Calculation and Uncertainty of Fast Radio Burst Structure Based on Smoothed Data

Studies of the time-domain structure of fast radio bursts (FRBs) require an accurate estimate of the FRB dispersion measure in order to recover the intrinsic burst shape. Furthermore, the exact dispersion measure is itself of interest when studying the time evolution of the medium through which multiple bursts from repeating FRBs propagate. A commonly used approach to obtain the dispersion measure is to take the value that maximizes the FRB structure in the time domain. However, various authors use differing methods to obtain this structure parameter and do not document the smoothing method used. Furthermore, there are no quantitative estimates of the error in this procedure in the FRB literature. In this article, we present a smoothing filter based on the discrete cosine transform, and show that computing the structure parameter by summing the squares of the derivatives and taking the square root (that is, the 2-norm, Σ ( d / dt ) 2 ) immediately lends itself to the calculation of the uncertainty of the structure parameter. We illustrate this with FRB 20181112A and FRB 20210117A data, which were detected by the Australian Square Kilometre Array Pathfinder, and for which high-time-resolution data are available.