The effects of aliasing and lock-in processes on palaeosecular variation records from sediments

Studies of sedimentary records of palaeointensity variation report periods as long as 50 kyr. Archaeointensity data show geomagnetic periods of 2 kyr with large ampli-tudes. Sampling of the sedimentary records can be as coarse as 8 kyr, so the apparent long periods could be caused by aliasing. The sedimentary lock-in process could smooth the record and remove short periods, thereby preventing aliasing from occurring. We examine possible effects of aliasing by creating a 100-kyr-long synthetic sequence of palaeointensity variation with a similar spectrum to that of archaeomagnetic data from the last 12 kyr and resampling at longer intervals. With no lock-in smoothing,aliasing produces spurious energy in the spectra at long periods. When smoothing by the sedimentation process is applied, the amplitudes of the aliased peaks are reduced but still cause significant, spurious, long-period energy in the spectra for some sedi- mentation rates. We restrict our analysis to palaeointensity data but similar problems may also exist for coarsely sampled directional data. To avoid aliasing we recommend a maximum sampling interval of 2 kyr

Information Loss and Anti-Aliasing Filters in Multirate Systems

This work investigates the information loss in a decimation system, i.e., in a downsampler preceded by an anti-aliasing filter. It is shown that, without a specific signal model in mind, the anti-aliasing filter cannot reduce information loss, while, e.g., for a simple signal-plus-noise model it can. For the Gaussian case, the optimal anti-aliasing filter is shown to coincide with the one obtained from energetic considerations. For a non-Gaussian signal corrupted by Gaussian noise, the Gaussian assumption yields an upper bound on the information loss, justifying filter design principles based on second-order statistics from an information-theoretic point-of-view.Comment: 12 pages; a shorter version of this paper was published at the 2014 International Zurich Seminar on Communication