1
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 2 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
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 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
4
GATE ECE 2014 Set 2
Numerical
+1
-0
Consider the periodic square wave in the figure shown. GATE ECE 2014 Set 2 Signals and Systems - Representation of Continuous Time Signal Fourier Series Question 8 English 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 ____
GATE ECE Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
CBSE
Class 12