Genomic signal processing has been used successfully in bioinformatics to analyze biomolecular sequences and gain varied insights into DNA structure, gene organization, protein binding, sequence evolution, etc. But challenges remain in finding the appropriate spectral representation of a biomolecular sequence, especially when multiple variable-length sequences need to be handled consistently. In this study, we address this challenge in the context of the well-studied problem of classifying genomic sequences into different taxonomic units (strain, phyla, order, etc.). We propose a novel technique that employs signal processing in tandem with Gaussian mixture models to improve the spectral representation of a sequence and subsequently the taxonomic classification accuracies. The sequences are first transformed into spectra, and projected to a subspace, where sequences belonging to different taxons are better distinguishable. Our method outperforms a similar state-of-the-art method on established benchmark datasets by an absolute margin of 6.06% accuracy.