91. A first-order low-pass filter of time constant T is excited with different input signals (with zero initial conditions up to t = 0). Match the excitation signals X, V, Z with the corresponding time responses for t ≥ 0:
Match List-I with List-II and select the correct answer:
List-I
List-II
X. Impulse
P. $$1 - {e^{ - {t \over T}}}$$
Y. Unit step
Q. $$t - T\left( {1 - {e^{ - {t \over T}}}} \right)$$
Z. Ramp
R. $${e^{ - {t \over T}}}$$
Match List-I with List-II and select the correct answer:
| List-I | List-II |
| X. Impulse | P. $$1 - {e^{ - {t \over T}}}$$ |
| Y. Unit step | Q. $$t - T\left( {1 - {e^{ - {t \over T}}}} \right)$$ |
| Z. Ramp | R. $${e^{ - {t \over T}}}$$ |
92. The transfer function of a discrete time LTI system is given by
$$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$
Consider the following statements:
S1 : The system is stable and causal for
$$ROC:\left| z \right| > {1 \over 2}$$
S2 : The system is stable but not causal for
$$ROC:\left| z \right| < {1 \over 4}$$
S3 : The system is neither stable nor causal for
$$ROC:{1 \over 4} < \left| z \right| < {1 \over 2}$$
Which one of the following statements is valid?
$$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$
Consider the following statements:
S1 : The system is stable and causal for
$$ROC:\left| z \right| > {1 \over 2}$$
S2 : The system is stable but not causal for
$$ROC:\left| z \right| < {1 \over 4}$$
S3 : The system is neither stable nor causal for
$$ROC:{1 \over 4} < \left| z \right| < {1 \over 2}$$
Which one of the following statements is valid?
93. Two systems with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by
94. The unilateral Laplace transform of f(t) is $${1 \over {{s^2} + s + 1}}.$$ Which one of the following is the unilateral Laplace transform of g(t) = t.f(t)?
95. A system with an input x(t) and output y(t) is described by the relation: y(t) = tx(t). This system is
96. Consider the function f(t) having Laplace transform
$$F\left( s \right) = {{{\omega _0}} \over {{s^2} + \omega _0^2}}{\mathop{\rm Re}\nolimits} \left| s \right| > 0$$
The final value of f(t) would be:
$$F\left( s \right) = {{{\omega _0}} \over {{s^2} + \omega _0^2}}{\mathop{\rm Re}\nolimits} \left| s \right| > 0$$
The final value of f(t) would be:
97. An LTI system with unit sample response
h[n] = 5δ[n] - 7δ[n - 1] + 7δ[n - 3] - 5δ[n - 4] is a
h[n] = 5δ[n] - 7δ[n - 1] + 7δ[n - 3] - 5δ[n - 4] is a
98. Let $$x\left( n \right) = {\left( {\frac{1}{2}} \right)^n}u\left( n \right),y\left( n \right) = {x^2}\left( n \right)$$ and y(ejω) be the Fourier transform of y(n). Then Y(ej0) is
99. Flat top sampling of low pass signals
100. The region of convergence of z-transform of the sequence
$${\left( {{5 \over 6}} \right)^n}u\left( n \right) - {\left( {{6 \over 5}} \right)^n}u\left( { - n - 1} \right)$$ must be
$${\left( {{5 \over 6}} \right)^n}u\left( n \right) - {\left( {{6 \over 5}} \right)^n}u\left( { - n - 1} \right)$$ must be
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