This study presents FLIGENT-Net, a multi-domain signal representation framework for gastric histopathological image classification that treats tissue images as complex two-dimensional signals whose diagnostic content is distributed across spatial, spectral, relational, and contextual domains. Using the GasHisSDB dataset, FLIGENT-Net investigates spatial representations extracted through a convolutional neural network (CNN), frequency-domain information obtained using the Fast Fourier Transform (FFT), graph-based relational modeling through a Graph Convolutional Network (GCN) acting as a graph-signal-processing operator, and global contextual modeling through a Vision Transformer (ViT). Rather than evaluating the framework solely according to classification accuracy, a systematic characterization was performed using individual and combined configurations, computational cost, training dynamics, interpretability, Pearson and Spearman correlation of importance maps, and Pixel Deletion analysis. FLIGENT-Net achieved 96.98% Accuracy, 95.45% Precision, 96.95% Recall, 96.20% F1-Score, and 0.9959 AUC-ROC. Notably, the simpler CNN+GCN configuration achieved a higher Accuracy of 97.76%, while CNN+GCN+FFT achieved 97.75%; this outcome shows that combining all four representation domains does not monotonically improve classification accuracy, reinforcing the characterization-oriented contribution of this study over a purely performance-driven one. The importance-map analysis revealed distinct patterns across representations, with low global Pearson and Spearman correlations. Pixel Deletion yielded a positive ∆AUC of 0.1450 for FLIGENT-Net. Overall, the results characterize distinct classification, computational, interpretability, and faithfulness profiles across multi-domain signal representations, offering a computational methods case study in spectral and graph-based image-signal analysis for biomedical applications.