1
GATE ECE 2023
MCQ (Single Correct Answer)
+1
-0.33
In the table shown below, match the signal type with its spectral characteristics.
Signal type | Spectral characteristics | ||
---|---|---|---|
(i) | Continuous, aperiodic | (a) | Continuous, aperiodic |
(ii) | Continuous, periodic | (b) | Continuous, periodic |
(iii) | Discrete, aperiodic | (c) | Discrete, aperiodic |
(iv) | Discrete, periodic | (d) | Discrete, periodic |
2
GATE ECE 2018
MCQ (Single Correct Answer)
+1
-0.33
Let 𝑥(𝑡) be a periodic function with period 𝑇 = 10. The Fourier series coefficients for this
series are denoted by 𝑎𝑘, that is
$$x\left( t \right) = \sum\limits_{k = - \infty }^\infty {{a_k}} {e^{jk{{2\pi } \over T}t}}$$
The same function 𝑥(𝑡) can also be considered as a periodic function with period T' = 40. Let bk be the Fourier series coefficients when period is taken as T'. If $$\sum\limits_{k = - \infty }^\infty {\left| {{a_k}} \right|} = 16$$, then $$\sum\limits_{k = - \infty }^\infty {\left| {{b_k}} \right|} = 16$$ is equal to
$$x\left( t \right) = \sum\limits_{k = - \infty }^\infty {{a_k}} {e^{jk{{2\pi } \over T}t}}$$
The same function 𝑥(𝑡) can also be considered as a periodic function with period T' = 40. Let bk be the Fourier series coefficients when period is taken as T'. If $$\sum\limits_{k = - \infty }^\infty {\left| {{a_k}} \right|} = 16$$, then $$\sum\limits_{k = - \infty }^\infty {\left| {{b_k}} \right|} = 16$$ is equal to
3
GATE ECE 2018
MCQ (Single Correct Answer)
+1
-0.33
Let the input be
u
and the output be
y
of a system, and the other parameters are real
constants. Identify which among the following systems is not a linear system:
4
GATE ECE 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.3
A periodic signal x(t) has a trigonometric Fourier series expansion
$$$x\left(t\right)=a_0\;+\;\sum_{n=1}^\infty\left(a_n\cos\;n\omega_0t\;+\;b_n\sin\;n\omega_0t\right)$$$
If $$x\left(t\right)=-x\left(-t\right)=-x\left(t-\mathrm\pi/{\mathrm\omega}_0\right)$$, we can conclude that
Questions Asked from Representation of Continuous Time Signal Fourier Series (Marks 1)
Number in Brackets after Paper Indicates No. of Questions
GATE ECE Subjects
Signals and Systems
Representation of Continuous Time Signal Fourier Series Discrete Time Signal Fourier Series Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Transmission of Signal Through Continuous Time LTI Systems Discrete Time Linear Time Invariant Systems Sampling Continuous Time Signal Laplace Transform Discrete Fourier Transform and Fast Fourier Transform Transmission of Signal Through Discrete Time Lti Systems Miscellaneous Fourier Transform
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics