1
GATE ECE 2009
MCQ (Single Correct Answer)
+1
-0.3
The Fourier series of a real periodic function has only

P. Cosine terms if it is even

Q. Sine terms if it is even

R. Cosine terms if it odd

S. Sine terms if it is odd

Which of the above statement are correct?
A
P and S
B
P and R
C
Q and S
D
Q and R
2
GATE ECE 2009
MCQ (Single Correct Answer)
+1
-0.3
A function is given by f(t) = sin2t +cos2t . Which of the following is true?
A
f has frequency components at 0 and $$1/2\mathrm\pi$$ Hz
B
f has frequency components at 0 and $$1/\mathrm\pi$$ Hz
C
f has frequency components at $$1/2\mathrm\pi$$ and $$1/\mathrm\pi$$ Hz
D
f has frequency components at 0, $$1/2\mathrm\pi$$ and $$1/\mathrm\pi$$ Hz
3
GATE ECE 2009
MCQ (Single Correct Answer)
+2
-0.6
Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)\,d\tau } $$ is
A
$$sF\left( s \right) - f\left( 0 \right)$$
B
$$\,{1 \over s}F\left( s \right)\,$$
C
$$\int\limits_0^s {F\left( \tau \right)d\tau } $$
D
$${1 \over s}\left[ {F\left( s \right) - f\left( 0 \right)} \right]$$
4
GATE ECE 2009
MCQ (Single Correct Answer)
+2
-0.6
The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence $$\left\{ {1,\,0,\,2,\,3} \right\}$$ is
A
$$\left[ {0,\, - 2 + 2j,\,2,\, - 2 - 2j} \right]$$
B
$$\left[ {2,\,2 + 2j,\,6,\,2\, - 2j} \right]$$
C
$$\left[ {6,\,1 - 3j,\,2,\,1 + 3j} \right]$$
D
$$\left[ {6,\, - 1 + 3j,\,0,\, - 1\, - 3j} \right]$$
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