Sinusoidal signal

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

1. the lower time limit,
2. the upper time limit,
3. the amplitude,
4. the time zeropoint (a fixed time where the signal shall attain a maximum), and
5. the frequency [inverse time units].

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

Figure 27: Time series generated by the simulator in the sample project sim-signal. Open circles: Original V photometry of IC4996#89. Dots: Two sinusoidal signals added by the simulator.

Example. The sample project sim-signal contains the simulation and analysis of two sinusoidal signals, one over the entire time base, one on a restricted time interval. In this sample project, the V photometry of IC4996#89 (see Example SigSpecNative, p.) is modified, according to the line

sim:add

in the file sim-signal.ini. The line

sim:signal 0 0 0.00727 2521.4542 4.68573

produces a sinusoidal signal over the entire time base (corresponding to the first two arguments being zero). The amplitude is 7.27 mmag, and the frequency is 4.68573 cycles per day. At HJD2452521.4542 the sinusoid shall attain zero value. Correspondingly, the line

sim:signal 2521 2525 0.00543 2524.2356 6.24512

is associated to a sinusoid with amplitude 5.43 mmag, frequency 6.24512 cycles per day, and a zeropoint at HJD2452524.2356. This signal is not generated for the entire time base but only from HJD2452521 to HJD2452525. Fig.27 displays the light curves of the original and the synthetic data.

The screen output contains the lines

*** simulator: add *****************************************

signal
signal

indicating that the simulator adds the synthetic values to the original observables, and that two sinusoids are generated.

Figure 28: Fourier spectra for the sample project sim-signal. Left: significance spectra. Right: DFT amplitudes. Top: original spectra (file SigSpecNative/s000000.dat). Bottom: spectra with two sinusoidal signals added. All spectra are plotted grey. The significant components are indicated by black dots with dashed drop lines (file SigSpecNative/result.dat for the top panels, file sim-signal/s000000.dat for the bottom panels). The default sig threshold of 5 is represented by a horizontal dashed line in the left panels.

Fig.28 (p.) compares the Fourier spectra of the synthetic time series to those of the original time series (as used in Example SigSpecNative, p., and displayed in Fig.2, p.. Both signals introduced by the simulator are identified, but the prewhitening of the component at 6.25 cycles per day is performed over the whole time base, although the signal is present only in an interval. This introduces additional noise, which causes the signal at 3.99 cycles per day to drop below the significance limit of 5 and avoids the detection of the component at 5.41 cycles per day.