Impulsfolge

Impulsfolge, or impulse sequence, is a time-domain signal consisting of a set of instantaneous events occurring at discrete moments in time. It is commonly modeled as a weighted sum of Dirac delta functions: x(t) = sum_k a_k δ(t − t_k). Each impulse has an area a_k, representing the instantaneous magnitude of the event, and the signal is nonzero only at the instants t_k.

A standard specialization is an impulse train, where the impulses occur at regular intervals t_k = kT and carry identical weights a_k = A, giving x(t) = A ∑_n δ(t − nT). The Fourier transform of an impulse train is another impulse train in the frequency domain, with spectral replicas spaced by ω_s = 2π/T. Impulsfolge plays a central role in the analysis of linear time-invariant systems, since any finite-duration signal can be expressed as a convolution of the impulse sequence with the system’s impulse response.

Connections to broader concepts include the impulse response, which characterizes a system’s output to a single impulse, and sampling, where a continuous signal is multiplied by an impulse train to produce discrete samples. Impulsfolge also appears in modeling discrete events such as neuronal spikes, packet arrivals in networks, or measurement impulses, where the timing and weight of each impulse carry essential information.

In summary, an impulse sequence provides a compact, mathematically tractable way to represent instantaneous events and to analyze systems through convolution and frequency-domain methods.