In this work, we present a new approach for shift invariant complex wavelet analysis of neuroelectric signals. A key idea is to preprocess the signal with the Hilbert transformer to yield an analytic signal, which is then wavelet transformed using the linear phase complex scaling and wavelet filters. In different scales, the total energy of the wavelet transform coefficients is shift invariant. The decimated analytic wavelet coefficients suffer no aliasing effects, which are predominant in conventional wavelet analysis. We show the usefulness of the present method in multi-scale analysis of the neuroelectric signal waveforms.