The application of the Burg algorithm for maximum entropy spectral analysis to the time domain signals obtained in a Fourier transform mass spectrometer (FTMS) has been further explored with particular attention to its high-resolution capabilities and with the purpose of exploring the effect of the choice of the MEM parameters such as the number of data points and the order of the time domain filter. We have found that, for a fixed number of data points, there is a range of values of filter elements for which the method provides spectra superior to those obtained in the traditional methods employing fast Fourier transforms (FFT). Our results for a single sinusoid corresponding to the mass of 127 u show that a stable peak frequency can be achieved which agrees with the FFT peak frequency to better than one part in a million. The highest resolution, defined as the peak frequency divided by the half-width, was 5.568 million. We have also used a signal made up of two closely spaced positive ions and show that, under certain experimental conditions, the FFT method cannot fully resolve the two peaks, while MEM, using very few data points, is able to separate the two unambiguously.