PYQs Based Test - 11 : Communications

A discrete memoryless source has an alphabet {a₁, a2, a3, a4} with corresponding probabilities $\left\{\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{8}\right\}$. The minimum required average codeword length in bits to represent this source for error-free reconstruction is ________

For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator frequency, then the image frequency (in MHz) is __________.

The frequency response H(f) of a linear time-invariant system has magnitude as shown in the figure.

Statement I: The system is necessarily a pure delay system for inputs which are bandlimited to −α ≤ f ≤ α.

Statement II: For any wide-sense stationary input process with power spectral density S${}_X$ (f), the output power spectral density 𝑆${}_Y$ (f) obeys S${}_Y$ (f) = S${}_X$ (f) for −α ≤ f ≤ α. Which one of the following combinations is true?

The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in the figure. The transition probabilities are as marked.

The parameter α lies in the interval [0.25, 1]. The value of α for which the capacity of this channel is maximized, is ________ (rounded off to two decimal places).

A message m(t) bandlimited to the frequency fm has a power of Pm. The power of the output signal in the figure is