Significance of frequencies



Every measurement is affected by noise that may be generated by many sources (e.g. observations, instrumentation, undetected frequencies).

For Fourier spectra, noise has the annoying effect that a peak that has been found may not be real.

The signal to noise ratio


Therefore, a criterium is needed to ensure that the signal is a real feature. Empirical results from observational analyses (Breger et al., 1993, A&A 271,482) and numerical simulations (Kuschnig et al., 1997, A&A 328, 544) have shown that the ratio between signal and noise in amplitude should not be lower than 4.0 to give good confidence.

What is the signal?
As signal we define either the amplitude of the respective peak in the Fourier spectrum or the amplitude of the least-squares solution for the peak.

What is the noise?
The noise is defined as the average amplitude in a frequency range that encloses the detected peak. The noise may be calculated before or after prewhitening the peak. The choice is beyond the scope of this manual.

Checking the significance of a frequency.


Let us assume that you have calculated a Fourier spectrum and detected a new peak.
  1. Select "Calculate noise at frequency" in the "Special" menu.
  2. By default the program loads the last frequency value from the frequency list in the Fit module into the frequency field of the dialog. If you want to calculate the noise for an other frequency type the new frequency value into the frequency field.
  3. Define the box size for the noise calculation. This value specifies the frequency range [frequency-boxsize/2, frequency+boxsize/2] which is being used for the calculation of the noise.
  4. Choose a step rate. Usually the step rate quality "High" provides a very good sampling.
  5. Select the type of data to use for the noise calculation. In most cases "Residuals at original" is what you need, unless you work on adjusted data.
  6. Press Calculate to start the calculation.
  7. After the calculation has been finished the noise result will be displayed in the text area in the lower part of the window. If the frequency has been selected from the combo box then even the signal to noise ratio will be shown.

Period04 also contains the possibility to calculate a noise spectrum. See "Calculate noise spectrum" for more details.