leakyintegraattoria
Leakyintegraattoria, or leaky integrator, is a dynamic system that accumulates input signals over time while allowing a fraction of the accumulated value to decay. In continuous-time form, the state x(t) evolves according to dx/dt = - (1/τ) x(t) + k u(t), where τ > 0 is a time constant and u(t) is the input. The parameter governs the leakage rate; larger leakage (smaller τ) causes faster decay.
In discrete time, y[n] = y[n-1] + α (u[n] - y[n-1]), or equivalently y[n] = (1 - α) y[n-1] + α u[n], with 0 <
Implementation commonly uses an RC circuit: a resistor in series with a capacitor where input voltage charges
Applications: smoothing and integration of slowly varying signals, estimating smoothed states in control systems, and as
Variants: leaky integrator with adaptive leakage, or multi-stage leaky integrators forming higher-order filters.
See also: Integrator, Exponential moving average, IIR filter, Leaky integrate-and-fire neuron.