In the circuit shown, assume that the opamp is ideal. If the gain ($${V_0}/{V_{in}}$$) is -12, the value of R (in K$$\Omega $$) is _____.

The modulation scheme commonly used for transmission from GSM mobile terminals is

A random binary wave $$y(t)$$ is given by $$$y\left( t \right) = \sum\limits_{n = - \infty }^\infty {{X_n}p\left( {t - nT - \phi } \right)} $$$

where $$p(t) = u(t) - u(t - T)$$, $$u(t)$$ is the unit step function and $$\phi $$ is an independent random variable with uniform distribution in $$[0, T]$$. The sequence $$\left\{ {{X_n}} \right\}$$ consists of independent and identically distributed binary valued random variables with $$P\left\{ {{X_n} = + 1} \right\} = P\left\{ {{X_n} = - 1} \right\} = 0.5$$ for each $$n$$.

The value of the autocorrelation $${R_{yy}}\left( {{{3T} \over 4}} \right)\underline{\underline \Delta } E\left[ {y\left( t \right)y\left( {t - {{3T} \over 4}} \right)} \right]\,\,$$

equals ------------ .

The impulse response of an LTI system can be obtained by