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In monitoring the depth of anaesthesia, raw EEG signals are recorded by means of an adhesive sensor attached to the forehead. The raw EEG signal is often corrupted by spike, low frequency and high frequency noise. Removal of such noise improves clinical utility and this paper presents a novel method which uses a double wavelet-based de-noising algorithm. The results of experimental simulations show that the proposed method reproduces the EEG signal almost noiselessly. The resultant data is suitable input for monitoring the depth of anaesthesia. We propose to build up a wavelet-based Depth of Anaesthesia (WDoA) based on discrete wavelet transform (DWT) and power spectral density (PSD) function. Findings give very close correlation between the WDoA and BIS Index values, through the whole scale from 100 to 0 with full recording time on patient. Simulation results demonstrate that this new index, WDoA, represents the DoA in all anaesthesia states reliably and accurately.