Signal Processing - Study Mode

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[#216] A system is described by the following differential equation, where u(t) is the input to the system and y(t) is the output of the system. y(t) + 5y(t) = u(t) When y(0) = 1 and u(t) is a unit step function, y(t) is

(A) 0.2 + 0.8e -5t

(B) 0.2 - 0.2e -5t

(C) 0.8 + 0.2e -5t

(D) 0.8 - 0.8e -5t

Correct Answer

(A) 0.2 + 0.8e -5t

[#217] Consider the following statements for continuous-time linear time invariant (LTI) systems. 1. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane. 2. There is no causal and BIBO stable system with a pole in the right half of the complex plane. Which one among the following is correct?

(A) Both 1 and 2 are true

(B) Both 1 and 2 are not true

(C) Only 1 is true

(D) Only 2 is true

Correct Answer

(D) Only 2 is true

[#218] The Fourier transform F{e -t u(t)} is equal to $${1 over {1 + j2pi f}}.$$ xa0 Therefore, $$Fleft{ {{1 over {1 + j2pi f}}}
ight}$$ xa0 is

(A) e f u(f)

(B) e -f u(f)

(C) e f u(-f)

(D) e -f u(-f)

Correct Answer

(C) e f u(-f)

[#219] A system with transfer function H(z) has impulse response h(n) defined as h(2) = 1, h(3) = -1 and h(k) = 0 otherwise. Consider the following statements. S 1 : H(z) is a low-pass filter. S 2 : H(z) is an FIR filter. Which of the following is correct?

(A) Only S 2 is true

(B) Both S 1 and S 2 are false

(C) Both S 1 and S 2 are true, and S 2 is a reason for S 1

(D) Both S 1 and S 2 are true, but S 2 is not a reason for S 1

Correct Answer

(A) Only S 2 is true

[#220] The Laplace transform of the causal periodic square wave of period T shown in the figure below is It

(A) $$Fleft( s ight) = frac{1}{{1 + {e^{ - frac{{sT}}{2}}}}}$$

(B) $$Fleft( s ight) = frac{1}{{sleft( {1 + {e^{ - frac{{sT}}{2}}}} ight)}}$$

(C) $$Fleft( s ight) = frac{1}{{sleft( {1 - {e^{ - frac{{sT}}{2}}}} ight)}}$$

(D) $$Fleft( s ight) = frac{1}{{1 - {e^{ - sT}}}}$$

Correct Answer

(B) $$Fleft( s ight) = frac{1}{{sleft( {1 + {e^{ - frac{{sT}}{2}}}} ight)}}$$