During the observation, the data regularly receive a time stamp, usually based on a caesium time standard or hydrogen maser at the observatory plus a signal from the Global Positioning System of satellites (GPS; see [96]). The TOA is defined as the arrival time of some fiducial point on the integrated profile with respect to either the start or the midpoint of the observation. Since the profile has a stable form at any given observing frequency (see Section 2.3), the TOA can be accurately determined by cross-correlation of the observed profile with a high S/N “template” profile obtained from the addition of many observations at the particular observing frequency.

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

Here, is the flux density of the pulsar, and are the receiver and sky noise temperatures, is the antenna gain, is the observing bandwidth, is the integration time, is the pulse width and is the pulse period (we assume ). Optimal results are thus obtained for observations of short period pulsars with large flux densities and small duty cycles (i.e. small ) using large telescopes with low-noise receivers and large observing bandwidths.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 dedispersion 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 dedispersion [134, 229] the incoming signals are dedispersed 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 online either using high speed devices such as field programmable gate arrays [65, 281] or completely in software [337, 344]. 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 [135] of features on nanosecond timescales in pulses from the 33-ms 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 [125], these incredibly bright bursts originate from regions less than 1 m in size.

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