An empirical analysis of the maximum entropy method (MEM) has been carried out with particular reference to the frequency content of the data used. Result are presented showing how the performance of the MEM relates to the frequency content of both the data and the blurring function. From an extensive survey using simulated data, certain clear patterns of performance have been established, including the ability of the MEM to reconstruct frequencies absent from the data. Conclusions from this survey are considered to have practical application, particularly in signal processing for surface characterisation and non-destructive testing. Results for real data, obtained from a plane compressional-wave ultrasonic transducer working in the pulse-echo mode with a selected test surface, are presented as an indication of the practical significance of the observed patterns of performance.