General principle:

You can generate your own signal (y1) as a sum of up to 3 sub-signals (y1,a, y1,b, and y1,c). You can generate a second signal (y2) in the same way.

You can also add some noise (\(E_1\) and \(E_2\)) to these sub-signals.

Noise characteristics:

First you have to set the length n of your x-signals and y-signal(s). You can generate some noise by setting σ to a value>0.

We define \(e_1\) and \(e_2\) as signals of length n with distributions: If you set "Noise type" to "white" the noise will be: If you set "Noise type" to "red" the noise at a location \(x_i\) will be defined as resulting from an ARIMA model of order (1,0,0) with autoregressive coefficient set to \(\sigma/11\).

Sub-signals characteristics:

Each sub-signal is designed as a sinusoid with a certain period T, amplitude A, and phase Φ: \(f(x)=Acos(2\pi(\frac{x}{T}+\phi))\). Breaks can be produced in the signals using xmin and xmax, so that:

Setting amplitude to 0 for some sub-signals results in their having no effect on the signal itself.