Apparatus for convoluting complex functions expressed as fourier series

摘要

The azimuth beamspread smear effect in a radar image is simulated by convoluting a terrain function with an antenna gain function for each sweep that the target object is within the antenna gain bandwidth. The initial grid map of elevation-reflectance terrain data is combined with aircraft position and antenna orientation data to provide composite terrain data required to compute a terrain function along each range arc. Each radar sweep generates a data raster of composite terrain data for the R range points within that sweep. The antenna bandwidth is a small sector, M sweeps wide, which moves across the scanned sector as the antenna rotates forming R range arcs. A constantly changing block of composite terrain data for the M sweeps and R points must be continuously maintained to generate the beamspread smear by convolution of the terrain function and the antenna function. The MxR block of terrain data is held in the form of a Fourier series for each range arc. Each range arc Fourier series requires a (2N+1) memory capacity (N sine terms, plus N cosine terms, plus one constant term). The total memory requirement for the MxR data block in Fourier series form is (2N+ 1)R. The terrain Fourier series for each point along the target range arc is multiplied by the antenna gain at that point (also expressed as a Fourier series) to provide the terrain-gain point product, or return signal power for that point. The terrain function Fourier series constantly changes as the antenna rotates, and is generated from the composite terrain data through an updating technique in which a new leading sweep is added to the MxR block and the previous trailing sweep is dropped. The antenna gain pattern is typically symmetrical and has a Fourier series with N term plus a constant. The antenna function is fixed for each antenna model, mode and operating circumstance.