Recent questions in Continuous-time Signals

A pulse having a rise time of $40 \mathrm{n \; sec}$ is displayed on a $\text{CRO}$ of $12 \; \mathrm{MHz}$ bandwidth. The rise time of the pulse as observed on the $\tex...

The $RC$ circuit shown in the figure isa low-pass filtera high-pass filtera band-pass filtera band-reject filter

Three functions $f_{1}(t), f_{2}(t)$ and $f_{3}(t)$, which are zero outside the interval $[0, T]$, are shown in the figure. Which of the following statements is correct?$...

The $\text{3-dB}$ bandwidth of the low-pass signal $e^{-t} u(t)$, where $u(t)$ is the unit step function, is given by$\frac{1}{2 \pi} \mathrm{Hz}$$\frac{1}{2 \pi} \sqrt{\...

The frequency response of a linear, time-invariant system is given by $H(f)=\dfrac{5}{1+j 10 \pi f}$. The step response of the system is$5\left(1-e^{-5 t}\right) u(t)$$5\...

The input and output of a continuous time system are respectively denoted by $x(t)$ and $y(t)$. Which of the following descriptions corresponds to a causal system?$y(t)=x...

The impulse response $h(t)$ of a linear time-invariant continuous time system is described by $h(t)=\exp (\alpha t) u(t)+\exp (\beta t) u(-t)$, where $u(t)$ denotes the u...

The pole-zero plot given below corresponds to aLow pass filterHigh pass filterBand pass filterNotch filter

The signal $x(t)$ is described by$x(t)=\left\{\begin{array}{ll}1 & \text { for }-1 \leq t \leq+1 \\0 & \text { otherwise }\end{array}\right.$Two of the angular frequencie...

Let $x(t)$ be the input and $y(t)$ be the output of a continuous time system. Match the system properties $\mathrm{P} 1, \mathrm{P} 2$ and $\mathrm{P} 3$ with system rela...

The impulse response $h(t)$ of a linear time-invariant continuous time system is given by $h(t)=\exp (-2 t) u(t)$, where $u(t)$ denotes the unit step function.The frequen...

The impulse response $h(t)$ of a linear time-invariant continuous time system is given by $h(t)=\exp (-2 t) u(t)$, where $u(t)$ denotes the unit step function.The output ...

Fourier series of the periodic function (period $2 \pi$ ) defined by$f(x)=\left\{\begin{array}{ll}0 & -\pi < x<0 \\ x & 0<x<\pi\end{array}\right.$ is$\frac{\pi}{4}+\sum_1...

The Laplace transform of the periodic function $f(t)$ described by the curve below, i.e.$f(t)=\left\{\begin{array}{c}\sin t \text { if }(2 n-1) \pi \leq t \leq 2 n \pi(n=...

The Fourier series of a real periodic function has onlycosine terms if it is evensine terms if it is evencosine terms if it is oddsine terms if it is oddWhich of the abov...

A function is given by $f(t)=\sin ^{2} t+\cos 2 t$. Which of the following is true?$f$ has frequency components at 0 and $1 / 2 \pi \; \mathrm{Hz}$$f$ has frequency compo...

Given that $F(s)$ is the one-sided Laplace transform of $f(t),$ the Laplace transform of $\displaystyle{}\int_{0}^{t} f(\tau) d \tau$ is$s F(s)-f(0)$$\dfrac{1}{s} F(s)$$\...