Abstract: A two-part method for reducing the noise contribution in a composite signal using the wavelet transform is described. The procedure involves the identification of subspaces in the reconstructed state space created by dynamical processes (either by deterministic noise or the signal itself), the separation of different subspaces and the separation of subspaces from stochastic noise. The method is used for non-linear de-noising (NLD) of magnetocardiograph or electrocardiograph time series signals by performing local projections in the reconstructed state space using the wavelet transform to identify and describe deterministic structures. Subspaces generated by any deterministic process are located and separated independently of its source.