# Practice Questions on Signals and Systems

 Q1. The inverse transform of the rectangular spectrum is: \begin{align*} X(j\omega)&=\begin{cases} \nonumber       1 &-2L\leq \omega \leq 2L\\       0 &|\omega|>2L     \end{cases} \end{align*}
 A. $\dfrac{1}{\pi }\sin (2Lt)$ B. $\dfrac{1}{2\pi t}\sin (2Lt)$ C. $\dfrac{1}{t}\sin (4Lt)$ D. $\dfrac{1}{\pi t}\sin (2Lt)$

 Q2. CTFT of $x(t)=5\text{ rect}\left[\dfrac{t-3}{20}\right]$ is:
 A. $100 \text{ sinc}(20f)e^{-j6\pi f}$ B. $25 \text{ sinc}(10f)e^{-j3\pi f}$ C. $25 \text{ sinc}(10f)e^{-j8\pi f}$ D. $250 \text{ sinc}(10f)e^{-j6\pi f}$

 Q3. The frequency response of a linear, time-invariant system is given by  $H(f)=\dfrac{3}{1+j6\pi f}$  The step response of the system is,
 A. $10(1-e^{-3t})u(t)$ B. $3(1-e^{-t/3})u(t)$ C. $(1-e^{-t/3})u(t)$ D. $\dfrac{1}{2}(1-e^{-3t}) u(t)$

 Q4. The inverse transform is $X(s)=\dfrac{10(s+1)}{s^2+4s+8}$
 A. $(10e^{-2t}\cos4t-5e^{-2t}\sin 4t)u(t)$ B. $(5e^{2t}\cos4t-5e^{-2t}\sin 4t)u(t)$ C. $(10e^{-2t}\cos4t-4e^{-2t}\sin 5t)u(t)$ D. $(10e^{-2t}\cos4t-10e^{-2t}\sin 4t)u(t)$

 Q5. The following system is $\dfrac{dy}{dt}+5ty(t)=2x(t)$
 A. time-varying, memoryless, non-linear B. casual, linear, memoryless C. time-invariant, memoryless, non-linear D. linear, casual, time-varying, has memory

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