# Signal Discontinuity [naive]¶

Naive solution to solve the frequency discontinuity between two concatenated signals.

## 1. Logistic function¶

Logistic function results in a sigmoidal curve, represented by equation in functions of t: $$\large f(t)=\frac{L}{1+e^{-k(t - t_0)}}$$

where:

• $L$ : maximum sigmoid's value;
• $t_0$ : t value which corresponds the median point of curve;
• $k$ : curve slope.

The sigmoid curve will be used as a parameter for a linear interpolation. This process is given by:

$$\large y=(1 - s)x_o + s x_i$$

where s is the sigmoid transition and $\large x_o, x_i$ are the two signal to have the transition.