Fast Correlation Estimation by a Random Reference Correlator

Fast correlation calculations are needed in many technological and scientific fields. Conventional digital correlators require fast and expensive analog-to-digital converters and digital multipliers. This paper describes the implementation of a fast, inexpensive, and unbiased correlation estimator. The estimator is based on the ternary Random Reference Correlation (RRC). Unbiasness is achieved by the addition of statistically independent, uniformly distributed auxiliary noise sources to the input signals. The use of a ternary quantizer eliminates the need of an A/D converter and multiplier, which are replaced by relatively simple logic circuits. A prototype system is described. Real-time correlations of signals, sampled at a rate of about 4 kHz, were achieved by the prototype system. Correlation errors were found to be in the range of one percent. Increasing the internal clock frequency and using faster logic components will improve system performance to perform real-time correlation calculations of signals sampled at 50 kHz.