Complex modulation signal

The SAR image cross-spectra is meant to quantify the spatial frequency content of the cross-section modulations. The modulations are the relative variation of the radar cross-section relatively to the mean radar cross section of the image. As we are interested with the frequency content due to wave modulation, we define the mean radar cross-section as the average of the radar cross-section over a prescribed image extension (typically 1 km x 1 km).

It writes:

\[I_{low} = |\overline{DN}|^2\star G\]

where \(\star\) operators stands for the convolution and with \(G\) a normalized Gaussian-filter with a customizable 1 km x 1 km standard deviations.

The complex Digital Number modulations thus writes:

(3)\[ \widetilde{DN} = \dfrac{\overline{DN}}{\sqrt{I_{low}}}\]

Computation of the sigma0 normalized variance

The normalized variance is the variance of the Digital number defined over a prescribed spatial extension. In the baseline L1B SLC processor, the variance is computed at a tile level.

It writes:

\[nv\triangleq\dfrac{\left\langle\left(m-\left\langle m\right\rangle\right)^2\right\rangle}{\left\langle m\right\rangle^2}\]

where \(m=\left|\widetilde{DN}\right|^2\) and \(\widetilde{DN}\) is defined in equation (3) .