99 \%$ of energy of $x(t)$ lies within $B \mathrm{~Hz}$ , then which of the following options is TRUE for the value of ${B}?$
MCQ · 2 marks
GATE EC · 2026Continuous-time Signals
Let $x_{1}(t)=\cos (2 \pi n t)$ and $x_{2}(t)=2 \sin (4 \pi n t)$ represent two sinusoids for a positive integer $n$ and $-\infty < t < \infty$ . Which of the following statements about $x_{1}(t)$ and $x_{2}(t)$ is/are valid?
MSQ · 2 marks
GATE EC · 2025Continuous-time Signals
Consider a continuous-time, real-valued signal $f(t)$ whose Fourier transform $F(\omega)=\int_{-\infty}^{\infty} f(t) \exp (-j \: \omega t) d t$ exists. Which one of the following statements is always TRUE?
MCQ · 1 mark

Browse this topic

More Continuous-time Signals questions

GATE EC 2016 Set 3 Q30 — Continuous-time Signals

Related questions