Fehlervektor

A Fehlervektor, also known as an error vector, is a mathematical concept used primarily in the fields of control theory, signal processing, and communications engineering. It represents the difference between a desired or reference signal and an actual or measured signal. In other words, it quantifies the error between the two signals.

The Fehlervektor is often used in the context of feedback control systems, where it helps to analyze and design controllers that can minimize the error between the system's output and the desired reference input. In signal processing, it is used to measure the distortion or noise introduced by a system. In communications engineering, it is used to analyze the performance of a communication channel.

The Fehlervektor can be represented mathematically as the difference between two vectors, where each vector represents a signal. For example, if x(t) is the reference signal and y(t) is the actual signal, then the Fehlervektor e(t) is given by e(t) = x(t) - y(t).

The magnitude of the Fehlervektor can be used to quantify the error, and its direction can provide information about the nature of the error. For example, if the Fehlervektor is always in the same direction, it may indicate a bias or offset in the system. If it is randomly varying, it may indicate noise or other forms of distortion.

In summary, the Fehlervektor is a fundamental concept in many areas of engineering and applied mathematics. It provides a way to quantify and analyze the error between two signals, and it is used in a wide range of applications, from control systems to communications engineering.