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In this paper we approach the challenges of partial discharges (PD) detection in high voltage cables using signal processing techniques based on time frequency methods combined with Recurrence Plot Analysis (RPA) and high order spectrum analysis (HOSA). Detection of PD poses many problems in terms of speed of calculation, selection criteria and multitude of causes which lead to the occurrence of PD. In order to overcome these drawbacks, we have developed an algorithm which uses the spectrogram to perform a fast detection of parts from the signal which are susceptible of PD activity. The second stage calculates for each zone a detection curve using the HOSA concept of bispectrum and RPA. The latter has been applied in many non-linear systems in order to characterize the process on the basis of the recurrence matrix obtained from a time series given by the system.