<p>This paper introduces an adaptive noise cancellation algorithm designed specifically for environments with impulsive noise, which includes sudden, high-intensity noise events. Unlike traditional methods that assume noise to follow a Gaussian distribution (smooth and predictable noise), this work models noise using alpha-stable distributions, which better represent real-world impulsive scenarios. The proposed algorithm features a dynamic step-size adjustment mechanism, automatically adapting based on the magnitude of the residual error, the energy of the input signal, and regularization parameters. This dynamic adaptation ensures stability and faster convergence, particularly during sudden high-intensity noise events. The algorithm also tracks peak noise levels, enabling it to scale the anti-noise signal to effectively match the amplitude of the noise, significantly improving noise cancellation performance. Simulation results confirm that the proposed method achieves better improvements in reducing noise levels, enhancing the clarity and quality of audio signals compared to existing traditional methods.</p>