Power transformer is one of the most important assets in an electric utility. However, a large number of existing power transformers worldwide have already approached or even exceeded their designed lifetimes. Any failure of a transformer can be disastrous. Therefore, the conditions of transformers need to be continuously monitored and evaluated. Since a transformer's condition is largely dependent on its insulation system, a number of diagnostic methods have been developed for assessing transformer insulation conditions over the past decades. Among these methods, partial discharge (PD) measurement is widely adopted due to its capability of providing continuously online monitoring and diagnosis of a transformer without disturbing its normal operation.PD is a rather complicated phenomenon and stochastic in nature. Properly performing online PD measurements of a transformer, effectively analysing the measured PD signals, and subsequently making an informed condition assessment on a transformer's insulation system are still challenging.This thesis is aimed at developing advanced signal processing techniques for online PD monitoring and diagnosis of power transformer insulation systems.PD signals acquired at substation environments are always coupled with extensive noise, which exhibits different distribution properties. Therefore, PD signal de-noising is an essential process for accurately extracting PD signals from the acquired noise-corrupted signals before further analysis. In this thesis, advanced signal processing techniques, such as wavelet transform (WT), empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), blind equalization (BE) and pre-whitening, have been investigated for removing discrete spectral interference (DSI) that exhibits sinusoidal behaviour at various frequencies. Mathematical morphology (MM) has also been investigated for suppressing white noise by adaptively selecting threshold values. To remove stochastic noise, fractal dimension and entropy analyses have been investigated. Based on these techniques, several adaptive PD signal de-noising methods have been proposed in this thesis for removing different types of noise. A number of case studies using PD signals acquired from both laboratory experiments and online PD measurements of field transformers are presented. These case studies demonstrate advantages of the proposed PD signal de-noising methods over conventional methods in PD signal de-noising.In this thesis, phase-resolved pulse sequence (PRPS) diagrams and kurtograms have also been proposed for consistent representations of PD patterns after the noise has been removed. Case studies have been provided to prove a PRPS diagram's capability for accurately and consistently ii representing PD patterns. This representation can minimize influences of different types of PD sensors and measurement systems on PD pattern construction. Results are presented to demonstrate that kurtograms can be used to represent PD patterns even in the presence of extensive w...