application of smoothing spline in sinusoidal modeling

The sinusoidal model has many applications in time series analysis‎, ‎signal processing‎, ‎regression‎, ‎and other phenomena that are repeated periodically‎. ‎on the other hand‎, ‎smoothing spline is a flexible and useful method in many fields‎. ‎in this article‎, ‎smoothing spline is applied to interpolate data generated from the sinusoidal model‎. ‎therefore‎, ‎a sinusoidal model is considered in three general forms‎. ‎then‎, ‎in a simulation study‎, ‎data sets are generated from each of the sinusoidal model forms‎, ‎and the effect of changing the model components is assessed‎. ‎besides‎, ‎the smoothing spline method is applied to estimate the related sinusoidal model‎, ‎and the performance of the smoothing spline for fitting a proper model to the sinusoidal data is studied‎. furthermore‎, ‎by fitting a proper sinusoidal model to each generated data set‎, ‎the performance of smoothing spline is compared with the sinusoidal model‎. the ‎sum of squares error criterion is applied to compare the performance of models‎. ‎the simulation results illustrate that smoothing spline has better performance for model fitting to sinusoidal data.