# Transfer function of a curve

• Alba19
In summary, to calculate the transfer function of a curve, one needs to understand system identification and the Laplace and Fourier transforms.

#### Alba19

How can i calculate transfer function of curve? for example from time response of a curve.

or transfer function of ferquency response .

It sounds that you are asking about something we call system identification.

After that, check the references of the article. A google search on "system identification" "time domain" also returns a number of useful web pages and video tutorials.

After studying, if you have more specific questions, post again.

And here is another good article at Wikipedia:

https://en.wikipedia.org/wiki/Transfer_function
Linear time-invariant systems
Transfer functions are commonly used in the analysis of systems such as single-input single-output filters, typically within the fields of signal processing, communication theory, and control theory. The term is often used exclusively to refer to linear time-invariant (LTI) systems, as covered in this article. Most real systems have non-linear input/output characteristics, but many systems, when operated within nominal parameters (not "over-driven") have behavior that is close enough to linear that LTI system theory is an acceptable representation of the input/output behavior.

The descriptions below are given in terms of a complex variable, s = σ + j ⋅ ω {\displaystyle s=\sigma +j\cdot \omega } , which bears a brief explanation. In many applications, it is sufficient to define σ = 0 {\displaystyle \sigma =0} (and s = j ⋅ ω {\displaystyle s=j\cdot \omega } ), which reduces the Laplace transforms with complex arguments to Fourier transforms with real argument ω. The applications where this is common are ones where there is interest only in the steady-state response of an LTI system, not the fleeting turn-on and turn-off behaviors or stability issues. That is usually the case for signal processing and communication theory.
Are you familiar with LTI systems, and transforms (like Laplace and Fourier transforms)?

anorlunda said:
It sounds that you are asking about something we call system identification.