Dynamic supply current (IDD) analysis has emerged as an effective way for defect oriented testing of analog circuits. In this paper, we propose using wavelet decomposition of IDD for fault detection in analog circuits. Wavelet transform has the property of resolving events in both time and frequency domain simultaneously unlike Fourier expansion which localizes a signal in terms of frequency only. Wavelet transform also has better sub-banding property and it can be easily adapted to current waveforms from different circuits. These make wavelet a more suitable candidate for fault detection in analog circuits than pure time-domain or pure frequency-domain methods. We have shown that for equivalent number of spectral components, sensitivity of wavelet based fault detection is much higher than Fourier or time-domain analysis for both catastrophic and parametric faults. Simulation results on benchmark circuits show that wavelet based method is on average 25 times more sensitive than DFT (Discrete Fourier Transform) for parametric faults and can be considered as a promising alternative for analog fault detection amidst measurement hardware noise and process variation.