GATE EC Digital Communications questions

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

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

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

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

The peak-to-peak input to an $8$-bit $\text{PCM}$ coder is $2$ volts. The signal power-to-quantization noise power ratio (in $d\text{B}$) for an input of $0.5 \cos \left(\omega_{m} t\right)$ is

For a given data rate, the bandwidth $\mathrm{B}_{p}$ of a $\text{BPSK}$ signal and the bandwidth $\text{B}_{0}$ of the $\mathrm{OOK}$ signal are related as

Compression in $\text{PCM}$ refers to relative compression of

In a $\text{PCM}$ system with uniform quantisation, increasing the number of bits from $8$ to $9$ will reduce the quantisation noise power by a factor of

The line code that has zero $\text{dc}$ component for pulse transmission of random binary data is

A communication channel has first-order low pass transfer function. The channel is used to transmit pulses at a symbol rate greater than the half-power frequency of the low pass function. Which of the network shown in the figure is can be used to equalise the received pulses?

The number of bits in a binary $\mathrm{PCM}$ system is increased from $n$ to $n+1$. As a result, the signal to quantization noise ratio will improve by a factor

A $\text{PAM}$ signal can be detected by using

A pulse train with a frequency of $1 \; \mathrm{MHz}$ is counted using a modulo $1024$ ripple-counter built with $\text{JK}$ flip flops. For proper operation of the counter, the maximum permissible propagation delay per flip flop stage is $\dots n \mathrm{Sec}$.

Coherent demodulation of $\text{FSK}$ signal can be effected using

The bit stream $01001$ is differentially encoded using $\text{'Delay and Ex OR'}$ scheme for $\text{DPSK}$ transmission. Assuming the reference bit as a $'1'$ and assigning phases of $'0'$ and $\pi$ for $1$’s and $0$’s respectively, in the encoded sequence, the transmitted phase sequence becomes