Frequency resolution

The adjustment of the frequency resolution $\delta f$ is consistent with Eq.3 in the CINDERELLA manual (Reegen 2009), where the total time interval width $T$ has to be provided by the user, because the time series is not incorporated by COMBINE. Moreover, the user is more flexible if allowed to specify a different value for $T$. This interval width is provided by means of the keyword dt in the file <infile>.ini, followed by a floating-point number. The default setting is that COMBINE determines the closest pair of frequencies and uses its inverse frequency spacing as $T$.

The second parameter, $\tau$, is specified using the keyword tol, again followed by a floating-point number, in full consistency with CINDERELLA. The default value is $\tau = 0$, forcing COMBINE to employ the Rayleigh frequency resolution.

The frequency tolerance permits linear combinations where

$$\alpha := \left\vert f-f^{\prime}\right\vert\le\delta f$$ (36)

only. The quantity $\alpha$ is the accuracy of a linear combination and provided in the output.