Analysis of discrete implementation of generalized cross correlator

Abstract

A common discrete implementation of the cross correlator uses a parabolic fit to the peak when the delay is not an integral multiple of the sampling period. This correspondence analyzes and assesses the pitfalls of this approach. It is shown that this yields a biased estimate of the time delay, with both the bias and variance of the estimate dependent on the location of the delay between samples, SNR, signal and noise bandwidths, and the prefilter or window used in the generalized correlator.

Subsample interpolation strategies for sensorless freehand 3D ultrasound

“…One of the few papers to address lateral interpolation is [9], in which the grid slopes algorithm is shown to be relatively unbiased in comparison with other techniques. More prone to bias are cosine [3,5,6], cubic spline [9] and parabolic interpolation [2,3,7]. Fourier reconstruction [3] has been shown to work well in the axial direction, provided the signal is bandlimited and the sampling frequency above the Nyquist limit.…”

A Novel Bio-Inspired Acoustic Ranging Approach for a Better Resolution Achievement

“…It has attracted considerable research attention over the past few decades in different technologies including radar, sonar, seismology, geophysics, ultrasonics, communication and medical ultrasound imaging. Various techniques are reported in the literature (Knapp & Carter, 1976;Carter, 1979;1987;Boucher & Hassab, 1981;Chen et al, 2004) and a complete review can be found in (Chen et al, 2006). Chen et.al in their review consider critical techniques, limitations and recent advances that have significantly improved the performance of time-delay estimation in adverse environments.…”

Estimation of subsample time delay differences in narrowband ultrasonic echoes using the Hilbert transform correlation

“…It introduces however an ambuigity since there can be several zero crossings, particularly if the cross correlation is narrowband. The Hilbert transform is defined as [2] 03 (4) where the integral is a Cauchy Principal Value (CPV) and …”

“…For correlator based estimators this is due to peak ambiguity, i.e., the possibility of selecting the wrong peak of the correlation. These estimators also need some kind of interpolation to obtain subsample resolution, e.g., a parabolic fit [4], [ l l], [14]. In 1121, a comparison of several methods is made.…”