Abstract: A method and apparatus for determining the value of a Doppler frequency shift component .DELTA.f present in a signal f .+-. .DELTA.f employing a correlation process which utilizes the Mellin transform and is scale invariant. The location of the correlation peak in the reference coordinate system used provides a measure of the magnitude of .DELTA.f. The sequence of steps involved in the correlation process when optical apparatus is used include forming a transmittance pattern of the signal f .+-. .DELTA.f, which has a horizontal scale that is the natural log of the time scale of the original signal, forming a similarly scaled transmittance pattern of the reference signal, f, and utilizing the first patttern in the input plane of a frequency plane correlator that has a holographic matched spatial filter that is produced from the second pattern and contains a term corresponding to the conjugate of the Mellin transform of the reference signal in its frequency plane.

Abstract: A method and electro-optical apparatus for correlating two functions, f.sub.1 (x,y) and f.sub.2 (x,y) which are shifted, scaled and rotated versions of each other without loss of signal-to-noise and signal-to-clutter ratios as compared to the autocorrelation case. The coordinates of two correlation peaks provide an indication of the scale and orientation differences between the two functions. In performing the method, the magnitudes of the Fourier transforms of the functions are obtained, .vertline.F.sub.1 (.omega..sub.x, .omega..sub.y).vertline. and .vertline.F.sub.2 (.omega..sub.x,.omega..sub.y).vertline. and then a polar coordinate conversion is performed, and the resultant functions F.sub.1 (r,.theta.) and F.sub.2 (r,.theta.) are logarithmically scaled in the r coordinate. The functions thus produced F.sub.1 (e.sup..rho.,.theta.) and F.sub.2 (e.sup..rho.,.theta.) are Fourier transformed to produce the Mellin transforms M.sub.1 (.omega..sub..rho., .omega..sub..theta.) and M.sub.2 (.omega..sub..rho.,.omega.

Abstract: A real-time radar processor utilizing a coherent optical system for provig target fine range and Doppler/azimuth angle data with increased signal-to-noise and signal-to-clutter ratios. Radar signals detected by a linear phased array or successive echo signals detected by the receiver are arranged in a 2-D input format for parallel processing in a multi-channel 1-D optical correlator. Target range and azimuth angle reference data may be stored in a matched spatial filter hologram or recorded in a 2-D format similar to that of the detected radar signals according to which of three different correlation configurations are employed in the optical system. The coordinates of the correlation peak in the output plane of the correlator are proportional to the target's fine range and Doppler/azimuth angle, depending upon the type of radar signals being processed.