91. Which of the following is a non-recursive system?
92. The amplitude spectrum of a Gaussian pulse is
93. Two random processes X and Y are such that RXY(t1, t2) = 0 for all t1 and t2 and further one of them has zero mean. The processes are
94. The Z - transform of a-nu(-n - 1) is,
95. What are poles and zeros of a system having following transfer function?
$$H\left( z \right) = \frac{{\left( {1 - {z^{ - 2}}} \right)}}{{\left( {1 + 1.3{z^{ - 1}} + 0.36{z^{ - 2}}} \right)}}$$
$$H\left( z \right) = \frac{{\left( {1 - {z^{ - 2}}} \right)}}{{\left( {1 + 1.3{z^{ - 1}} + 0.36{z^{ - 2}}} \right)}}$$
96. The auto-correlation function Rx(τ) of a random process has the property that Rx(0) is equal to
97. Match List-I with List-II and select the correct answer using the options given below:
List-I [Function in time domain f(t)]
List-II [Property]
a. $$\sin {\omega _0}tu\left( {t - {t_0}} \right)$$
1. $$\frac{{{\omega _0}}}{{{s^2} + \omega _0^2}}$$
b. $$\sin {\omega _0}\left( {t - {t_0}} \right)u\left( {t - {t_0}} \right)$$
2. $$\left\{ {\frac{{{\omega _0}}}{{{s^2} + \omega _0^2}}} \right\}{e^{ - {t_0}s}}$$
c. $$\sin {\omega _0}\left( {t - {t_0}} \right)u\left( t \right)$$
3. $$\frac{{{e^{ - {t_0}s}}}}{{\sqrt {{s^2} + \omega _0^2} }}\sin \left( {{\omega _0}{t_0} + {{\tan }^{ - 1}}\frac{{{\omega _0}}}{s}} \right)$$
d. $$\sin {\omega _0}tu\left( t \right)$$
4. $$ - \frac{1}{{\sqrt {{s^2} + \omega _0^2} }}\sin \left( {{\omega _0}{t_0} - {{\tan }^{ - 1}}\frac{{{\omega _0}}}{s}} \right)$$
| List-I [Function in time domain f(t)] | List-II [Property] |
| a. $$\sin {\omega _0}tu\left( {t - {t_0}} \right)$$ | 1. $$\frac{{{\omega _0}}}{{{s^2} + \omega _0^2}}$$ |
| b. $$\sin {\omega _0}\left( {t - {t_0}} \right)u\left( {t - {t_0}} \right)$$ | 2. $$\left\{ {\frac{{{\omega _0}}}{{{s^2} + \omega _0^2}}} \right\}{e^{ - {t_0}s}}$$ |
| c. $$\sin {\omega _0}\left( {t - {t_0}} \right)u\left( t \right)$$ | 3. $$\frac{{{e^{ - {t_0}s}}}}{{\sqrt {{s^2} + \omega _0^2} }}\sin \left( {{\omega _0}{t_0} + {{\tan }^{ - 1}}\frac{{{\omega _0}}}{s}} \right)$$ |
| d. $$\sin {\omega _0}tu\left( t \right)$$ | 4. $$ - \frac{1}{{\sqrt {{s^2} + \omega _0^2} }}\sin \left( {{\omega _0}{t_0} - {{\tan }^{ - 1}}\frac{{{\omega _0}}}{s}} \right)$$ |
98. Which one of the following operations is not commutative?
99. The signals x1(t) are band limited to 4π rad/sec and 10π rad/sec respectively. The minimum sampling rate required for sampling the signal x1(2t) + x2$$\left( {\frac{{\text{t}}}{2}} \right)$$ is:
100. A random variable X is defined by the double exponential distribution ρx(X) = ae-b|x| - ∞ < x < ∞
Where a and b are +ve constants. What is the relation between a and b so that ρx(X) is a probability density function?
Where a and b are +ve constants. What is the relation between a and b so that ρx(X) is a probability density function?
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