## 1. Differentiation

### 1.2. Description

Differentiation of the signal using the centrall difference formula

The central difference formula provides a relatively accurate estimation by calculating the function values at two equally spaced points on either side of the point of interest.

In this formula, \(f'(x_0)\) represents the derivative of the function \(f(x_0)\) at the point \(x_0\). The step size \(h\) determines the distance between the points used for approximation. By taking the difference of the function values at \(x_0 + h\) and \(x_0 - h\), divided by \(2h\), we obtain an approximation of the derivative at \(x_0\).

It is important to choose an appropriate step size to ensure accuracy in the approximation. A large step size may introduce truncation errors, while a small step size may amplify round-off errors.

The central difference formula is widely used in numerical differentiation due to its improved accuracy compared to other finite difference methods, such as the forward and backward difference formulas.

### 1.3. Input

Any equidistant signal (see Signal Types ).