GATE EC 2012 Question Paper (12-Feb-2012) (Shift 2)

The unilateral Laplace transform of f(t) is $\frac{1}{s^2+s+1}$. The unilateral Laplace transform of t f(t) is

With initial condition x(1) = 0.5 , the solution of the differential equation $t\frac{dx}{dt}+x=t$ is

The diodes and capacitors in the circuit shown are ideal. The voltage V(t) across the diode D₁ is:

The circuit shown in the figure is:

A source generates three symbols with probability 0.25, 0.25, 0.50 at a rate of 3000 symbols per second. Assuming independent generation of symbols, the most efficient source encoder would have average bit rate of