Speckle ensemble statistics of logarithmically scaled data (radar)

It is shown that statistics of logarithmically scaled (averaged) radar data can be described by simple analytical expressions using Riemann's zeta function and Eule's psi function. This achievement makes possible the proper qualification of the impact of such transformation on the physical interpretation of remote sensing data and derived data (i.e. field-averaged mean and standard deviation). The standard deviation for Rayleigh-fading objects is a constant at a logarithmic scale and depends on the number k only. Averaging at a logarithmic scale of radar data, which themselves result from the linear averaging over k independent samples or looks, introduces an offset dependent on the number k only. This offset does not depend on the mean level of the signal and therefore is the same for all Rayleigh-fading objects in the scene.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>