Q1.The input and output of a continuous time system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal system ?
Answer : Option CExplaination / Solution:
The output of causal system depends only on present and past states only.
In option (A) y(0) depends on x(- 2) and x(4).
In option (B) y(0) depends on x(1).
In option (C) y(0) depends on x(- 1).
In option (D) y(0) depends on x(5).
Thus only in option (C) the value of y(t) at t = 0 depends on x(- 1) past value.
In all other option present value depends on future value.
The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric conductor is given by the following expression The cross-sectional dimensions of the waveguide are given as a = 0.08 m and b = 0.033 m. The mode of propagation inside the waveguide is
Answer : Option CExplaination / Solution:
We have the expression,
and the cross sectional dimension is
a = 0.08 m, b = 0.033m
Now, we compare the equation for TEm,n mode whose Hz is given as
Q6.The impulse response h(t) of a linear time invariant continuous time system is
described by where u(-t) denotes the unit
step function, and α and β are real constants. This system is stable if
Answer : Option DExplaination / Solution:
This system is stable only when bounded input has bounded output For stability αt < 0 for t > 0 that implies α < 0 and βt > 0 for t > 0 that implies β > 0. Thus, α is negative and β is positive.