impulsresponsanalyse

Impulsresponsanalyse is the study of how a dynamic system responds to a brief input, ideally an impulse. It seeks to characterize the system by its impulse response, h(t), which is the output produced when the input is the Dirac delta δ(t). For linear time-invariant systems, the impulse response fully determines the input-output relation: y(t) = ∫ x(τ) h(t−τ) dτ (convolution). The Fourier transform of h(t) yields the frequency response, H(ω).

Experimentally, a true impulse is rarely available, so short excitations such as a sweep, a maximum-length sequence, or a pink-noise burst are used. The impulse response is recovered by deconvolution or cross-correlation of the recorded output with the known input. Processing steps often include windowing, normalization, and noise reduction; care is needed to separate the linear response from nonlinear effects and to mitigate leakage from finite data length.

Impulsresponsanalyse is central in acoustics (room impulse responses, speaker testing), audio engineering (equalization, reverberation modeling), and control engineering (system identification and controller design). It is also used in structural engineering, seismology, and economics, where impulse response functions describe how variables react to shocks. The concept connects to Green's functions in physics and to transfer functions in signal processing.

Limitations include the assumption of linearity and time invariance; nonlinearities, time-varying dynamics, and measurement noise can distort estimates. Impulse response methods provide a complete description only for linear time-invariant systems; when those conditions fail, alternative models such as nonlinear or adaptive methods are required.