The Effects of Bias on Polarity-Coincidence Detection

Citation

Squire, William Dean (1964) The Effects of Bias on Polarity-Coincidence Detection. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/MDEF-MH25. https://resolver.caltech.edu/CaltechETD:etd-12092002-094452

Abstract

A polarity-coincidence detector with biased polarity indicators (biased hard limiters) is studied to determine the effects of the bias on the detector output mean value, output variance, and output signal-to-noise power ratio. The mean value of the detector output is derived for the case of Gaussian input signal and Gaussian input noise, with arbitrary spectra for the signal and noise. The mean value is expressed as a function of the input signal-to-noise power ratio, and as a function of the biases in the input channel and the reference channel polarity indicators. It is shown that the effect of bias is to introduce a spurious component in the output mean value. The variance of the defector output is derived for the cage of Gaussian input signal and Gaussian input noise, with RC low-pass spectra for signal and noise, for small input signal-to-noise power ratios only. The variance is expressed as a function of the biases in the input channel and reference channel polarity indicators, and as a function of the input signal-to-noise band-width radio. It is shown that the effect of bias is to introduce a spurious component in the output variance. The output signal-to-noise power ratio (the square of the output mean divided by the output variance) is derived for both an ideal polarity-coincidence detector (no bias) and for a biased polarity-coincidence detector. The output signal-to-noise power ratio is expressed as a function of the input signal-to-noise power ratio, the biases in the input channel and the reference channel polarity indicators, and input signal-to-noise band-width ratio, for small input signal-to-noise power ratios only. It is shown that the output signal-to-noise power ratio of an ideal polarity-coincidence detector is degraded from that of a correlation detector. When the input signal-to-noise band-width ratio is unity, the degradation is about 1.4 db. The degradation increases to about 2.2 db. when the input signal-to noise band-width ratio becomes either very small or very large. It is also shown that the output signal-to-noise power ratio of a biased polarity-coincidence detector is degraded from that of an ideal polarity-coincidence detector. A simple expression for the degradation is presented. Limits on the biases are given, such that when the biases are smaller than these limits, the degradation of the output signal-to-noise power ratio is negligible.

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