GATE EC Communications questions

A superheterodyne receiver is to operate in the frequency range $550 \; \mathrm{kHz}-1650 \; \mathrm{kHz}$, with the intermediate frequency of $450 \; \mathrm{kHz}$. Let $\mathrm{R}=\frac{\mathrm{C}_{\operatorname{max}}}{\mathrm{C}_{\text{min}}}$ denote the required capacitance ratio of the local oscillator and $\text{I}$ denote the image frequency …

If $E_{b^{\prime}}$ the energy per bit of a binary digital signal, is $10^{-6}$ watt-sec and the one-sided power spectral density of the white noise, $\mathrm{N}_{0}=10^{-5} \mathrm{~W} / \mathrm{Hz}$, then the output $\text{SNR}$ of the matched filter is

The input to a linear delta modulator having a step-size $\Delta=0.628$ is a sine wave with frequency $f m$ and peak amplitude $E_{m}$. If the sampling frequency $f_{s}=40 \; \mathrm{kH} \mathrm{z}$, the combination of the sine-wave frequency and the peak amplitude, where slope overload will take place is

If $\text{S}$ represents the carrier synchronization at the receiver and $\rho$ represents the bandwidth efficiency, then the correct statement for the coherent binary $\text{PSK}$ is

The line-of-sight communication requires the transmit and receive antennas to face each other. If the transmit antenna is vertically polarized, for best reception the receive antenna should be

For a bit-rate of $8 \; \mathrm{kbps}$, the best possible values of the transmitted frequencies in a coherent binary FSK system are

A $1 \; \mathrm{MHz}$ sinusoidal carrier is amplitude modulated by a symmetrical square wave of period $100 \; \mu \mathrm{sec}$. Which of the following frequencies will NOT be present in the modulated signal?

A person with a receiver is $5 \; \mathrm{Km}$ away from the transmitter. What is the distance that this person must move further to detect a $3-d B$ decrease in signal strength?

An angle-modulated signal is given by $s(t)=\cos 2 \pi\left(2 \times 10^{6} t+30 \sin 150 t+40 \cos 150 t\right)$.The maximum frequency and phase deviations of $s(t)$ are

The PSD and the power of a signal $g(t)$ are, respectively, $\mathrm{S}_{\text{g}}(\omega)$ and $\text{P}_{\text{g}}$. The PSD and the power of the signal $a \text{g}(t)$ are, respectively,

A video transmission system transmits $625$ picture frames per second. Each frame consists of a $400 \times 400$ pixel grid with $64$ intensity levels per pixel. The data rate of the system is

The frequency range for satellite communication is

The amplitude modulated wave form $s(t)=A_{c}\left[1+K_{a} m(t)\right] \cos \omega_{c} t$ is fed to an ideal envelope detector. The maximum magnitude of $\mathrm{K}_{0} m(t)$ is greater than $1$. Which of the following could be the detector output?

In an $\text{FM}$ system, a carrier of $100\; \mathrm{MHz}$ is modulated by a sinusoidal signal of $5 \; \mathrm{kHz}$. The bandwidth by Carson's approximation is $1 \; \mathrm{MHz}$. If $y(t)=(\text{modulated waveform})^{3}$, then by using Carson's approximation, the bandwidth of $y(t)$ around $300 \; \mathrm{MHz}$ and the spacing of spectral …

A message $m(t)$ bandlimited to the frequency $f_{m}$ has a power of $P_{m}$. The power of the output signal in given figure is

In a digital communication system employing Frequency Shift Keying $\text{(FSK)}$, the $0$ and $1$ bit are represented by sine waves of $10 \; \mathrm{kHz}$ and $25 \; \mathrm{kHz}$ respectively. These waveforms will be orthogonal for a bit interval of

A modulated signal is given by, $$s(t)=m_{1}(t) \cos \left(2 \pi f_{c} t\right)+m_{2}(t) \sin \left(2 \pi f_{c} t\right)$$ where the baseband signal $m_{1}(t)$ and $m_{2}(t)$ have bandwidths of $10 \; \mathrm{kHz}$ and $15 \; \mathrm{kHz}$, respectively. The bandwidth of the modulated signal, in $\mathrm{kHz}$, is

The input to a channel is a bandpass signal. It is obtained by linearly modulating a sinusoidal carrier with a single-tone signal. The output of the channel due to this input is given by $$y(t)=(1 / 100) \cos \left(100 t-10^{-6}\right) \cos \left(10^{6} t-1.56\right)$$ The group delay $\left(t_{g}\right)$ and the phase delay $\left(t_{p}\right)$ in …

Four independent messages have bandwidths of $100 \mathrm{~Hz}, 200 \mathrm{~Hz}$, and $400 \mathrm{~Hz}$, respectively. Each is sampled at the Nyquist rate, and the samples are time division multiplexed ($\text{TDM}$) and transmitted. The transmitted sample rate (in $\mathrm{Hz}$ ) is

The input to a matched filter is given by $s(t) = \left\{\begin{matrix} 10\\ 0 \end{matrix}\right. \begin{array}{ll} \sin \left(2 \pi \times 10^{6} t\right) & 0<1<10^{-4} \mathrm{sec} \\ & \text{otherwise} \end{array}$ The peak amplitude of the filter output is