Successful pulsar timing requires optimal TOA precision which largely depends on the signaltonoise 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 () using large telescopes with lownoise 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 [110, 185] 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 finite impulse response filter devices [16] or completely in software [290, 297]. Offline data reduction, while diskspace 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 traveltime 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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