Nikola Šerman, prof. emeritus Linear Theory
firstname.lastname@example.org Transfer Function Concept Digest
4. TRANSFER FUNCTION
According to (3.5), function f(t) n-th derivative L-transform generally depends on the function itself as well as on its initial conditions.
When initial conditions are equal to zero, i.e. when it holds:
Function f(t) n-th derivative L-transform becomes an algebraic product of F(s) and the n-th power of s:
In the time domain relationship between output and input is defined by a differential equation (2.1) . However, when moved to the frequency domain by (4.2) the same relationship takes a simple algebraic fraction form. This form is called transfer function.
It can be expressed as:
Due to the transfer function definition (4.3) or (4.4), the output Y(s) L-transform can be obtained by a simple multiplication of the transfer function H(s) with the input X(s) L-transform:
This simple frequency domain algebraic relationship between input, output and the transfer function makes the transfer function concept such a powerful tool in dealing with complex linear dynamic systems.