Analysis Of Binarized Hartley Phase-Only Filter Performance With Respect To Stochastic Noise

Binary phase-only filters (BPOF) are a viable candidate for the replacement of matched filters in real-time image processing and pattern recognition applications. The original BPOFs were binarized versions of the real or imaginary parts of the Fourier transform. Recently, a filter has been proposed which is the binarized Hartley transform. In this paper, the noise performance of the binarized Hartley phase-only filter is analyzed and compared to other BPOFs as well as the phase-only and matched filter. It is well known that the matched filter optimizes signal-to-noise ratio. Further, it can be shown that the matched filter phase is the optimum phase-only filter. A bound on the BPOF signal-to-noise ratio relative to that of the phase-only filter is derived. Finally, the analysis is applied to the generalized form of the binarized Hartley transform.