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.
- \(y_1=y_{1,a}+y_{1,b}+y_{1,c} + E_1\)
- \(y_2=y_{2,a}+y_{2,b}+y_{2,c} + E_2\)
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:
- \(e_1\sim\mathcal{N}(0,\sigma_1)\)
- \(e_2\sim\mathcal{N}(0,\sigma_2)\)
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:
- If x \(\in [x_{min},x_{max}]\), \(y(x)=f(x)\)
- If x \(\notin [x_{min},x_{max}]\), \(y(x)=0\)
Setting amplitude to 0 for some sub-signals results in their having no effect on the signal itself.