<p>Bearings are indispensable components in various industrial machines. Due to equipment operational noise, environmental noise, and component coupling, vibration signals that reflect the condition of bearings are often subject to substantial noise interference. The superimposition of noise and variations in rotational speed further complicates the extraction of bearing fault features. This study proposes a noise reduction method for bearing fault signals under variable speed conditions to address the above challenges. By utilizing peak search and least squares fitting techniques, an algorithm is designed to capture fault pulses with non-uniform intervals under varying speeds, thereby facilitating noise removal. The proposed method is validated through simulations, experimental setups, and publicly available datasets. The results from all experiments demonstrate that the proposed noise reduction method outperforms existing methods and effectively extracts frequency-modulated impacts caused by bearing faults under variable speed conditions. Compared with other methods, the approach presented in this study offers valuable insights for noise reduction of bearing fault signals in variable speed operations and shows potential for practical applications.</p>