Collaborative large language model (LLM) inference enables real-time, privacy-preserving AI services on resource-constrained edge devices by partitioning computational workloads between client devices and edge servers. However, this paradigm is severely hindered by communication bottlenecks caused by the transmission of high-dimensional intermediate activations, exacerbated by the autoregressive decoding structure of LLMs, where bandwidth consumption scales linearly with output length. Existing activation compression methods struggle to simultaneously achieve high compression ratios, low reconstruction error, and computational efficiency. This paper proposes FourierCompress, a novel, layer-aware activation compression framework that exploits the frequency-domain sparsity of LLM activations. We rigorously demonstrate that activations from the first Transformer layer exhibit strong smoothness and energy concentration in the low-frequency domain, making them highly amenable to near-lossless compression via the Fast Fourier Transform (FFT). FourierCompress transforms activations into the frequency domain, retains only a compact block of low-frequency coefficients, and reconstructs the signal at the server using conjugate symmetry, enabling seamless hardware acceleration on DSPs and FPGAs. Extensive experiments on Llama 3 and Qwen2.5 models across 10 commonsense reasoning datasets demonstrate that FourierCompress preserves performance remarkably close to the uncompressed baseline, outperforming Top-k, QR, and SVD. FourierCompress bridges the gap between communication efficiency (an average 7.6x reduction in activation size), near-lossless inference (less than 0.3% average accuracy loss), and significantly faster compression (achieving over 32x reduction in compression time compared to Top-k via hardware acceleration) for edge-device LLM inference.

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