time case can be expressed as

where u(k), y(k); k = 1, 2, 3, ... are the measured input and output respectively and is the lth-order Volterra kernel, or lth-order nonlinear impulse response. The Volterra series is an extension of the linear convolution integral. Most of the earlier identification algorithms assumed that just the first two, linear and quadratic, Volterra kernels are present and used special inputs such as Gaussian white noise and correlation methods to identify the two