Ambiguities in the harmonic retrieval problem using non-uniform sampling

Harmonic retrieval is an important problem in signal processing and has received a lot of attention. However, solutions to the problem are generally based on uniform sampling with a rate equal to or greater than the Nyquist rate, in order to avoid certain overlapping (ambiguities) of the spectrum. An investigation is carried out for the detection and estimation of ambiguities in the harmonic retrieval problem, in the case of non-uniform sampling at a rate lower than the Nyquist rate, using differential geometry. An approach for the calculation of the maximum number of ambiguous generator sets of frequencies, associated with a given non-uniform sampling, is also presented and it is then used for identifying unambiguous groups of irregular samples