This paper proposes GSPRec to address two challenges in graph-based recommender systems: the suppression of user feature signals due to overreliance on low-pass filtering and the omission of sequential dynamics in graph construction. GSPRec is a graph spectral model that incorporates temporal transitions through sequentially informed graph construction and applies frequency-aware filtering in the spectral domain. It encodes item transitions via multi-hop diffusion, enabling the use of a symmetric Laplacian for spectral processing. To capture user preferences, we design a dual filtering mechanism: a Gaussian bandpass filter that extracts mid-frequency user-level patterns and a lowpass filter that preserves global trends. Extensive experiments on four public datasets demonstrate that GSPRec consistently outperforms baseline models, achieving an average improvement of 6.77% on NDCG@10. Further analysis reveals that both sequential graph augmentation and bandpass filtering offer complementary benefits.