Efficient algorithm for designing a ternary valued filter yielding maximum signal to noise ratio

Abstract

An efficient algorithm for designing a ternary valued filter yielding the highest signal to noise ratio (SNR) is utlined. Numerical evaluations using the image of a tank indicate that using such a filter can provide an improvement in SNR of ~5 dB over the conventional binary phase-only filter (BPOF). This is superior to the 1-dB improvement obtained for that image by varying the threshold line angle (TLA) in filter binarization. Simulation results are presented. They agree with the numerically computed SNRs.

Advanced Concepts in Distortion-Invariant Phase-Only Filter Design

“…The POFs and BPOFs as introduced originally are allpass, i.e., these filters have unit magnitude at all frequencies. Recently, it has been shown that the noise tolerance 8 , 9 and correlation peak sharpiness 1 0 of these filters can be maximized by setting some frequencies to have zero magnitude. The set of frequencies for which the filter magnitude is nonzero is known as the Region of Support (ROS).…”

“…With the help Eq. (9). To prove that this is true, let us assume that the filters of simulation examples, we have shown that for the particular result in angle 13i * 15* when we use Eq.…”

“…(4) must equal the phase of the complex correlations response at the origin when this BPOF is B. Binary Phase-Only Filters used. When the BPOF of this form, using 0 as the We have shown elsewhere 9 that the optimal BPOF TLA, produces the same 0 as the phase of the correla-(OBPOF) takes the form tion response at origin, we call such a BPOF a feasible…”

“…(26) and (39 (31 ) and (41 )). The other type of results that we refer to as 'simtulatiorn results' are obtained bv producing correlation outputs and then estimating SNtRs and i('1Fs from equations (2) and (9). PCE can be obtained from single correlation output.…”

“…In ordy,' or real. 9 Since a constant factor times the magniSection 2 we introduce a simple SNR model that includes tude of H does not affect the SNR in Eq. (4), these optidetector-noise effects.…”