Exponential trend

The keyword sim:exp is given with five floating-point parameters. They specify

1. the lower time limit,
2. the upper time limit,
3. the coefficient $E_0$,
4. the time zeropoint $t_0$, and
5. the exponent $X$.

The polynomial trend is generated by the relation

$$E\left( t\right) := E_0\,\mathrm{e}^{X\left( t-t_0\right)}\: .$$ (23)

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

Figure 30: Time series generated by the simulator in the sample project sim-exp. The sampling represents the V photometry of IC4996#89. The simulator replaces the origninal observable by two exponential functions, one over the entire time base, and the other one on an interval between HJD$2452521.4532$ and HJD$2452526.8832$.

Example. The sample project sim-exp contains the simulation and analysis of two exponential trends, one over the entire time base, one on a restricted time interval, corresponding to the lines

sim:exp 2521.4532 2526.8832 1.3256 2526.7384  0.65834
sim:exp    0         0      2.2841 2520.8562 -0.03425

in the file sim-exp.ini. The sampling of the V photometry of IC4996#89 is used, and the simulator replaces the original observable values, according to the line

sim:replace

The screen output contains the expression exponential trend to indicate that such a trend is generated. In this example, the entry is found twice. The resulting light curve is displayed in Fig.30.

SIGSPEC detects 54 significant signal components, which are not discussed here.