Sample and hold (S/H) circuits exhibit a nonlinear behavior due to the input signal dependence of the sampling switch. In this paper, we develop a mixed signal model of this nonlinearity, where the need for a mixed signal description arises from the continuous-time input and sampled output of the S/H. The model is derived by employing a Volterra series expansion. Analysis of the model reveals that as the input signal passes through the S/H, its bandwidth expands, so the signal at the MOS switch output has a bandwidth two or three times larger than the input signal. Under the assumption that the signal at the MOS switch output is sampled above its Nyquist rate, a digital correction method is presented which relies on the theory of pth degree Volterra series inverses. An adaptive blind estimation technique working in tandem with the correction method is also derived for identifying the parameters characterizing the S/H nonlinearity. Numerical simulations are presented demonstrating that for oversampled input signals, the proposed digital calibration achieves a significant spurious free dynamic range (SFDR) improvement at a relatively modest computational cost.