GATE EC Digital Communications questions

A modulated signal is $y(t)= m(t)\cos(40000\pi t)$, where the baseband signal $m(t)$ has frequency components less than $5$ KHz only. The minimum required rate (in KHz) at which $y(t)$ should be sampled to recover $m(t)$ is _______.

In a $PCM$ system, the signal $m(t)=\left \{\sin(100\pi t)+\cos(100\pi t) \right \}V$ is sampled at the Nyquist rate. The samples are processed by a uniform quantizer with step size $0.75$ $V$. The minimum data rate of the $PCM$ system in bits per second is ______.

An M-level PSK modulation scheme is used to transmit independent binary digits over a band-pass channel with bandwidth $100$ kHz. The bit rate is $200$ kbps and the system characteristic is a raised-cosine spectrum with $100 \%$ excess bandwidth. The minimum value of M is __________

The bit rate of a digital communication system is $R$ kbits/s. The modulation used is $32$-QAM. The minimum bandwidth required for ISI free transmission is

Bits $1$ and $0$ are transmitted with equal probability. At the receiver, the pdf of the respective received signals for both bits are as shown below. If the detection threshold is $1,$ the $BER$ will be

Bits $1$ and $0$ are transmitted with equal probability. At the receiver, the pdf of the respective received signals for both bits are as shown below. The optimum threshold to achieve minimum bit error rate $(BER)$ is

In a baseband communications link, frequencies upto $3500\:Hz$ are used for signaling. Using a raised cosine pulse with $75\%$ excess bandwidth and for no inter-symbol interference, the maximum possible signaling rate in the symbols per second is

A BPSK scheme operating over an AWGN channel with noise power spectral density of $\frac{N_o}{2}$, uses equiprobable signals $s_1(t)=\sqrt{\frac{2E}{T}}\sin(\omega_ct)$ and $s_2(t)=-\sqrt{\frac{2E}{T}}\sin(\omega_ct)$ over the symbol interval $(0,T)$. If the local oscillator in a coherent receiver is ahead in phase by $45^\circ$ with respect to the …

A speech signal, band limited to $4 \; \mathrm{kHz}$ and peak voltage varying between $+5 \mathrm{V}$ and $-5 \mathrm{V}$, is sampled at the Nyquist rate. Each sample is quantized and represented by $8$ bits. If the bits $0$ and $1$ are transmitted using bipolar pulses, the minimum bandwidth required for distortion free transmission is

A speech signal, band limited to $4 \; \mathrm{kHz}$ and peak voltage varying between $+5 \mathrm{V}$ and $-5 \mathrm{V}$, is sampled at the Nyquist rate. Each sample is quantized and represented by $8$ bits. Assuming the signal to be uniformly distributed between its peak to peak value, the signal to noise ratio at the quantizer output is

A speech signal, band limited to $4 \; \mathrm{kHz}$ and peak voltage varying between $+5 \mathrm{V}$ and $-5 \mathrm{V}$, is sampled at the Nyquist rate. Each sample is quantized and represented by $8$ bits. The number of quantization levels required to reduce the quantization noise by a factor of $4$ would be

In a $\text{PCM}$ system, if the code word length is increased from $6$ to $8$ bits, the signal to quantization noise ratio improves by the factor

In the output of a DM speech encoder, the consecutive pulses are of opposite polarity during time interval $t_{1} < t < t_{2}.$ This indicates that during this interval

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 levels $-0.25 \mathrm{~V}$ and $+0.25 \mathrm{~V}$ with equal probability: when binary $1$ is transmitted, the voltage at the detector can have any value between $0$ and …

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 in Group $2.$ …

Three analog signals, having bandwidths $1200 \mathrm{~Hz}$, $600 \mathrm{~Hz}$ and $600 \mathrm{~Hz}$, are sampled at their respective Nyquist rates, encoded with $12$ bit words, and time division multiplexed. The bit rate for the multiplexed signal is

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 using two modulation schemes, namely Bìnary PSK (BPSK) and Quadrature PSK (QPSK). Let $\mathrm{B}_{1}$ and $\mathrm{B}_{2}$ be the bandwidth requirements of BPSK and QPSK respectively. …

A signal is sampled at $8 \; \mathrm{kHz}$ and is quantized using $8$-bit uniform quantizer. Assuming $\mathrm{SNR}_q$ for a sinusoidal signal, the correct statement for $P C M$ signal with a bit rate of $R$ is

At a given probability of error, binary coherent $\text{FSK}$ is inferior to binary coherent $\text{PSK}$ by

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