Random steps

This module generates steps following two random processes:

1. the constant attained by the synthetic observable throughout each step follows a Gaussian distribution with an expected value 0,
2. a Poisson process is used to define when a step has to be incorporated.

The keyword sim:rndsteps is given with four floating-point parameters. They specify

1. the lower time limit,
2. the upper time limit,
3. the standard deviation of the Gaussian distribution defining the constants attained throughout each step,
4. the expected time range for the Poisson distribution of steps.

If the lower and upper time limits are both set zero, the steps are generated for the entire time base.

Figure 34: Time series generated by the simulator in the sample project sim-rndsteps. The sampling represents the V photometry of IC4996#89. The original observable values are replaced by the simulator.

Example. The sample project sim-rndsteps illustrates the simulation and analysis of random steps upon the sampling of the V photometry of IC4996#89. The simulator replaces the original observable values, according to the line

sim:replace

in the file sim-rndsteps.ini. The line

sim:rndsteps   0 0 0.5 0.07

in the file sim-rndsteps.ini produces random steps the values of which are distributed according to a Gaussian with standard deviation 0.5. The expected distance in time of consecutive steps 0.07 days. The resulting light curve is displayed in Fig.34.

Figure: Typical significance spectrum for random steps, based on the sampling of the V photometry of IC4996#89. Each constant in the step function displayed in Fig.34 contributes a spectral window to this DFT.

Since the observables are constant between the steps, one may consider each of the corresponding time intervals to contribute a spectral window to the DFT, or significance spectrum, correspondingly. The significance spectrum associated to the light curve in Fig.34 is displayed in Fig.35 and respresents such a superposition of spectral windows.