Volterra explorer
A second-order Volterra model describes a system by its memory: a linear kernel h₁ that weighs the recent past, and a quadratic kernel h₂ that weighs products of past inputs. Move the sliders and watch where the extra harmonics come from.
y(t) = h₀ + Στ h₁(τ) x(t−τ) + Στ₁,τ₂ h₂(τ₁,τ₂) x(t−τ₁) x(t−τ₂)
Input
Linear kernel h₁
Quadratic kernel h₂
Drives the model with Gaussian white noise and estimates h₁ and h₂ by cross-correlation (Lee–Schetzen), without looking at the true kernels.
Response
input linear part quadratic part output
Output spectrum
linear part quadratic part. The quadratic kernel creates energy at 0, 2f and at sums and differences of input tones.
h₁(τ)
true recovered
h₂(τ₁, τ₂)
Left: true kernel. Press “Recover kernels” to see the estimate beside it.