Confusion Regarding Bi Linear Transform
The bi linear transform is the transform from the Laplace Transform Domain to the Z Transform.

The Laplace Transform Domain is a regular plane.
This transform transforms vertical lines in the Laplace domain into circles in the Z Domain.
Hence the Fourier Vertical Line in Laplace Domain (The Y Vertical Lines) is transformed into the unit circle in the Z Transform.

I'm a little inaccurate here, since the whole left side of the plane is transformed into the inner part of the Z Plane and the right hand of the Laplace transform it transformed to the outer part of the Z Plane (Out of the unit circle).

This transform is used to derive Digital Filters from their Analog Laplace domain representation.