The growing concern over antibiotic resistance and the limitations of small molecule-based therapies has prompted significant interest in membrane-active peptides (MAPs), such as antimicrobial peptides (ABPs), cell-penetrating peptides (CPPs), and anticancer peptides (ACPs). These peptides hold therapeutic potential due to their ability to selectively interact with microbial and cancer cell membranes, yet challenges remain in optimizing their specificity and minimizing off-target effects such as hemolysis. To address these challenges, we present a computational framework based on Fourier transform-based sequence encoding for predicting the functional activity and safety profiles of diverse MAP classes. This method extracts oscillatory patterns from the physicochemical properties of amino acids within peptide sequences, thereby capturing sequence-order information critical for peptide functionality. We apply this encoding strategy in conjunction with nonlinear support vector machines (SVMs) to build interpretable predictive models, which outperform traditional models that rely on amino acid composition or deep learning-based approaches. Feature selection is optimized through MISTIC (Model Informed Selection Through Importance and Contribution), a novel framework that identifies and prioritizes the most informative features from the Fourier-derived data, enhancing both model accuracy and transparency. Our results show that Fourier-based models achieve strong predictive performance, with area under the ROC curve (AUC) scores ranging from 0.85 to 0.95, using a significantly smaller number of features (59–144) compared to deep learning models. Importantly, our approach provides clear insights into the biological relevance of sequence-order features, revealing distinct patterns associated with different MAP classes, such as antibacterial, hemolytic, anticancer, and mammalian-targeting peptides. This interpretable framework offers a promising pathway for the rational design of therapeutic peptides, paving the way for safer and more effective treatments with minimized toxicity.