Betragsantwort

Betragsantwort refers to the magnitude of a system's response to a sinusoidal input signal. In control theory and signal processing, it is a crucial characteristic of a linear time-invariant (LTI) system. When a sinusoidal input of a specific frequency and amplitude is applied to an LTI system, the steady-state output will also be sinusoidal at the same frequency. The betragsantwort quantifies how the amplitude of this output sinusoid relates to the amplitude of the input sinusoid.

The betragsantwort is typically expressed as a function of frequency, often denoted as |G(jω)|, where G(jω) is the frequency response of the system. This function reveals how the system amplifies or attenuates signals at different frequencies. For instance, a system with a high betragsantwort at a certain frequency will produce an output with a significantly larger amplitude than its input at that frequency, indicating amplification. Conversely, a low betragsantwort signifies attenuation.

Understanding the betragsantwort is essential for analyzing system behavior, designing controllers, and filtering signals. It helps predict how a system will react to various input frequencies and informs decisions about system stability and performance. Plots of the betragsantwort versus frequency, often called Bode plots, are widely used to visualize and interpret a system's frequency-domain characteristics. These plots provide a comprehensive overview of a system's gain across its operating frequency range.