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For an arbitrary Hermitian period-$T$ Jacobi operator, we assume aperturbation by a Wigner-von Neumann type potential to devise subordinatesolutions to the formal spectral equation for a (possibly infinite) real set,$S$, of the spectral parameter. We employ discrete Levinson type techniques toachieve this, which allow the analysis of the asymptotic behaviour of thesolution. This enables us to construct infinitely many spectral singularitieson the absolutely continuous spectrum of the periodic Jacobi operator, whichare stable with respect to an $l^1$-perturbation. An analogue of thequantisation conditions from the continuous case appears, relating thefrequency of the oscillation of the potential to the quasi-momentum associatedwith the purely periodic operator.

Spectral results for perturbed periodic Jacobi matrices using the discrete Levinson technique