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Trade-offs in nonlinearly recorded matched filters

Here, we introduce a general nonlinearly-recorded matched filter that we term as the Fractional Power Filter (FPF). The Classical Matched Filter (CMF), the Phase-Only Filter (POF) and the Inverse Filter (IF) are special cases of the FPF. It is shown that by varying the degree of nonlinearity used in forming the FPFs, we can trade-off the noise tolerance of the filter against its correlation peak sharpness. It is also shown that the fractional power concept can be extended to distortion-invariant composite filters.