Linear sensors –Laplace transforms and Convolution

Non-linear sensors – Volterra integrals

Hysteresis

The existence of non-vanishing Volterra kernels gives rise to the phenomenon of hysteresis, i.e. the output evidently depends on previous values of the input. Even a linear sensor with memory will exhibit an apparently hysteretic behaviour if a stimulus of a high enough frequency (typically higher than the first characteristic frequency, pole or zero) is applied to it. True hysteresis, as encountered in magnetics, arises when the second order kernel has a very long  time constant in the second order kernel. Hysteresis is not necessarily a complication. It may be used to provide noise immunity in threshold sensing devices. An intentionally hysteretic voltage sensor is the Schmitt Trigger used extensively to combat noise in timer or counter instruments.