A first-order nonuniform multilevel quantized DPLL is analyzed in the presence of a phase- and frequency-step signal plus Gaussian noise. The system is modeled as a homogeneous finite Markov chain. In this way, closed-form expressions are obtained for the steady-state probabilities, the mean and rms values of the phase error, and the mean number of samplings to slip a cycle or to reach acquisition. Numerical results are also presented.
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D'Andrea et al. (1980) studied this question.
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