1
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
2
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:
3
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
4
GATE ECE 2014 Set 2
Numerical
+1
-0
Consider the periodic square wave in the figure shown.
The ratio of the power in the 7th harmonic to the power in the 5th harmonic for this waveform is closest in value to _______.
Your input ____
Questions Asked from Representation of Continuous Time Signal Fourier Series (Marks 1)
Number in Brackets after Paper Indicates No. of Questions
GATE ECE Subjects
Network Theory
Control Systems
Electronic Devices and VLSI
Analog Circuits
Digital Circuits
Microprocessors
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
Communications
Electromagnetics
General Aptitude