Calculates periodically varying values for given observation times.
signalgen(tt, ytype, pf = 1)numeric vector: Observation times \(t_1,\ldots,t_n\) (see Details).
character string: Specifying the shape of the periodic fluctuation (see Details). Possible choices are "const", "sine", "trian","peak".
positive numeric value: Fluctuation period \( p_f\).
numeric vector: Values \(y_{f;1},\ldots,y_{f;n}\).
The values \(y_{f;1},\ldots,y_{f;n}\) with fluctuation period \(p_f\) and related to observation times \(t_1,\ldots,t_n\) are generated using
$$y_{f;i}=f\left(\frac{t_i}{p_f}\right), i=1,\ldots,n. $$
Depending on ytype (see above), \(f\) is defined as:
$$ f_{const}(t) = 0,$$
$$f_{sine}(t)= \sin\left(\frac{2\pi t}{p_f}\right),$$
$$f_{trian}(t)= 3\varphi_{1}(t), \quad 0\leq \varphi_{1}(t)\leq\frac{2}{3},$$
$$f_{trian}(t)= 6-6\varphi_{1}(t),\quad \frac{2}{3}<\varphi_{1}(t)\leq 1,$$
$$f_{peak}(t)= 9\exp\left(-3p_f^2\left(\varphi_{1}(t)-\frac 23\right)^2\right),\quad 0\leq \varphi_{1}(t)\leq\frac{2}{3},$$
$$f_{peak}(t)= 9\exp\left(-12p_f^2\left(\varphi_{1}(t)-\frac 23\right)^2\right),\quad \frac{2}{3}<\varphi_{1}(t)\leq 1,$$
with \(\varphi_1(t) = t mod1 = (t-\lfloor t/p_f \rfloor p_f)/p_f\) = (t%%1)/pf. \(f_{const}\) means that there is no (periodic) fluctuation, \(f_{sine}\) defines a sine function, \(f_{trian}\) defines a triangular shaped periodic function and \(f_{peak}\) a periodically repeating peak.
Thieler, A. M., Backes, M., Fried, R. and Rhode, W. (2013): Periodicity Detection in Irregularly Sampled Light Curves by Robust Regression and Outlier Detection. Statistical Analysis and Data Mining, 6 (1), 73-89
Thieler, A. M., Fried, R. and Rathjens, J. (2016): RobPer: An R Package to Calculate Periodograms for Light Curves Based on Robust Regression. Journal of Statistical Software, 69 (9), 1-36, <doi:10.18637/jss.v069.i09>
Applied in tsgen (see there for an example).