Existing permanental processes often impose constraints on kernel types or stationarity, limiting the model's expressiveness. To overcome these limitations, we propose a novel approach utilizing the sparse spectral representation of nonstationary kernels. Additionally, we introduce a deep kernel variant by hierarchically stacking multiple spectral feature mappings, further enhancing the model's expressiveness to capture complex patterns in data. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of our approach, particularly in scenarios with pronounced data nonstationarity. Additionally, ablation studies are conducted to provide insights into the impact of various hyperparameters on model performance.