Successful pulsar timing requires optimal TOA precision which largely depends on the signal-to-noise
ratio (S/N) of the pulse profile. Since the TOA uncertainty is roughly the pulse width divided by
the S/N, using Equation (3
) we may write the fractional error as
One of the main problems of employing large bandwidths is pulse dispersion. As discussed in
Section 2.4, pulses emitted at lower radio frequencies travel slower and arrive later than those
emitted at higher frequencies. This process has the effect of “stretching” the pulse across a
finite receiver bandwidth, increasing and therefore increasing
. For normal pulsars,
dispersion can largely be compensated for by the incoherent de-dispersion process outlined in
Section 3.1.
The short periods of millisecond pulsars offer the ultimate in timing precision. In order to fully exploit
this, a better method of dispersion removal is required. Technical difficulties in building devices with very
narrow channel bandwidths require another dispersion removal technique. In the process of coherent
de-dispersion [110, 185] the incoming signals are de-dispersed over the whole bandwidth using a filter
which has the inverse transfer function to that of the interstellar medium. The signal processing
can be done on-line either using finite impulse response filter devices [16] or completely in
software [290, 297]. Off-line data reduction, while disk-space limited, allows for more flexible analysis
schemes [21].
The maximum time resolution obtainable via coherent dedispersion is the inverse of the total
receiver bandwidth. The current state of the art is the detection [111] of features on nanosecond
timescales in pulses from the
pulsar B0531+21 in the Crab nebula shown in Figure 21
.
Simple light travel-time arguments can be made to show that, in the absence of relativistic
beaming effects [104], these incredibly bright bursts originate from regions less than
in
size.
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