The linear growth of KV cache bottlenecks long-context LLMs, yet RoPE-induced oscillations complicate Key cache quantization. To address this issue, we propose SpectrumQuant, a frequency-domain framework that utilizes the Discrete Cosine Transform (DCT) to convert these oscillations into sparse spectral representations. Specifically, our pipeline integrates dominant frequency extraction, hybrid bit-width allocation, and high-frequency pre-emphasis to maximize fidelity while minimizing memory footprint. To eliminate computational overhead, we develop fused Triton kernels featuring deferred inverse transformation and on-chip sparse accumulation. Extensive experiments on several benchmarks confirm SpectrumQuant achieves efficient compression with performance and latency comparable to FP16 baselines.