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

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

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.
Signal Processing mcq question image

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) and y(t) (with Fourier transforms X(f) and Y(f) respectively) be related as shown in the figure. Then Y(f) is
Signal Processing mcq question image

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
Signal Processing mcq question image

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,
Signal Processing mcq question image

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

$$ - \frac{1}{2}, - \frac{1}{2}x\left( t \right)$$

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

A

x(t) ↔ Xn

B

x(t) ↔ Xn+1

C

x(t) ↔ X

D

x(n) ↔ Xn

Consider the system shown in the figure below. The transfer function $$\frac{{Y\left( z \right)}}{{X\left( z \right)}}$$ of the system is
Signal Processing mcq question image

A

$$\frac{{1 + a{z^{ - 1}}}}{{1 + b{z^{ - 1}}}}$$

B

$$\frac{{1 + b{z^{ - 1}}}}{{1 + a{z^{ - 1}}}}$$

C

$$\frac{{1 + a{z^{ - 1}}}}{{1 - b{z^{ - 1}}}}$$

D

$$\frac{{1 - b{z^{ - 1}}}}{{1 - a{z^{ - 1}}}}$$

For the discrete-time system shown in the figure, the poles of the system transfer function are located at
Signal Processing mcq question image

A

2, 3

B

$$\frac{1}{2},3$$

C

$$\frac{1}{2},\frac{1}{3}$$

D

$$2,\frac{1}{3}$$

The impulse response and the excitation function of a linear time invariant causal system are shown in figure (a) and (b) respectively. The output of the system at t = 2 sec is equal to
Signal Processing mcq question image

A

0

B

$$\frac{1}{2}$$

C

$$\frac{3}{2}$$

D

1

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

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