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One period (0, T) each of two periodic waveforms W<sub>1</sub> and W<sub>2</sub> are shown in the figure. The magnitudes of the nth Fourier series coefficients of W<sub>1</sub> and W<sub>2</sub>, for n ≥ 1, n is odd, are respectively proportional to<br><img src="/images/question-image/electronics-and-communications-engineering/signal-processing/1681542331-one-period-0-t-each-of-two-periodic.jpg" title="Signal Processing mcq question image" alt="Signal Processing mcq question image">
A
|n|<sup>-3</sup> and |n|<sup>-2</sup>
B
|n|<sup>-1</sup> and |n|<sup>-3</sup>
C
|n|<sup>-1</sup> and |n|<sup>-2</sup>
D
|n|<sup>-4</sup> and |n|<sup>-2</sup>
Correct Answer:
|n|<sup>-1</sup> and |n|<sup>-2</sup>
Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {a
k
} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):
1. The complex Fourier series coefficients of x(3t) are {a
k
} where k is integer valued.
2. The complex Fourier series coefficients of x(3f) are {3a
k
} where k is integer valued.
3. The fundamental angular frequency of x(3t) is 6π rad/s.
For the three statements above, which one of the following is correct?
A
Only 2 and 3 are true
B
Only 1 and 3 are true
C
Only 3 is true
D
Only 1 is true
The magnitude and phase of the complex Fourier series coefficient a
k
of a periodic signal x(t) are shown in the figure. Choose the correct statement from the four choices given. Notation: C is the set of complex number, R is the set of purely real numbers, and P is the set of purely imaginary numbers.
A
$$x\left( t \right) \in R$$
B
$$x\left( t \right) \in P$$
C
$$x\left( t \right) \in \left( {C - R} \right)$$
D
The information given is not sufficient to draw any conclusion about x(t)
Let x(t) be a periodic function with period T = 10. The Fourier series coefficients for this series are denoted by $${a_k}$$ , 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 b
k
be the Fourier series coefficients when period is taken as T'. If $$\sum\limits_{k = - \infty }^\infty {\left| {{a_k}} \right|} = 16,$$ then $$\sum\limits_{k = - \infty }^\infty {\left| {{b_k}} \right|} $$ is equal to
A
256
B
64
C
16
D
4
Let x(t) and y(t) (with Fourier transforms X(f) and Y(f) respectively) be related as shown in the figure. Then Y(f) is
A
$$ - \frac{1}{2}X\left( {\frac{f}{2}} \right){e^{ - j2\pi f}}$$
B
$$ - \frac{1}{2}X\left( {\frac{f}{2}} \right){e^{j2\pi f}}$$
C
$$ - X\left( {\frac{f}{2}} \right){e^{j2\pi f}}$$
D
$$ - X\left( {\frac{f}{2}} \right){e^{ - j2\pi f}}$$
The Laplace transform of the causal periodic square wave of period T shown in the figure below is It
A
$$F\left( s \right) = \frac{1}{{1 + {e^{ - \frac{{sT}}{2}}}}}$$
B
$$F\left( s \right) = \frac{1}{{s\left( {1 + {e^{ - \frac{{sT}}{2}}}} \right)}}$$
C
$$F\left( s \right) = \frac{1}{{s\left( {1 - {e^{ - \frac{{sT}}{2}}}} \right)}}$$
D
$$F\left( s \right) = \frac{1}{{1 - {e^{ - sT}}}}$$
The function x(t) is shown in the figure. Even and odd parts of a unit-step function u(t) are respectively,
A
$$\frac{1}{2},\frac{1}{2}x\left( t \right)$$
B
$$ - \frac{1}{2},\frac{1}{2}x\left( t \right)$$
C
$$\frac{1}{2}, - \frac{1}{2}x\left( t \right)$$
D
$$ - \frac{1}{2}, - \frac{1}{2}x\left( t \right)$$
Select a suitable figure from the Answer Set which will substitute the question mark so that a series is formed by the figures A, B, C and D taken in order. The number of the selected figure is the answer.
A
1
B
2
C
3
D
4
E
5
Select a suitable figure from the Answer Set which will substitute the question mark so that a series is formed by the figures A, B, C and D taken in order. The number of the selected figure is the answer.
A
1
B
2
C
3
D
4
E
5
Select a suitable figure from the Answer Set which will substitute the question mark so that a series is formed by the figures A, B, C and D taken in order. The number of the selected figure is the answer.
A
1
B
2
C
3
D
4
E
5
Select a suitable figure from the Answer Set which will substitute the question mark so that a series is formed by the figures A, B, C and D taken in order. The number of the selected figure is the answer.
A
1
B
2
C
3
D
4
E
5
