PSRCHIVE user documentation: psrstat

On-Pulse and Off-Pulse Region Finding Algorithms and Options

cumulative

The on-pulse region is estimated using the cumulative profile, and is defined as the region between the last bin to fall below a threshold fraction [default: 10%] of the total flux and the first bin to rise above 1.0-threshold times the total flux.

The cumulative profile is computed by replacing the value in each phase bin with the integrated sum of all preceding phase bins; stated differently, the cumulative profile is to the pulse profile as the cumulative probability is to the probability density (i.e. the pulse profile is treated as a histogram). This raises some important points for consideration:

  1. The integrated sum of all preceding phase bins depends on the rotational phase of the pulse profile. Stated differently, how is the cumulative distribution defined on a circle (i.e. when the probability density is cyclic)?
  2. The variance in each phase bin of the cumulative sum increases linearly; therefore, the noise statistics that should be applied when comparing integrated flux to thresholds should also vary with phase and will depend on the rotational phase of the pulse profile.
In an incomplete attempt to work around the first issue, caused by the cyclic property of pulse profiles, the PeakCumulative class computes the cumulative profile twice; it shifts the profile by 180 degrees between trials and takes the solution that results in the narrowest pulse.

The second issue (linear increase in variance with pulse phase) is ignored in the current implementation.

minimum

This algorithm can be used to find either the on-pulse or off-pulse region; by default, it is configured to search for the off-pulse (minimum). It first smooths the pulse profile using a box-car function (e.g. mean or median) and then sets the off- or on-pulse region to span the width of the box-car, centred on where the smoothed profile reaches its minimum [default] or maximum value.

Because it searches for an extremum in noisy data, this algorithm will always under-estimate the true off-pulse mean or over-estimate the true on-pulse mean.