In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: $${\beta _{DC}}$$ = 60, $${V_{BE}}$$ = 0.7V, $${h_{ie}} \to \,\,\infty $$, $${h_{fe}} \to \,\,\infty $$. The capacitance C_C can be assumed to be infinite.

The small-signal gain of the amplifier $${{{V_c}} \over {{V_s}}}$$ is

The following question refer to wide sense stationary stochastic process:

It is desired to generate a stochastic process (as voltage process) with power spectral density

$$$S\left( \omega \right) = {{16} \over {16 + {\omega ^2}}}$$$

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

The following question refer to wide sense stationary stochastic process:

The parameters of the system obtained in Q. 12 would be

Let $$g\left( t \right){\mkern 1mu} {\mkern 1mu} \,\,\,\,\,{\mkern 1mu} = {\mkern 1mu} {\mkern 1mu} p\left( t \right){}^ * p\left( t \right)$$ where $$ * $$ denotes convolution and $$p(t) = u(t) - u(t-1)$$ with $$u(t)$$ being the unit step function

The impulse response of filter matched to the signal $$s(t) = g(t)$$ $$ - \delta {\left( {t - 2} \right)^ * }\,\,g\left( t \right)$$ is given as: