Correlation Function for a 1/f Spectrum

The performance of ground surveillance radars depends on the spatial correlation, or spectrum, of the radar returns. Many radar terrain images are suspected to have a I/f spatial spectrum. This spectrum is thought to be difficult to handle mathematically in modeling and analysis because of its singularity at zero frequency and its infinite energy. A two-dimensional, band-limited I/f spectrum has neither of these problems: this is convenient for modeling and analysis in any practical system because the sensor measuring of an image always introduces band limiting, even if the natural phenomena are not band limited. Also shows the presence of terrain with a 1/f spectrum will not be readily apparent from the correlation function of the terrain image because the shape of the correlation function is largely determined by the sensor band limit and not by the underlying spectrum.