Noise and Error Effects
Robert J. Marks · Oxford University Press eBooks · 2009
Exact interpolation using the cardinal series from unaliased samples assumes that (a) the values of the samples are known exactly, (b) the sample locations are known exactly (c) an infinite number of terms are used in the series, and (d) sampling is performed at a sufficiently fast rate. Deviation from these requirements results in interpolation error due to (a) data noise (b) jitter (c) truncation and (d) aliasing respectively. The perturbation to the interpolation from these sources of error is the subject of this chapter. If noise is superimposed on sample data, the corresponding interpolation will be perturbed. In this section, the nature of this perturbation is examined. The effect of data noise on continuous sampling interpolation is treated in Section 10.3.1.2. The multidimensional case is the topic of Section 8.10.2. Suppose that the signal we sample is corrupted by real additive zero mean wide sense stationary noise, ξ (t).