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) $

 View Ans

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.

$250 \text{ sinc}(10f)e^{-j6\pi f}$

 View Ans

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) $

 View Ans

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.

\((10e^{-2t}\cos4t-10e^{-2t}\sin 4t)u(t)\)

 View Ans

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

 View Ans


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