Signal Processing - Study Mode

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[#406] Consider a system whose input r and output y are related by the equation $$yleft( t
ight) = intlimits_{ - infty }^infty {xleft( {t - au }
ight)} hleft( {2 au }
ight)d au $$ Where h(t) is shown in the graph Which of the following four properties are possessed by the system? BIBO: Bounded input gives a bounded output Causal: The system is causal. LP : The system is low pass. LTI: The system is linear and time-invariant.

(A) Causal, LP

(B) BIBO, LTI

(C) BIBO, Causal, LTI

(D) LP, LTI

Correct Answer

(B) BIBO, LTI

[#407] A Hilbert transformer is a

(A) Non-linear system

(B) Non-causal system

(C) Time-varying system

(D) Low-pass system

Correct Answer

(A) Non-linear system

[#408] The trigonometric Fourier series of a periodic time function can have only

(A) Cosine terms

(B) Sine terms

(C) Cosine and sine terms

(D) Dc and cosine terms

Correct Answer

(D) Dc and cosine terms

[#409] The Fourier transform of a signal h(t) is $$Hleft( {jomega }
ight) = {{left( {2cos omega }
ight)left( {sin omega }
ight)} over omega }$$ The value of h(0) is

(A) $${1 over 4}$$

(B) $${1 over 2}$$

(C) 1

(D) 2

Correct Answer

(C) 1

[#410] The output y(t) of a linear time invariant system is related to its input x(t) by the following equation: y(t) = 0.5x(t - t d + T) + x(t - t d ) + 0.5x(t - t d -T). The filter transfer function H(ω) of such a system is given by

(A) $$left( {1 + cos ,omega T} ight){e^{ - jomega {t_d}}}$$

(B) $$left( {1 + 0.5cos omega T} ight){e^{ - jomega {t_d}}}$$

(C) $$left( {1 - cos omega T} ight){e^{ - jomega {t_d}}}$$

(D) $$left( {1 - 0.5cos omega T} ight){e^{ - jomega {t_d}}}$$

Correct Answer

(A) $$left( {1 + cos ,omega T} ight){e^{ - jomega {t_d}}}$$