Using the periodic time shift mode


In order to account for light time effects, Period04 does also allow to include a periodic time shift in your least-squares calculations. In this case the fitting formula is extended in the following way:
The periodic time shift parameters are labelled with the subscript pts. Z denotes the zero point and Ωi, Αi and Φi the parameters of frequency i.

Please note:
This calculation mode can only be selected when the expert mode is activated.

Let us assume that you already read in a data set and extracted some frequencies.

1. Select the periodic time shift mode


First, activate the expert mode by selecting "Expert mode" in the "File" menu. You will notice that a new menu, "Options", has appeared. This menu contains the entry "Set fitting function" which provides two choices:
Standard formula and Standard formula with periodic time shift. Click on the latter.

2. Set parameters for the periodic time shift


By inspection of your data you might already have a rough estimate of frequency and amplitude for the periodic time shift. You can either enter these values into the respective field directly, or use the Search PTS start values button to search for a good start value for the periodic time shift parameters within a user-defined range of frequencies and amplitudes.

The lower frequency limit is calculated from the time base of the data set. You should not search for frequencies with lower values since for these frequencies the time base of the data is too short to allow a reliable determination of the periodic time shift.
The number of shots refers to the number of initial parameter values that are being tested.

3. Improving the parameters and the fit


The next step is to improve the periodic time shift parameters by means of a least-squares fit. In order to start this calculation press Improve PTS. Please note that the common frequency parameters will be kept fixed during this calculation.

Now it is time to make a least-squares fit that considers all parameters as variable. For this purpose press Improve all. Do not use 'Calculate', as for a proper fit of a periodic time shift, the frequencies also have to be redetermined!

Please note:
If the start values are not good enough it might occur that the least-squares algorithm gets trapped in a false local minimum. Generally, nonlinear fitting requires some judgement from the user.

Please see 'Tutorial 2' for a step-by-step procedure using an example time string.