Ewan D. Barr edited minres2.tex  over 8 years ago

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It is reasonable to assume that more extreme pulsars with faster spin periods than are currently known will be found given the sensitivity of SKA1. If we assume a J0437$-$4715-like pulsar with a 500-$\mu$s spin period, it would require $\sim$200~ns time resolution observations to be able to fully resolve all of the structure in its pulse profile. Na\"ively speaking 200~ns time resolution would imply 5~MHz frequency channels via a reciprocal bandwidth argument. However due to the shape of the impulse response of polyphase filterbanks, it is not possible to achieve 200-ns time resolution with 5-MHz frequency channels while meeting the stringent spectral leakage requirements of SKA1. Through simulation of various polyphase filters, we find that using a 22-tap filter allows us to meet the spectral purity requirements of SKA1 and achieve an effective time resolution of two time samples (i.e. 200~ns for a 10-MHz channel).  The 200-ns resolution described above is required only 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 interstellar medium (ISM), we consider 200-ns time resolution to be unnecessarily high for SKA1\_Low. The pulsar-related science goals of SKA1\_Low (probing the ISM, emission mechanism studies, etc.) do not require ultra-high such high  time resolution; therefore, a larger sampling interval would be acceptable. Currently the LFAA design implies that channel widths of 800~kHz will be delivered to the CSP for processing. By the same arguments as above, this would provide $\sim$2.5~$\mu$s effective time resolution. This is $\sim3$ times better than the resolution achievable with LOFAR. We consider this resolution to be acceptable for achieving pulsar science goals with SKA1\_Low. The above frequency and time resolutions allow us to suggest rewordings for requirements 2691 and 2692 such that they are framed in terms of fractional resolutions of spin period with an absolute resolution limit: