PYQs Based Test - 11 : Communications

A message signal m(t) = A ${}_m$ sin (2πf ${}_m$ t) is used to modulate the phase of a carrier A ${}_c$ cos (2πf ${}_c$ t) to get the modulated signal y(t) = A ${}_c$ cos (2πf ${}_c$ t + m(t)). The bandwidth of y(t)

A sinusoidal message signal having root mean square value of 4 V and frequency of 1 kHz is fed to a phase modulator with phase deviation constant 2 rad / volt. If the carrier signal is c(t) = 2cos(2π10⁶t). the maximum instantaneous frequency of the phase modulated signal (rounded off to one decimal place) is _______ Hz.

Let c(t) = A${}_c$ cos (2πf${}_c$ t) and m(t) = cos (2πf${}_m$ t). It is given that f${}_c$ ≫ 5f${}_m$. The signal c(t) + m(t) is applied to the input of a non-linear device, whose output vₒ(t) is related to the input vᵢ(t) as v₀(t) = avᵢ(t) + bvᵢ²(t) where a and b are positive constants. The output of the non-linear device is passed through an ideal band-pass filter with center frequency f${}_c$ and bandwidth 3 f${}_m$, to produce an amplitude modulated (AM) wave. If it is desired to have the side band power of the AM wave to be half of the carrier power, then a/b is

For the modulated signal x(t) = m(t) cos (2πf${}_c$ t), the message signal m(t) = 4 cos (1000πt) and the carrier frequency f${}_c$ is 1 MHz. The signal x(t) is passed through a demodulator, as shown in the figure below. The output y(t) of the demodulator is

A binary random variable X takes the value +2 or -2. The probability P(X = +2) = α. The value of α (rounded off to one decimal place), for which the entropy of X is maximum, is