21. What will be the Laplace transform for f(t) = e-btu(t)?
22. The even and odd components of the signal x(t) = e-2t cos t are respectively,
23. A band-limited lowpass signal is sampled at twice its Nyquist rate with fs = 2000 sps. The signal is band-limited to
24. For a given transmitted pulse p(t), 0 ≤ t ≤ T, the impulse response of a filter matched to the received signal is
25. If \[x\left( n \right) = \left\{ \begin{array}{l}
{\left( {\frac{1}{2}} \right)^n};\,0 \le n \le \left( {N - 1} \right)\\
0;\,{\rm{otherwise}}
\end{array} \right.\] then x(z) is equal to
26. Consider a single input single output discrete-time system with x[n] as input and y[n] as output, where the two are related as
\[y\left[ n \right] = \left\{ {\begin{array}{*{20}{c}}
{n\left| {x\left[ n \right]} \right|,}&{{\text{for }}0 \leqslant n \leqslant 10} \\
{x\left[ n \right] - x\left[ {n - 1} \right],}&{{\text{otherwise}}}
\end{array}} \right.\]
Which one of the following statements is true about the system?
\[y\left[ n \right] = \left\{ {\begin{array}{*{20}{c}} {n\left| {x\left[ n \right]} \right|,}&{{\text{for }}0 \leqslant n \leqslant 10} \\ {x\left[ n \right] - x\left[ {n - 1} \right],}&{{\text{otherwise}}} \end{array}} \right.\]
Which one of the following statements is true about the system?
27. The covariance function, Cx(τ), of a stationary stochastic process, x(t), is said to be positive definite. This means that
28. A composed signal is given by x(t) = cos(ωt) + sin(ωt) + sin2(ωt) + cos(ωt) + sin2(ωt). The odd component is
29. The signal x(n) shown in the above figure is a

30. Which of the following is NOT one of the representations of discrete-time signals?
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