Let  where. The value of d in the range , such that  is __________.        

The signum function is given by

The Fourier series expansion of sgn has

Let  be a function defined by , where [x] represents the integer part of x. (That is, it is the largest integer which is less than or equal to x). The value of the constant term in the Fourier series expansion of g(x) is __________.        

A function y(t) satisfies the following differential equation: , where δ(t) is the delta function.  Assuming zero initial condition and denoting the unit step function by u(t), y(t) can be of the form

For the system

with u as unit impulse and with zero initial state, the output, y, becomes

A single input single output system with y as output and u as input, is described by

For the above system find an input u(t), with zero initial condition, that produces the same output as with no input and with the initial conditions.