Stufenimpuls

Stufenimpuls is a term used in German-language literature to describe a signal that produces a step-like change in a quantity, typically an input signal that switches from one level to another at a defined time. In many contexts it is closely related to the concept of a step input or Heaviside step, and it is mainly discussed in signal processing, control theory and related fields.

Mathematically, a stepped input can be modeled as a function that is constant before a chosen moment t0 and constant (often at a different level) afterward. A common form is u(t) = A for t ≥ t0 and u(t) = 0 for t < t0, which can be written compactly using the Heaviside step function H(t−t0). The derivative of a step function is a Dirac delta impulse, illustrating the close connection between steps and impulses in time-domain analysis.

Applications of Stufenimpuls include exciting linear time-invariant systems to obtain the step response, which characterizes how the system accumulates or reacts to a sudden change. In practice, real signals approximate a theoretical step with a finite rise time, affecting the measured response and the interpretation of the system’s transfer function.

Relation to other concepts: Stufenimpuls is distinct from the Dirac delta impulse, which represents an ideal instantaneous impulse, and from the pure Heaviside step function itself. Understanding these relationships helps in analyzing system behavior through time-domain responses and corresponding transforms (Laplace, Fourier).

See also: Heaviside function, Dirac delta, step response, impulse response, transfer function.