Spiders are able to extract crucial information, such as the location prey, predators, mates, and even broken threads from propagating web vibrations. The complex structure of the web suggests that the morphology itself might provide computational support in form of a mechanical signal processing system -often referred to as morphological computation. We present preliminary results on identifying these computational aspects in naturally spun webs. A recently presented definition for physical computational systems, consisting of three main elements: (i) a mathematical part, (ii) a computational setup with a theoretical and real part, and (iii) an interpretation, is employed for the first time, to characterize these morphological computation properties. Signal transmission properties of a real spider orb web, as the real part of a morphological computation setup, is investigated in response to step transverse inputs. The parameters of a lumped system model, as the theoretical part of a morphological computation setup, are identified empirically and with the help of an earlier FEM model for the same web. As the possible elements of a computational framework, the web transverse signal filtering, attenuation, delay, memory effect, and deformation modes are briefly discussed based on experimental data and numerical simulations.