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Analysis of power signals is generally done by Discrete Wavelet Transform using db4 wavelet. But this method is not shift invariant. We propose a new method of Power Quality Analysis based on Dual Tree Complex Wavelet Transform exploiting its remarkable property of shift invariance. Firstly, the shift invariance property of DTCWT is established by comparing the wave energy at each decomposition level of a sinusoidal signal with leading and lagging phase sinusoidal signals. Different types of defects in power signals are simulated and several features are extracted using DTCWT up to 10 levels using MATALB. The database thus created is used for training a neural network. The performance of neural network is checked with a different set of data.