The longitudinal components of the recorded magnetisations in a number of thin film disk media were determined from captured isolated replay pulses using inverse filtering techniques. The computed magnetisations exhibit asymmetry in the tails in the approach to saturation. These recovered magnetisation transitions and their derivatives were linearly superposed to investigate the persistence of recorded magnetisation with recording density. Furthermore, the recovered magnetisation distributions were employed to investigate the effect of transition shape on the noise power spectral densities. The results are compared with experimental observations.