Consider an angle modulated signal x(t) = 6cos[2π x 10⁶t + 2sin(8000πt) + 4cos(8000pt)] V. The average power of x(t)

A signal as shown in figure is applied to a matched filter. Which of the following represents the output of this matched filter?

Noise with double-sided power spectral density on K over all frequencies is passed through a RC low pass filter with 3 dB cut-off frequency of f_c. The noise power at the filter output is

A source alphabet consists of N symbols with the probability of the first two symbols being the same. A source cncoder increases the probability of the first symbol by a small amount $\epsilon$ and decreases that of the second by$\epsilon$. After encoding, the entropy of the source

Let X and Y be two statistically independent random variables uniformly distributed in the ranges (-1,1) and (-2,1) respectively. Let Z = X + Y, then the probability that [Z$\le$-2] is

In delta modulation, the slope overload distortion can be reduced by

Let Y and Z be the random variables obtained by sampling X(t) at t = 2 and t = 4 respectively. Let W = Y - Z. The variance of W is

If S(f) is the power spectral density of a real, wide-sense, stationary random process, then which of the following relations is true?

c(t) and m(t) are used to generate an FM signal. If the peak frequency deviation of the generated FM signal is three times the transmission bandwidth of the AM signal, then the coefficient of the term $\cos[2\pi(1008 \times 10^3t)] $ in the FM signal (in terms of the Bessel coefficients) is

The following question refer to wide sense stationary stochastic processes.

It is desired to generate a stochastic process (as voltage process) with power spectral density S ($\omega$) = $\dfrac{16}{16 + \omega^2}$ By driving a Linear-Time-Invariant system by zero mean white noise (as voltage process) with power spectral density being constant equal to 1. The system which can perform the desired task could be:

An analog signal is band-limited to 4kHz, sampled at the Nyquist rate and the samples are quantized into 4 levels. The quantized levels are assumed to be independent and equally probable. If we transmit two quantized samples per second, the information rate is

The noise at the input to an ideal frequency detector is white. The detector is operating above threshold. The power spectral density of the noise at the output is

It is desired to generate a stochastic process (as voltage process) with power spectral density S (^_$\omega$) = ^{$\dfrac{16}{16 + \omega^2}$} by driving a linear-time-invariant system by zero mean white noise (as voltage process) with power spectral density being equal to 1. It refers to wide sense stationary stochastic processes.

What would be the parameters of the system obtained?

X(t) is a random process with a constant mean value of 2 and the autocorrelation function R_x ($\tau$) = 4$\lfloor e^{-0.2 | d} + 1 \rfloor$.

Let X be the Gaussian random variable obtained by sampling the process at t = ti and let Q ($\alpha$) = $\int_\infty^\infty \dfrac{1}{\sqrt {2\pi}} e^{\dfrac{-y^2}{2}} dy$ The probability that [ x $\le$ 1 ] is

Consider a binary symmetric channel (BSC) with probability of error being p. To transmit a bit, say 1, we transmit a sequence of three 1s. The receiver will represent 1 if at least two bits are 1. The probability that the transmitted bit will be received in error is

Match the following:

The minimum step-size required for a Delta-Modulator operating at 32 K samples/sec to track the signal is x (t ) = 125t (u (t ) − u (t − 1)) + (250 − 125t ) (u (t − 1) − u (t − 2)). (Here u (t) is the unit-step function.) So that slope-overload is avoided, would be

Two 4-ray signal constellations are shown. It is given that ^$\phi_1$ and ^$\phi_2$ constitute an orthonormal basis for the two constellations. Assume that the four symbols in both the constellations are equiprobable. Let ^{$\dfrac{N_0}{2}$} denote the power spectral density of white Gaussian noise.

If these constellations are used for digital communications over an AWGN channel, then which of the following statements is true?

Two 4-ray signal constellations are shown. It is given that ^$\phi_1$ and ^$\phi_2$ constitute an orthonormal basis for the two constellations. Assume that the four symbols in both the constellations are equiprobable. Let ^{$\dfrac{N_0}{2}$} denote the power spectral density of white Gaussian noise.

The ratio of the average energy of constellation 1 to the average energy of constellation 2 is

Noise with uniform power spectral density of N_oW/Hz is passed through a filter ^{_{$H(\omega) = 2 \ exp(-j\omega t_d)$}} followed by an ideal low-pass filter of bandwidth B Hz. The output noise power in Watts is

An AM signal and a narrow-band FM signal with identical carriers, modulating signals and modulation indices of 0.1 are added together. The resultant signal can be closely approximated by

Consider a binary digital communication system with equally likely 0s and 1s. When binary 0 is transmitted the detector input can lie between the levels - 0.25 V and + 0.25 V with equal probability: when binary 1 is transmitted, the voltage at the detector can have any value between 0 and 1 V with equal probability. If the detector has a threshold of 0.2 V (i.e., if the received signal is greater than 0.2 V, the bit is taken as 1), the average bit error probability is

Consider the signal x (t) shown in Fig. Let h (t) denote the impulse response of the filter matched to x (t), with h (t) being non-zero only in the interval 0 to 4 sec. The slope of h (t) in the interval 3 < t < 4 sec is

A source produces binary data at the rate of 10 kbps. The binary symbols are represented as shown in the figure given below. The source output is transmitted using two modulation schemes, namely Binary PSK (BPSK) and Quadrature PSK (QPSK). Let B₁ and B₂ be the bandwidth requirements of BPSK and QPSK respectively. Assume that the bandwidth of he above rectangular pulses is 10 kHz, B₁ and B₂ are

A message signal is given by m (t) = ^{$\dfrac{1}{2} cos\omega_1 t - \dfrac{1}{2} sin\omega_2 t$}cos sin amplitude-modulated with a carrier of frequency _{^$\omega_0$}to generator s (t) + m (t) [1 + m (t)] cos_{^$\omega_0$}t. What is the power efficiency achieved by this modulation scheme?