In this work, a new methodology is proposed for the online and non-invasive extraction of partial discharge (PD) pulses from raw measurement data obtained using a simplified setup. This method enables the creation of sub-windows with optimized size, each containing a single candidate PD pulse. The proposed approach integrates mathematical morphological filtering (MMF) with kurtosis, a first-order Savitzky-Golay smoothing filter, the Otsu method for thresholding, and a specific technique to associate each sub-window with the phase angle of the applied voltage waveform, enabling the construction of phase-resolved PD (PRPD) patterns. The methodology was validated against a commercial PD detection device adhering to the IEC (International Electrotechnical Commission) standard. Experimental results demonstrated that the proposed method, utilizing an off-the-shelf 8-bit resolution data acquisition system and a low-cost high-frequency current transformer (HFCT) sensor, effectively diagnoses and characterizes PD activity in high-voltage equipment, such as surge arresters and instrument transformers, even in noisy environments. It was able to characterize PD activity using only a few cycles of the applied voltage waveform and identify low amplitude PD pulses with low signal-to-noise ratio signals. Other contribution of this work is the diagnosis and fault signature obtained from a real surge arrester (SA) with a nominal voltage of 192 kV, corroborated by destructive disassembly and internal inspection of the tested equipment. This work provides a cost-effective and accurate tool for real-time PD monitoring, which can be embedded in hardware for continuous evaluation of electrical equipment integrity.