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<br><img src="/images/question-image/electronics-and-communications-engineering/signal-processing/1681541943-let-xt-and-yt-with-fourier-transforms-xf.jpg" title="Signal Processing mcq question image" alt="Signal Processing mcq question image">

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)

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
Signal Processing mcq question image

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 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

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

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 Fourier transform of a signal x(t), denoted by X(jω), is shown in the figure. Let y(t) = x(t) + ejtx(t). The value of Fourier transforms of y(t) evaluated at the angular frequency ω = 0.5 rad/s is

A

0.5

B

1

C

1.5

D

2.5

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

A rectangular pulse train s(t) as shown in the figure is convolved with the signal cos²(4π × 10³t). The convolved signal will be a
Signal Processing mcq question image

A

DC

B

12 kHz sinusoid

C

8 kHz sinusoid

D

14 kHz sinusoid

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 pole-zero pattern of a certain filter is shown in figure. The filter must be of the following type
Signal Processing mcq question image

A

Low-pass

B

High-pass

C

All-pass

D

Band-pass

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

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