Digital Communication Systems · Communications · GATE ECE
Marks 1
A digital communication system transmits through a noiseless bandlimited channel $[-W, W]$. The received signal $z(t)$ at the output of the receiving filter is given by $z(t) = \sum\limits_{n} b[n]x(t-nT)$ where $b[n]$ are the symbols and $x(t)$ is the overall system response to a single symbol. The received signal is sampled at $t = mT$. The Fourier transform of $x(t)$ is $X(f)$. The Nyquist condition that $X(f)$ must satisfy for zero intersymbol interference at the receiver is ______.
Let H(X) denote the entropy of a discrete random variable X taking K possible distinct real values. Which of the following statements is/are necessarily true?
A symbol stream contains alternate QPSK and 16-QAM symbols. If symbols from this stream are transmitted at the rate of 1 mega-symbols per second, the raw (uncoded) data rate is _________ mega-bits per second (rounded off to one decimal place).
Marks 2
The information bit sequence {1 1 1 0 1 0 1 0 1} is to be transmitted by encoding with Cyclic Redundancy Check 4 (CRC-4) code, for which the generator polynomial is $C(x) = x^4 + x + 1$. The encoded sequence of bits is ____.
Consider a channel over which either symbol xA or symbol xB is transmitted. Let the output of the channel Y be the input to a maximum likelihood (ML) detector at the receiver. The conditional probability density functions for y given xA and xB are :
$${f_{\left. Y \right|{x_A}}}(y) = {e^{ - (y + 1)}}u(y + 1)$$,
$${f_{\left. Y \right|{x_B}}}(y) = {e^{(y - 1)}}(1 - u(y - 1))$$,
where, u( . ) is the standard unit step function. The probability of symbol error for this system is _________ (rounded off to two decimal places).
$$\,{u_o}(t) = 5\,\cos \,(20000\,\pi \,t);\,0 \le \,\,t\, \le \,T,$$ and
$${u_o}(t) = 5\,\cos \,(22000\,\pi \,t);\,0 \le \,\,t\, \le \,T,$$
where T is the bit-duration interval and t is in seconds. Both $${u_o}(t)$$ and $${u_1}(t)$$ are zero output the interval $$0 \le \,\,t\, \le \,T$$. With a matched filter (correlator ) based receiver, the smallest positive value of T (in milliseconds) required to have $${u_o}(t)$$ and $${u_1}(t)$$ uncorrelated is
If the bits 0 and 1 are transmitted using bipolar pulses, the minimum bandwidth required for distortion free transmission is
Assuming the signal to be uniformly distributed between its peak values, the signal to noise ratio at the quantizer output is
The number of quantitization levels required to reduce the quantization noise by a factor of 4 would be
x(t) = 125t(u(t) - u (t - 1) + (250 - 125t) (u (t - 1) - u (t - 2 )) so that slope - overload is avoided, would be
Group
1. FM
2. DM
3. PSK
4. PCM
Group 2
P: Slope overload
Q: $${\mu - law}$$
R: Envelope detector
S: Capture effect
T: Hilbert transform
U: Matched filter
The source output is transmitted using two modulation schemes, namely Binary PSK (BPSK) and Quadrature PSK (QPSK).
Let $${B_1}$$ and $${B_2}$$ be the bandwidth requirements of BPSK and QPSK respectively. Assuming that the bandwidth of the above rectangular pulses is 10 kHz, $${B_1}$$ and $${B_2}$$ are
Marks 8
Marks 10
(a) Sketch the impulse response, h(t), of the matched filter.
(b) Sketch the output, y(t), of the matched filter. Fully label your diagram.
(c) If the input to the matched filter consists of the signal, x(t), plus additive white noise of two sided spectral density of $${10^{ - 6}}$$ watts/Hz, find the maximum output SNR of the matched filter.
