Introduction
The Bilinear Transformation is a commonly used technique in the design of Infinite Impulse Response (IIR) filters. It is a mapping between the continuous-time s-plane and the discrete-time z-plane. The Bilinear Transformation allows us to design analog filters in the s-plane and then convert them into digital filters in the z-plane.

Bilinear Transformation: S-plane to Z-plane
The correct answer is option B, which states that the Bilinear Transformation maps the S-plane to the Z-plane. Let's understand this in detail.

S-plane and Z-plane
- The S-plane is a complex plane used to represent the Laplace transform domain. It consists of the real axis (representing real frequencies) and the imaginary axis (representing imaginary frequencies).
- The Z-plane, on the other hand, is a complex plane used to represent the Z-transform domain. It consists of the unit circle (representing the unit delay) and the interior of the circle (representing the frequency response of the digital filter).

Bilinear Transformation Formula
The Bilinear Transformation formula is given by:
s = 2/T * ( (1 - z^-1) / (1 + z^-1) )
where s is the Laplace transform variable, z is the Z-transform variable, and T is the sampling period.

Conversion Process
Now, let's understand how the Bilinear Transformation maps the S-plane to the Z-plane:
1. The Bilinear Transformation formula takes an analog transfer function in the s-plane and converts it into a discrete transfer function in the z-plane.
2. This conversion process involves replacing the complex variable s with the expression obtained from the Bilinear Transformation formula.
3. By substituting the Bilinear Transformation formula into the analog transfer function, we obtain the digital transfer function in terms of the variable z.
4. This digital transfer function represents the frequency response of the IIR filter in the z-plane.

Advantages of Bilinear Transformation
- The Bilinear Transformation is a widely used technique because it preserves the stability of the analog filter.
- It also ensures that the frequency response of the digital filter matches the frequency response of the analog filter at the Nyquist frequency.

Conclusion
In conclusion, the Bilinear Transformation is a mapping from the S-plane to the Z-plane. It allows us to design analog filters in the s-plane and convert them into digital filters in the z-plane. The Bilinear Transformation formula plays a key role in this conversion process by replacing the complex variable s with an expression involving the Z-transform variable z. This technique is widely used in the design of IIR filters due to its stability and frequency response matching properties.