How do we represent a pairing of a periodic signal with its fourier series coefficients in case of continuous time fourier series?

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

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

One period (0, T) each of two periodic waveforms W₁ and W₂ are shown in the figure. The magnitudes of the nth Fourier series coefficients of W₁ and W₂, for n ≥ 1, n is odd, are respectively proportional to

A

|n|-3 and |n|-2

B

|n|-1 and |n|-3

C

|n|-1 and |n|-2

D

|n|-4 and |n|-2

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)

Which of the following statements is/are false regarding modern periodic table?
1. Elements in the modern periodic table are arranged in decreasing order of their atomic numbers.
2. Elements in the modern periodic table are arranged in increasing order of their atomic masses.
3. In the modern periodic table, isotopes are placed in adjacent groups.
4. Elements in modern periodic table are arranged in increasing order of their atomic numbers.

A

only 1

B

only 4

C

1, 2 and 4

D

1, 2 and 3

If the Fourier series coefficients of a signal are periodic then the signal must be

A

Continuous-time, periodic

B

Discrete-time, periodic

C

Continuous-time, non-periodic

D

Discrete-time, non-periodic

What is the outcome of a periodic convolution of signals in case of continuous time fourier series?

A

Division in frequency domain

B

Multiplication in frequency domain

C

Convolution is easier

D

Addition of signals in frequency domain

Which two of the following are true regarding the distance-vector and link-state routing protocols?
1. Link state sends its complete routing table out all active interfaces on periodic time intervals.
2. Distance vector sends its complete routing table out all active interfaces on periodic time intervals.
3. Link state sends updates containing the state of its own links to all routers in the internetwork.
4. Distance vector sends updates containing the state of its own links to all routers in the internetwork.

A

1 only

B

3 only

C

2 and 3 only

D

None of the above

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 time system which operates with a continuous time signal and produces a continuous time output signal is _________

A

CTF system

B

DTF System

C

Time invariant System

D

Time variant System