Let X(t) be a white Gaussian noise with power spectral density $$\frac{1}{2}$$W/Hz. If X(t) is input to an LTI system with impulse response $$e^{-t}u(t)$$. The average power of the system output is ____________ W (rounded off to two decimal places).
The frequency of occurrence of 8 symbols (a-h) is shown in the table below. A symbol is chosen and it is determined by asking a series of "yes/no" questions which are assumed to be truthfully answered. The average number of questions when asked in the most efficient sequence, to determine the chosen symbol, is _____________ (rounded off to two decimal places).
| Symbols | a | b | c | d | e | f | g | h |
|---|---|---|---|---|---|---|---|---|
| Frequency of occurrence | $$\frac{1}{2}$$ | $${1 \over 4}$$ | $${1 \over 8}$$ | $${1 \over {16}}$$ | $${1 \over {32}}$$ | $${1 \over {64}}$$ | $${1 \over {128}}$$ | $${1 \over {128}}$$ |
The open loop transfer function of a unity negative feedback system is $$G(s) = {k \over {s(1 + s{T_1})(1 + s{T_2})}}$$, where $$k,T_1$$ and $$T_2$$ are positive constants. The phase cross-over frequency, in rad/s, is
A closed loop system is shown in the figure where $$k>0$$ and $$\alpha > 0$$. The steady state error due to a ramp input $$(R(s) = \alpha /{s^2})$$ is given by
