GATE EC Digital Communications questions

A single bit, equally likely to be $0$ and $1$, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density $N_{0}/2.$ Binary signaling with $0 \mapsto p(t),$ and $1 \mapsto q(t),$ is used for the transmission, along with an optimal receiver that minimizes the bit-error probability. Let …

A voice signal $m(t)$ is in the frequency range $5\:kHz$ to $15\:kHz$. The signal is amplitude-modulated to generated an AM signal $f(t)=A\left(1+m(t)\right)\cos 2\pi f_{c}t,$ where $f_{c}=600\: kHz.$ The AM signal $f(t)$ is to be digitized and archived. This is done by first sampling $f(t)$ at $1.2$ times the Nyquist frequency, and then …

Consider a binary channel code in which each codeword has a fixed length of $5\: bits$. The Hamming distance between any pair of distinct codewords in this code is at least $2$. The maximum number of codewords such a code can contain is __________.

A binary source generates symbols $X\in \left \{ -1,1 \right \}$ which are transmitted over a noisy channel.The probability of transmitting $X=1$ is $0.5.$ Input to the threshold detector is $R=X+N$.The probability density function $f_{N}\left ( n \right )$ of the noise $\text{N}$ is shown below. If the detection threshold is zero, then the …

Which one of the following statements about differential pulse code modulation (DPCM) is true?

In a digital communication system, the overall pulse shape $p(t)$ at the receiver before the sampler has the Fourier transform $P(f)$. If the symbols are transmitted at the rate of $2000$ symbols per second, for which of the following cases is the inter symbol interference zero?

In binary frequency shift keying (FSK), the given signal waveforms are $$u_{0}(t)=5\, \cos(20000\pi t)\, ;0\leq t\leq T \text{, and } \\ u_{1}(t)=5\, \cos(22000\pi t)\, ;0 \leq t \leq T,$$ where $T$ is the bit-duration interval and $t$ is in seconds.Both $u_{0}(t)$ and $u_{1}(t)$ are zero outside the interval $0\leq t\leq T$. With a matched filter …

A sinusoidal message signal is converted to a PCM signal using a uniform quantizer. The required signal-to-quantization noise ratio (SQNR) at the output of the quantizer is $40$ dB. The minimum number of bits per sample needed to achieve the desired SQNR is __________

Consider binary data transmission at a rate of $56$ kbps using baseband binary pulse amplitude modulation (PAM) that is designed to have a raised-cosine spectrum. The transmission bandwidth (in kHz) required for a roll-off factor of $0.25$ is ________

A digital communication system uses a repetition code for channel encoding/decoding. During transmission, each bit is repeated three times ($0$ is transmitted as $000$, and $1$ is transmitted as $111$). It is assumed that the source puts out symbols independently and with equal probability. The decoder operates as follows: In a block of three …

A speech signal is sampled at $8$ $kHz$ and encoded into $PCM$ format using $8$ bits/sample. The $PCM$ data is transmitted through a baseband channel via $4$-level $PAM$. The minimum bandwidth (in $kHz$) required for transmission is _________

An ideal band-pass channel $500 \: Hz –2000 \:Hz$ is deployed for communication. A modem is designed to transmit bits at the rate of $4800$ bits/s using $16-QAM$. The roll-off factor of a pulse with a raised cosine spectrum that utilizes the entire frequency band is __________

A binary baseband digital communication system employs the signal $$p(t) = \begin{cases}\large\frac{1}{\sqrt T_s},&0\leq t\leq T_s \\ \: 0, & \text{otherwise} \end{cases}$$ for transmission of bits. The graphical representation of the matched filter output $y(t)$ for this signal will be

The transmitted signal in a GSM system is of $200$ kHz bandwidth and $8$ users share a common bandwidth using TDMA. If at a given time $12$ users are talking in a cell, the total bandwidth of the signal received by the base station of the cell will be at least (in kHz) ___________.

Consider a binary, digital communication system which uses pulses $g(t)$ and $-g(t)$ for transmitting bits over an AWGN channel. If the receiver uses a matched filter, which one of the following pulses will give the minimum probability of bit error?

The modulation scheme commonly used for transmission from GSM mobile terminals is

A three bit pseudo random number generator is shown. Initially the value of output $Y\equiv Y_{2} Y_{1} Y_{0}$ is set to $111.$ The value of output $Y$ after three clock cycles is

In a code-division multiple access $(\text{CDMA})$ system with $N = 8$ chips, the maximum number of users who can be assigned mutually orthogonal signature sequences is ________.

Let $Q(\sqrt{\gamma})$ be the BER of a BPSK system over an AWGN channel with two-sided noise power spectral density $N_{0}/2.$ The parameter $\gamma$ is a function of bit energy and noise power spectral density. A system with two independent and identical AWGN channels with noise power spectral density $N_{0}/2$ is shown in the figure. The BPSK …

Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms $s_{1}( t )= \alpha \cos 2\pi f_1 t$, and $s_2(t) = \alpha \cos 2 \pi f_2 t$ where $\alpha = 4$ mV. Assume an AWGN channel with two-sided noise power spectral density $\frac{N_o}{2}= 0.5 \times 10^{-12}$ W/Hz. Using an optimal receiver and the relation …