Graph-based recommendation systems are effective at modeling collaborative patterns but often suffer from two limitations: overreliance on low-pass filtering, which suppresses user-specific signals, and omission of sequential dynamics in graph construction. We introduce GSPRec, a graph spectral model that integrates temporal transitions through sequentially-informed graph construction and applies frequency-aware filtering in the spectral domain. GSPRec encodes item transitions via multi-hop diffusion to enable the use of symmetric Laplacians for spectral processing. To capture user preferences, we design a dual-filtering mechanism: a Gaussian bandpass filter to extract mid-frequency, user-level patterns, and a low-pass filter to retain global trends. Extensive experiments on four public datasets show that GSPRec consistently outperforms baselines, with an average improvement of 6.77% in NDCG@10. Ablation studies show the complementary benefits of both sequential graph augmentation and bandpass filtering.