Recent questions tagged gate2004-ec

A rectangular pulse train $s(t)$ as shown in the figure is convolved with the signal $\cos ^{2}\left(4 p \times 10^{3} t\right)$. The convolved signal will be a$\text{DC}...

Consider the sequence $x[n]=\left[\begin{array}{lll}-4- \uparrow{j} 5 & 1+j 2 & 4\end{array}\right]$The conjugate anti-symmetric part of the sequence is$[-4-j 2.5 \quad j...

A causal $\text{LTI}$ system is described by the difference equation\[2 y[n]=\alpha y[n-2]-2 x[n]+\beta x[n-1]\]The system is stable only if$|\alpha|=2, \quad|\beta|<2$$|...

A causal system having the transfer function $\mathrm{H}(s)=\frac{1}{s+2}$ is excited with $10 u(t)$. The time at which the output reaches $99 \%$ of its steady state val...

The impulse response $h|n|$ of a linear time invariant system is given as\[h[n]=\left\{\begin{array}{cc}-2 \sqrt{2} & n=1,-1 \\4 \sqrt{2} & n=2,-2 \\0, & \text { otherwis...

Let $x(t)$ and $y(t)$ (with Fourier transforms $X(f)$ and $Y(f)$ respectively) be related as shown in the given figure.Then $Y(f)$ is$-\frac{1}{2} X(f / 2) e^{-j 2 \pi f}...

A system has poles at $0.01 \mathrm{~Hz}, 1 \mathrm{~Hz}$ and $80 \mathrm{~Hz}$; zeros at $5 \mathrm{~Hz}, 100 \mathrm{~Hz}$ and $200 \mathrm{~Hz}$. The approximate phase...

Consider the signal flow graph shown in the figure below. The gain $\frac{x_{5}}{x_{1}}$ is$\frac{1-\left(b e+c f+d g\right)}{a b c}$$\frac{b e d g}{1-(b e+c f+d g)}$$\fr...

If $A=\left[\begin{array}{cc}-2 & 2 \\ 1 & -3\end{array}\right]$, then $\sin A t$ is$\frac{1}{3}\left[\begin{array}{cc}\sin (-4 t)+2 \sin (-t) & -2 \sin (-4 t)+2 \sin (-t...

The open-loop transfer function of a unity feedback system is $G(s)=\frac{K}{s\left(s^{2}+s+2\right)(s+3)}$The range of $\mathrm{K}$ for which the system is stable is$\fr...

For the polynomial $P(s)=s^{5}+s^{4}+2 s^{3}+2 s^{2}+3 s+15$, the number of roots which lie in the right half of the s-plane is$4$$2$$3$$1$

The state variable equations of a system are:$\begin{array}{l} 1. \; x_{1}=-3 x_{1}-x_{2}+u \\ 2. \; x_{2}=2 x_{1} \\ \quad y=x_{1}+u \end{array}$The system iscontrollabl...

Given $A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$, the state transition matrix $e^{A t}$ is given by$\left[\begin{array}{cc}0 & e^{-t} \\ e^{-t} & 0\end{a...

Consider the signal $x(t)$ shown in the figure. Let $h(t)$ denote the impulse response of the filter matched to $x(t)$, with $h(t)$ being non-zero only in the interval 0 ...

Consider a binary digital communication system with equally likely $0$'s and $1$'s. When binary 0 is transmitted the voltage at the detector input can lie between the lev...

A random variable $\mathrm{X}$ with uniform density in the interval $0$ to $1$ is quantized as follows:$\begin{array}{ll} \qquad \text{If 0 < X < 0.3,} & \text{x}_{4} = 0...

Choose the correct one from among the alternatives $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ after matching an item from Group $1$ with the most appropriate item i...

Consider a system shown in the figure. Let $X(f)$ and $Y(f)$ denote the Fourier transforms of $X(t)$ and $y(t)$ respectively. The ideal HPF has the cutoff frequency $10 \...

A parallel plate air-filled capacitor has plate area of $10^{-1} \mathrm{~m}^{2}$ and plate separation of $10^{-3} \mathrm{~m}$. It is connected to a $0.5 \mathrm{~V}, 3....

A source produces binary data at the rate of $\text{10 kbps.}$ The binary symbols are represented as shown in the figure given below.The source output is transmitted usin...

Consider a $300 \; \Omega$, quarter-wave long (at $1 \; \mathrm{GHz}$ ) transmission line as shown in the figure. It is connected to a $10 \mathrm{~V}, 50 \; \Omega$ sour...

In a microwave test bench, why is the microwave signal amplitude modulated at $1 \; \mathrm{kHz}$?To increase the sensitivity of measurementTo transmit the signal to a fa...

If $\overrightarrow{\mathrm{E}}=\left(\hat{a}_{x}+j \vec{a}_{y}\right) e^{\beta a-k a t}$ and $\overrightarrow{\mathrm{H}}=\left(\frac{k}{\omega \mu}\right)\left(\hat{a}_...

Consider an impedance $\mathrm{Z = R + j X }$ marked with point $\mathrm{P}$ in an impedance Smith chart as shown in the figure. The movement from point $\mathrm{P}$ alon...

A plane electromagnetic wave propagating in free space in incident normally on a large slab of loss-less, non magnetic, dielectric material with $\varepsilon>\varepsilon_...

A lossless transmission line is terminated in a load which reflects a part of the incident power. The measured VSWR is $2.$ The percentage of the power that is reflected ...