1
GATE EE 2014 Set 1
MCQ (Single Correct Answer)
+1
-0.3
For a periodic square wave, which one of the following statements is TRUE?
A
The Fourier series coefficients do not exist
B
The Fourier series coefficients exist but the reconstruction converges at no point
C
The Fourier series coefficients exist and the reconstruction converges at most points.
D
The Fourier series coefficients exist and the reconstruction converges at every point
2
GATE EE 2014 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Let f(t) be a continuous time signal and let F($$\omega$$) be its Fourier Transform defined by $$F\left(\omega\right)=\int_{-\infty}^\infty f\left(t\right)e^{-j\omega t}dt$$. Define g(t) by $$g\left(t\right)=\int_{-\infty}^\infty F\left(u\right)e^{-jut}du$$. What is the relationship between f(t) and g(t)?
A
g(t) would always be proportional to f(t)
B
g(t) would be proportional to f(t) if f(t) is an even function
C
g(t) would be proportional to f(t) only if f(t) is a sinusoidal function
D
g(t) would never be proportional to f(t)
3
GATE EE 2014 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Let $$X\left(z\right)=\frac1{1-z^{-3}}$$ be the Z–transform of a causal signal x[n]. Then, the values of x[2] and x[3] are
A
0 and 0
B
0 and 1
C
1 and 0
D
1 and 1
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