A Hilbert transformer is a

In the following scheme, if the spectrum M(f) of m(t) is as shown, then the spectrum Y(f) of y(t) will be:

As x is increased from $$ - \infty \,\,to\,\infty $$, the function $$f(x) = {{{e^x}} \over {1 + {e^x}}}$$

The derivative of the symmetric function drawn in Fig .1 will look like