Two independent random variables X and Y are uniformly distributed in the interval [-1, 1]. The probability that max [X, Y] is less than 1/2 is

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$10³t)] in the FM signal (in terms of the Bessel coefficients) is

Consider the pulse shape s(t) as shown. The impulse response h(t) of the filter matched to this pulse is

Let m (t) = cos [ (4^{_$\pi$ $\times$} 10³) t] be the message signal and c(t) = 5 cos[(2^{_$\pi$ $\times$} 10⁶)t] be the carrier. c(t) and m(t) are used to generate an AM signal. The modulation index of the generated AM signal is 0.5. Then the quantity ^{$\dfrac{Total sideband power}{Carrier power}$} is

Match the following:||||| |---|---|---|---| | | Column-I| | Column-II| | P| Power efficient transmission of signals| 1| Conventional AM| | Q| Most bandwidth efficient transmission of voice signals| 2| FM| | R| Simplest receiver structure| 3| VSB| | S| Bandwidth efficient transmission of signals with significant dc component| 4| SSB-SC|

Four messages band limited to W, W, 2W and 3 W respectively are to be multiplexed using Time Division Multiplexing (TDM). The minimum bandwidth required for transmission of this TDM signal is

In the following scheme, if the spectrum M(f) of m(t) is as shown, then the spectrum Y(f) of y(t) will be

Which of the following analog modulation schemes requires the minimum transmitted power and minimum channel bandwidth?

A binary symmetric channel (BSC) has a transition probability of 1/8. If the binary transmit symbol X is such that P(X = 0) = 9/10, then the probability of error for an optimum receiver will be

If E denotes expectation, then the variance of a random variable X is given by

At a given probability of error, the binary coherent FSK is inferior to binary coherent PSK by

An output of a communication channel is a random variable $\nu$ with the probability density function as shown in figure. The mean square value of $\nu$ is

A four-phase and an eight-phase signal constellation are shown in the figure below

Assuming high SNR and that all signals are equally probable, the additional average transmitted signal energy required by the 8-PSK signal to achieve the same error probability as the 4-PSK signal is

A DSB-SC signal is to be generated with a carrier frequency fc = 1 MHz using a nonlinear device with the input-output characteristic V₀ = a₀v_i + a₁v_i³ where a0 and a1 are constants. The output of the nonlinear device can be filtered by an appropriate band-pass filter. Let v_i = A'_c cos (2$\pi$f'_c t) + m(t) where m(t) is the message signal. The value of f'_c (in MHz) is

A four-phase and an eight-phase signal constellation are shown in the figure below.

For the constraint that the minimum distance between pairs of signal points be d for both constellations, the radii r₁, and r₂ of the circles are

During transmission over a certain binary communication channel, bit errors occur independently with probability p. The probability of AT MOST one bit in error in a block of n bits is given by

A uniformly distributed random variable X with probability density function f_x (x) = $\dfrac{1}{10}$(u (x + 5) - u (x - 5)) Where u (.) is the unit step function is passed through a transformation given in the figure below. The probability density function of the transformed random variable Y would be

A zero-mean white Gaussian noise signal is passed through an ideal lowpass filter of bandwidth 10 kHz. The output is then uniformly sampled with sampling period 0.03 m. The samples so obtained would be

Consider the frequency modulated signal 10 cos [2$\pi$ x 10⁵ t + 5 sin (2$\pi$ x 1500 t) + 7.5 sin (2$\pi$ x 1000 t)] with carrier frequency of 10⁵ Hz. The modulation index is

The distribution function F_x (x) of a random variable x is shown in the figure. The probability that x = 1 is

In the output of a DM speech encoder, the consecutive pulses are of opposite polarities during time interval t₁ ^$\le$ t ^$\le$ t₂. This indicates that during this interval,

A 100 MHz carrier of 1 V amplitude and a 1 MHz modulating signal of 1 V amplitude are fed to a balanced modulator. The output of the modulator is passed through an ideal high-pass filter with cut-off frequency of 100 MHz. The output of the filter is added with 100 MHz signal of 1 V amplitude and 90⁰ phase shift as shown in the figure. The envelope of the resultant signal is

Directions :The amplitude of a random signal is uniformly distributed between - 5 V and 5 V.

If the signal to quantization noise ratio required in uniformly quantizing the signal is 43.5 dB, the step of the quantization is approximately

Directions :The amplitude of a random signal is uniformly distributed between - 5 V and 5 V.

If the positive values of the signal are uniformly quantized with a step size of 0.05 V, and the negative values are uniformly quantized with a step size of 0.1 V, the resulting signal to quantization noise ration is approximately

A communication channel with AWGN operating at a signal to noise ration SNR >> 1 and bandwidth B has capacity C₁. If the SNR is doubled keeping constant, the resulting capacity C₂ is given by