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In this paper, we derive a novel implementation of some very computationally demanding matched filter-bank-based spectral estimators, namely the amplitude and phase estimator (APES), the amplitude spectrum Capon (ASC) estimator, and the power spectrum Capon (PSC) estimator. Filter-bank-based spectral estimation methods that adopt data-dependent filter banks can provide spectra characterized by a significantly improved resolution compared to classical approaches. However, the computational complexity of the currently available implementation algorithms, is extremely high. A novel technique is introduced that provides efficient algorithms for the computation of the APES, ASC, and PSC spectra. The proposed method is based on suitable displacement representations of all pertinent data matrices, that are subsequently utilized for the computation of the associated complex valued polynomials. The computational complexity of the proposed algorithms is lower than all relevant existing methods.