deletions | additions       diff --git a/minres.tex b/minres.tex  index 66e19e5..26fd578 100644  --- a/minres.tex  +++ b/minres.tex 
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where $k$ is the slope of the line fit to the spectrum of the pulsar, $S/N$ is the signal-to-noise ratio at the y-intercept (approximately the $S/N$ in the first harmonic) and it is assumed that harmonics past $S/N\sim1$ are not important. By eye, increasing the S/N by two orders of magnitude will add around 100 to 300 harmonics for 0437 and 2241, so 2048 phase bins should suffice for observing these pulsars with SKA1.  Now, it is reasonable to assume that more extreme pulsars with faster spin periods than currently known will be found given the sensitivity of SKA1. Taking the example of a sub-millisecond pulsar with a 500 $\mu$s spin period that requires 2048 phase bins to resolve all the structure in its pulse profile, we find that this implies a maximum time resolution of 200~ns. Na\"ively speaking 200~ns time resolution would imply 5~MHz frequency channels via a reciprocal bandwidth argument. However due to the nature of the temporal response of polyphase filterbanks, we suggest that the required channel width here is actually closer to 10~MHz (the true required channel  bandwidth here depends on the exact nature of the polyphase filter applied to the data). The 200~ns resolution described above is only required for high-precision pulsar timing, where we need to resolve the highest spin harmonics in the pulsars we observe. Due to the deleterious effects of the ISM, we consider 200~ns time resolution to be unnecessarily high for SKA1\_Low. For the pulsar-related science goals of SKA1_Low, a coarser resolution would be acceptable. Currently the SKA1\_Low LFAA design implies channel widths of 800~kHz being delivered to the CSP for processing. By the same arguments as above, this would provide roughly 1.6~$\mu$s effective time resolution. This is roughly 4 times better than the resolution acheivable with LOFAR.   The  above frequency and time resolutions allow us to suggest rewording for requirements 2691 and 2692 such that they are framed in terms of fractional resolutions of spin period with an absolute limit resolution limit:  \begin{itemize}  \item \textbf{SKA1-SYS\_REQ-2961:} \textit{\bf SKA1\_Mid Pulsar Timing resolution.} The SKA1\_Mid when in pulsar timing mode shall resolve a pulsar's pulse profile with up to 2048 equal-width, contiguous phase bins  of 200 ns: maximum resolution 200~ns.  \item \textbf{SKA1-SYS\_REQ-2962:} \textit{\bf SKA1\_Low Pulsar Timing resolution.} The SKA1\_Low when in pulsar timing mode shall resolve a pulsar's pulse profile with up to 2048 equal-width, contiguous phase bins of maximum resolution 1.6~us.  \end{itemize}  These two requirements should constrain both the acceptable channel widths provided to the SKA1 pulsar timing instruments and the polyphase filterbank design used to channelise the digitized baseband voltages. We envisage these requirements as being identical at level 2:  \begin{itemize}  \item \textbf{SKA-CSP.MID\_REQ-2961-00:} \textit{\bf CSP\_Mid Pulsar Timing resolution.} The CSP\_Mid when in pulsar timing mode shall resolve a pulsar's pulse profile with up to 2048 equal-width, contiguous phase bins of maximum resolution 200~ns.  \item \textbf{SKA-CSP.LOW\_REQ-2962-00:} \textit{\bf CSP\_Low Pulsar Timing resolution.} The CSP\_Low when in pulsar timing mode shall resolve a pulsar's pulse profile with up to 2048 equal-width, contiguous phase bins of maximum resolution 1.6~us.  \end{itemize}  At level 3 it is necessary to define ``effective time resolution'' to provide design constraints to the SKA1 beamformers  \begin{itemize}  \item \textbf{SKA1-SYS\_REQ-2961:} \textbf{SKA-CSP.MID.CBF\_REQ-2961-00-00:}  \textit{\bf SKA1\_Mid CSP\_Mid  Pulsar Timing resolution.} The SKA1\_Mid CSP\_Mid  when in pulsar timing mode shall resolve a pulsar's pulse profile with up  to better than 0.05\% 2048 equal-width, contiguous phase bins  ofits spin period with a  maximum resolution of 200 ns. 200~ns.  \item \textbf{SKA1-SYS\_REQ-2962:} \textbf{SKA-CSP.LOW.CBF\_REQ-2962-00-00:}  \textit{\bf SKA1\_Low CSP\_Low  Pulsar Timing resolution.} The SKA1\_Low CSP\_Low  when in pulsar timing mode shall resolve a pulsar's pulse profile with up  to better than 0.05\% 2048 equal-width, contiguous phase bins  ofits spin period with a  maximum resolution of 200 ns. 1.6~us.  \end{itemize}  These two requirements should constrain both the acceptable channel widths provided to the SKA1 pulsar timing instruments and the polyphase filterbank design used to channelise the digitized baseband voltages.  While the above requirements would appear to satisfy the needs of the pulsar community, the practicality of these requirements is seriously undermined by the computational burden of performing coherent dedispersion at low frequencies on 10 MHz channels. This burden only becomes more difficult to manage as we move to larger dispersion measures (DMs). As such, the requirements suggested above need a modifier that allows them to change with DM. This modifier is provided by the physical limitations that interstellar scattering places on the minimum resolvable feature width in a pulse profile. This is discussed in detail below.