In a PCA system, the signal $$m(t) = \{ \sin (100\,\pi \,t)\, + \cos (100\,\pi \,t\} $$ V is sampled at the Nyquist rate. The samples are processed by a uniform quantizer with step size 0.75 V. The minimum data rate of the PCM system in bits per second is________________

A binary random variable X takes the value of 1 with probability 1/3. X is input to a casade of 2 independent identical binary symmetric channels (BSCs) each with crossover probability 1/2. The output of BSCs are the random variables $${Y_1}$$ and $${Y_2}$$ as shown in the figure.

Consider an FM signal $$f\left(t\right)\;=\;\cos\left[2{\mathrm{πf}}_\mathrm c\mathrm t\;+\;{\mathrm\beta}_1\sin\;2{\mathrm{πf}}_1\mathrm t\;+\;{\mathrm\beta}_2\sin\;2{\mathrm{πf}}_2\mathrm t\right]$$ . The maximum deviation of the instantaneous frequency from the carrier frequency f_c is

In the root locus plot shown in the figure, the pole/zero marks and the arrows have been removed. Which one of the following transfer functions has this root locus?