## An alternative method

The alternative method we propose first Fourier transforms the time series p(t). Then it applies the traditional log-Fourier transformation (described above) to the spectrum of the original time trace. We call this new domain the Fourier-log-Fourier domain(). We denote as the variable of the new domain after the original stretch.

In this domain the intended trace stretch is carried out by a simple scaling of the series' coefficients:
 (4)

Comparing (2) and (4), we find that the stretching in the and in the domain differ only in the exponantial scaling factor.

The number of samples for a well sampled representation of our input data in the domain is:

 (5)

This expression derives directly from equation (3) by interchanging the role of the frequency and time axis. Especially, note the symmetry of the non logarithmic factor of (3) and (5).

 3|c|Logarithmic trace stretch - An overview 3|c| 3|c| Interpolation Log-Fourier transformation FL Fourier-Log-Fourier transformation FLF Interpolation according to (1): stretch by multiplication: stretch by multiplication: 3|c|Disadvantages Each stretch requires a new interpolation. Overhead calculations: FL. Long traces after logarithmic stretch. Comparatively,expensive overhead calculations: FLF. 3|c|Advantages Easy to implement. No overhead calculations. Each stretch is a simple multiplication. Each stretch is a simple multiplication. Shorter traces in the transform domain.