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; [64]). The TOA of this mean pulse is then defined as the arrival time of some fiducal point on the profile. Since the mean profile has a stable form at any given observing frequency (§ 2.2), the TOA can be accurately determined by a simple cross-correlation of the observed profile with a high signal-to-noise ``template'' profile obtained from the addition of many observations of the pulse profile at the particular observing frequency.

Success in pulsar timing hinges on how precisely the fiducial point can be determined. This is largely dependent on the signal-to-noise ratio (SNR) of the mean pulse profile. The uncertainty in a TOA measurement is given roughly by the pulse width divided by the SNR. Using Equation (3), we can express this as a fraction of the pulse period:

In this expression
and
are the receiver and sky noise temperatures,
*G*
is the gain of the antenna,
is the observing bandwidth,
is the integration time,
*W*
is the pulse width and
*P*
is the pulse period (we assume
). Optimum results are thus obtained for observations of short
period pulsars with large flux densities and narrow duty cycles (*W*
/
*P*) 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 § 2.3, the velocity of the pulsed radiation through the ionised interstellar medium is frequency-dependent: pulses emitted at higher radio frequencies travel faster and arrive earlier than those emitted at lower frequencies. This process has the effect of ``stretching'' the pulse across a finite receiver bandwidth, reducing the apparent signal-to-noise ratio and therefore increasing . For most normal pulsars, this process can largely be compensated for by the incoherent de-dispersion process outlined in § 3.1 .

To exploit the precision offered by millisecond pulsars, a more precise 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 [90] 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 either on-line using finite impulse response filter devices [14] or off-line in software [219, 222]. The on-line approach allows for large bandwidths to be employed and real-time viewing of the data. Off-line reduction, while slow and computationally expensive, allows for more flexible data reduction schemes as well as periodicity searches to be carried out.

The maximum time resolution obtainable via coherent dedispersion is the inverse of the receiver bandwidth. For bandwidths of 10 MHz, this technique makes it possible to resolve features on time-scales as short as 100 ns. This corresponds to probing regions in the neutron star magnetosphere as small as 30 m!

Binary and Millisecond Pulsars at the New Millennium
Duncan R. Lorimer
http://www.livingreviews.org/lrr-2001-5
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