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Abstract

Geodetic and geophysical observations result in discretization of the object or phenomenon of interest. The observation involves errors on the knowledge of a continuous signal due to the loss of information in the sampling procedure. Analytical formulation of the L1-norm and L2-norm sampling error of a periodic signal is determined, which embodies the amplitude, phase, bias, and periodicity of the sampling error. Additionally, observations are normally takes time, therefore cannot be considered to refer to an epoch in time (or space). During this time span, temporal variations of the observable alias the measurement. Similarly, often a phenomenon considered to be point-wise consists of integrated information of an area. The error effect of the temporal and spatial smoothing is determined here for 1-D and 2-D signals, furthermore a method for de-smoothing is presented.