Digital Alias-free Signal Processing

18

Adapting Signal Processing to Sampling Nonuniformities

Introducing irregularities into a sampling process leads to the nonorthogonality of nonuniformly sampled discrete basis functions. If the DFT is performed on such a basis this nonorthogonality leads to significant errors in the estimation of signal parameters. Apparently the pattern of the nonuniform sampling point sequence defines this nonorthogonality and the errors related to it. However, at intentional pseudo-randomization of sampling this pattern is given a priori. Therefore it should be possible to use this information to suppress the errors caused by sampling nonuniformities. In other words, it should be possible to adapt processing of nonuniformly sampled signals to the involved specific sampling nonuniformity, which should lead to significantly better nonuniform signal processing results. However, it is not clear how to achieve this. One approach to this problem is suggested in Chapter 15 and is further considered here. This type of adapted signal processing is discussed for applications requiring processing of both the temporal and spatial signals.

18.1 Cross-interference Coefficients

As shown in Section 15.2, irregularities of the sampling point stream lead to cross-interference between the signal components. It is hard to overestimate the role this effect plays in processing nonuniformly sampled signals. There is no doubt that it is impossible to achieve high precision at processing this type of digital signal ...