Signals and Systems
Representation of Continuous Time Signal Fourier Series
Marks 1Marks 2
Fourier Transform
Marks 1Marks 2Marks 5
Continuous Time Signal Laplace Transform
Marks 1Marks 2Marks 5
Discrete Time Signal Fourier Series Fourier Transform
Marks 1Marks 2
Discrete Fourier Transform and Fast Fourier Transform
Marks 1Marks 2
Discrete Time Signal Z Transform
Marks 1Marks 2
Continuous Time Linear Invariant System
Marks 1Marks 2Marks 5
Discrete Time Linear Time Invariant Systems
Marks 1Marks 2Marks 4Marks 5
Transmission of Signal Through Continuous Time LTI Systems
Marks 1Marks 2Marks 5
Transmission of Signal Through Discrete Time Lti Systems
Marks 1Marks 2Marks 4
Miscellaneous
Marks 1Marks 2
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

A
$$(i)\to(a),(ii)\to(b),(iii)\to(c),(iv)\to(d)$$
B
$$(i)\to(a),(ii)\to(c),(iii)\to(b),(iv)\to(d)$$
C
$$(i)\to(d),(ii)\to(b),(iii)\to(c),(iv)\to(a)$$
D
$$(i)\to(a),(ii)\to(c),(iii)\to(d),(iv)\to(b)$$
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
A
256
B
64
C
16
D
4
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:
A
GATE ECE 2018 Signals and Systems - Representation of Continuous Time Signal Fourier Series Question 5 English Option 1
B
$$y\left( t \right) = \int\limits_0^t {{e^{\alpha \left( {t - \tau } \right)}}} \beta u\left( \tau \right)d\tau $$
C
y = au + b, b $$ \ne $$ 0
D
y = au
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
A
$$a_n$$ are zero for all n and $$b_n$$ are zero for n even
B
$$a_n$$ are zero for all n and $$b_n$$ are zero for n odd
C
$$a_n$$ are zero for n even and $$b_n$$ are zero for n odd
D
$$a_n$$ are zero for n odd and $$b_n$$ are zero for n even
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