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 𝑎

$$x\left( t \right) = \sum\limits_{k = - \infty }^\infty {{a_k}} {e^{jk{{2\pi } \over T}t}}$$

The same function 𝑥(𝑡) can also be considered as a periodic function with period T' = 40. Let b

_{𝑘}, 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 b

_{k}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 to2

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 7

^{th}harmonic to the power in the 5^{th}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

Signals and Systems

Representation of Continuous Time Signal Fourier Series Fourier Transform Continuous Time Signal Laplace Transform Discrete Time Signal Fourier Series Fourier Transform Discrete Fourier Transform and Fast Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Discrete Time Linear Time Invariant Systems Transmission of Signal Through Continuous Time LTI Systems Sampling Transmission of Signal Through Discrete Time Lti Systems Miscellaneous

Network Theory

Control Systems

Digital Circuits

General Aptitude

Electronic Devices and VLSI

Analog Circuits

Engineering Mathematics

Microprocessors

Communications

Electromagnetics