Discrete Fourier preprocessing transforms for the binary phase-only filter

Two useful discrete Fourier preprocessing transforms (DFPTs), say, class 1 and class 2, are applied to the binary phase-only filter. The class-1 DFPT is very close to the discrete Fourier transform (DFT); therefore it preserves the properties similar to those for the DFT. The Class-2 DFPT's are location sensitive and are able to recognize the partial-shape-like input pattern that is the partial set of the pattern in the filter. The Class-2 DFPT's generate a delta-function-like correlation peak whose intensity is larger than that obtained by the DFT. These are different from the DFT-based binary phase-only filter. The elements of the DFPT's are very simple, containing only ±1 and 0; some even contain sparse 61 values and plenty of zeros. Therefore the DFPT's are suitable for either optical or electrical implementation.