Pre-trained foundation models have demonstrated remarkable success in audio, vision and language, yet their potential for general machine signal modeling with arbitrary sampling rates-covering acoustic, vibration, and other industrial sensor data-remains under-explored. In this work, we propose a novel foundation model ECHO that integrates an advanced band-split architecture with frequency positional embeddings, enabling spectral localization across arbitrary sampling configurations. Moreover, the model incorporates sliding patches to support inputs of variable length without padding or cropping, producing a concise embedding that retains both temporal and spectral fidelity and naturally extends to streaming scenarios. We evaluate our method on various kinds of machine signal datasets, including previous DCASE task 2 challenges (2020-2025), and widely-used industrial signal corpora. Experimental results demonstrate consistent state-of-the-art performance in machine signal anomaly detection and fault classification, confirming the effectiveness and generalization capability of the proposed model. We open-sourced ECHO on https://github.com/yucongzh/ECHO.