Deep brain stimulation (DBS) is widely used as a treatment option for patients with movement disorders. In addition to its clinical impact, DBS has been utilized in the field of cognitive neuroscience wherein the answers to several fundamental questions underpinning the mechanisms of neuromodulation in decision making rely on how a burst of DBS pulses, usually delivered at clinical frequency, i.e., 130 Hz, perturb participants' choices. It was observed that neural activities recorded during DBS were contaminated with stereotype large artifacts, which lasts for a few milliseconds, as well as a low-frequency (slow) signal (~1-2 Hz) that can persist for hundreds of milliseconds. While the focus of the most of methods for removing DBS artifact was on the former, the artifact removal of the slow signal has not been addressed. In this work, we propose a new method based on combining singular value decomposition (SVD) and normalized adaptive filtering to remove both large (fast) and slow artifacts in local field potentials recorded during a cognitive task in which bursts of DBS were utilized. Using synthetic data, we show that our proposed algorithm outperforms four commonly used techniques in the literature, namely, (1) Normalized least mean square adaptive filtering, (2) Optimal FIR Wiener filtering, (3) Gaussian model matching, and (4) Moving average. The algorithm's capabilities are further demonstrated by its ability to effectively remove DBS artifacts in local field potentials recorded from the subthalamic nucleus during a verbal Stroop task, highlighting its utility in real-world applications.