1
GATE EE 2017 Set 1
+1
-0.3
Let $$z\left(t\right)=x\left(t\right)\ast y\left(t\right)$$, where "*" denotes convolution. Let C be a positive real-valued constant. Choose the correct expression for z(ct).
A
$$c.x\left(ct\right)\ast y\left(ct\right)$$
B
$$x\left(ct\right)\ast y\left(ct\right)$$
C
$$c.x\left(t\right)\ast y\left(ct\right)$$
D
$$c.x\left(ct\right)\ast y\left(t\right)$$
2
GATE EE 2016 Set 1
+1
-0.3
The value of $$\int_{-\infty}^{+\infty}e^{-t}\partial\left(2t-2\right)dt$$. where $$\partial\left(t\right)$$ is the Dirac delta function, is
A
$$\frac1{2e}$$
B
$$\frac2e$$
C
$$\frac1{e^2}$$
D
$$\frac1{2e^2}$$
3
GATE EE 2015 Set 1
Numerical
+1
-0
A moving average function is given by $$y\left(t\right)=\frac1T\int_{t-T}^tu\left(\tau\right)d\tau$$. If the input u is a sinusoidal signal of frequency $$\frac1{2T}Hz$$, then in steady state, the output y will lag u (in degree) by ________.
4
GATE EE 2013
+1
-0.3
For a periodic signal the $$v\left(t\right)=30\sin100t\;+\;10\cos300t\;+\;6\sin\left(500t\;+\;\frac{\mathrm\pi}4\right)$$ fundamental frequency in radians/s is
A
100
B
300
C
500
D
1500
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Medical
NEET