The analysis of the time ordered data of Dark Matter experiments is becoming more and more challenging with the increase of sensitivity in the ongoing and forthcoming projects. Combined with the well-known level of background events, this leads to a rather high level of pile-up in the data. Ionization, scintillation as well as bolometric signals present common features in their acquisition timeline: low frequency baselines, random gaussian noise, parasitic noise and signal characterized by well-defined peaks. In particular, in the case of long-lasting signals such as bolometric ones, the pile-up of events may lead to an inaccurate reconstruction of the physical signal (misidentification as well as fake events). We present a general method to detect and extract signals in noisy data with a high pile-up rate and qe show that events from few keV to hundreds of keV can be reconstructed in time ordered data presenting a high pile-up rate. This method is based on an iterative detection and fitting procedure combined with prior wavelet-based denoising of the data and baseline subtraction. We have tested this method on simulated data of the MACHe3 prototype experiment and shown that the iterative fitting procedure allows us to recover the lowest energy events, of the order of a few keV, in the presence of background signals from a few to hundreds of keV. Finally we applied this method to the recent MACHe3 data to successfully measure the spectrum of conversion electrons from Co57 source and also the spectrum of the background cosmic muons.