A new method to evaluate the thermally stimulated depolarization current curves based on the direct signal analysis is first applied here to the fitting of computer-generated curves to test its validity and accuracy. The method consists in finding the N elementary curves that best fit the experimental spectrum. The adjustment of the tau(0) values associated with each energy bin is also included in the fitting. The results are presented for a monoenergetic peak and a peak generated with a Gaussian broadened energy distribution both with a single tau(0). Good agreement is also found when a random noise of width sigma(0) less than or equal to 0.01 J(max) is added to the data to simulate experimental errors. Experimental complex curves corresponding to the gamma and beta overlapping relaxations in DGEBA-EDA epoxy resin system are separated into their fine structure components. The complex band corresponding to water dipoles physisorbed in different sites of the microporosity of bituminous coal is analyzed and different processes are identified. The results are compared to those performed on cleaned peaks. Finally, the TSDC peak corresponding to the glass transition temperature in bisphenol-A polycarbonate is analyzed and could only be fitted by using a Vogel-Fulcher expression for the temperature dependence of the relaxation times.