The question asks to identify the incorrect statement regarding the Transfer Function of a linear Time-Invariant (LTI) system.

Analyzing Transfer Function Statements

Let's analyze each statement:

• Statement A: "The ratio of Laplace transform of the output to the Laplace transform of the input variable under the assumption that all initial conditions are zero."

  This is the correct definition of a transfer function for an LTI system. Mathematically, if $ Y(s) $ is the Laplace transform of the output $ y(t) $ and $ U(s) $ is the Laplace transform of the input $ u(t) $, then the transfer function $ G(s) $ is given by:

  $ G(s) = \frac{Y(s)}{U(s)} \quad \text{(with zero initial conditions)} $

• Statement B: "The ratio of Fourier transform of the output to Fourier transform of the input variable."

  This statement is incorrect. The transfer function is fundamentally defined using the Laplace transform, not the Fourier transform. While the frequency response $ G(j\omega) $ (related to the Fourier transform) can be derived from the transfer function $ G(s) $ by setting $ s = j\omega $, the definition itself is based on Laplace transforms.

• Statement C: "The higher power of the complex variable 's' in the denominator of the transfer function determines the order of the system."

  This is a correct statement. The order of an LTI system is defined by the degree of the denominator polynomial of its transfer function $ G(s) $.

• Statement D: "It is an expression in s-domain relating the output and input of linear time invariant system in terms of the system parameters and is independent of the input."

  This statement accurately describes the characteristics of a transfer function. It represents the system's input-output relationship in the s-domain, depends only on system parameters (not the input), and is valid for LTI systems.

Conclusion

Based on the analysis, the incorrect statement regarding the Transfer Function of an LTI system is the one defining it as the ratio of Fourier transforms instead of Laplace transforms.