Signals and Systems
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
GATE ECE Subjects
Signals and Systems
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics