1
GATE ECE 2018
+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
2
GATE ECE 2018
+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
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
3
GATE ECE 2017 Set 1
+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. The ratio of the power in the 7th harmonic to the power in the 5th harmonic for this waveform is closest in value to _______.