# Principle of Derivative Algorithm

To obtain se(t)se(t — s)* from the beat signal, a controllable delay line is usually involved in nonlinearity correction algorithms. The delay line technique provides a controllable time delay sref of the original signal without changing its amplitude. Therefore, the nonlinear error phase can be calculated from Eq. 5.3.8 as

**Meta et al. [15] proposed an estimation algorithm which is genetic to all nonlinearity models. This algorithm regards the difference of ***e(t*_{r}) in beat signal as the derivative of *e(t _{r})*

**in the case that the time delay**

*s*

_{re}f**is far smaller than**

*PRI*

**. Therefore, the nonlinear phase error can be approximated as**

Thus, *s(t _{r})* can be estimated as

The algorithm in [15], referred to as derivative algorithm, is an efficient method with simple processing steps. If *s _{re}f* is far smaller than PRI, it will give an accurate estimation of transmitted nonlinearity. However, it is inherently a biased algorithm since it is based on the derivative approximation, which makes it inapplicable in high resolution imaging. Moreover, estimation performance decreases sharply as time delay increases.