The processing of NMR data has traditionally relied on the Fourier Transform (FT) due to its simplicity, speed, and usefulness in visualising the spectrum [1,2]. The FT, however, is inherently limited in resolution and requires significant, and largely manual, pre and post-processing, which includes phasing, baseline correction, apodisation, and peak picking [3]. High resolution NMR spectroscopy, on the other hand, offers a large number of data points that would theoretically enable close peaks to be resolved. Although FT-based algorithms are computationally simple, they are not able to capitalize on this offering to achieve the highest permissible resolution. Attempts to circumvent these drawbacks and achieve a higher resolution have generally focused on subspace and singular value decomposition methods such as the celebrated matrix pencil (MPM) [4]. Such methods are theoretically able to achieve the required resolution, but come with a substantial and onerous computational cost that makes them impractical for fids with a large number of data points. In recent work we focused on this problem and proposed a localisation strategy for the MPM that significantly reduces its computational cost and enables its implementation in high resolution NMR [5]. The new algorithm, LocMaP, is capable of achieving superior resolution, accuracy and reliability with respect to the classical MPM due to its full use of the data dimensionality that is offered by the number of data points. In this work, we overview LocMaP and present an extended implementation of the method to cover the full spectral width of the fid. We also demonstrate the improved performance of the algorithm using experimentally acquired NMR data.