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

Abstract

Binary phase-only filters (BPOFs) 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 that is the binarized Hartley transform. In this paper, the noise performance of the binarized Hartley phase-only filter is analyzed and compared with other BPOFs as well as with the phase-only and matched filters. It is well known that the matched filter optimizes the 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.