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21 September 2007 High-resolution correlation
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In the basic correlation process a sequence of time-lag-indexed correlation coefficients are computed as the inner or dot product of segments of two signals. The time-lag(s) for which the magnitude of the correlation coefficient sequence is maximized is the estimated relative time delay of the two signals. For discrete sampled signals, the delay estimated in this manner is quantized with the same relative accuracy as the clock used in sampling the signals. In addition, the correlation coefficients are real if the input signals are real. There have been many methods proposed to estimate signal delay to more accuracy than the sample interval of the digitizer clock, with some success. These methods include interpolation of the correlation coefficients, estimation of the signal delay from the group delay function, and beam forming techniques, such as the MUSIC algorithm. For spectral estimation, techniques based on phase differentiation have been popular, but these techniques have apparently not been applied to the correlation problem . We propose a phase based delay estimation method (PBDEM) based on the phase of the correlation function that provides a significant improvement of the accuracy of time delay estimation. In the process, the standard correlation function is first calculated. A time lag error function is then calculated from the correlation phase and is used to interpolate the correlation function. The signal delay is shown to be accurately estimated as the zero crossing of the correlation phase near the index of the peak correlation magnitude. This process is nearly as fast as the conventional correlation function on which it is based. For real valued signals, a simple modification is provided, which results in the same correlation accuracy as is obtained for complex valued signals.
© (2007) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
D. J. Nelson "High-resolution correlation", Proc. SPIE 6697, Advanced Signal Processing Algorithms, Architectures, and Implementations XVII, 669709 (21 September 2007);


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