1. A method for accurately estimating Fourier Transform mass spectrometry signal parameters comprising: (i) obtaining a time-series of voltage or current measurements of the time-dependent image charge generated upon two or more detector plates by whose motion inside an analyzer is essentially sinusoidal in one or more component directions; (ii) taking a discrete Fourier transform of the obtained time-series to produce a spectrum; and (iii) constructing maximum-likelihood estimates of a) frequency (f 0 ), b) amplitude |α|, c) phase (arg(α)), and d) decay time constant (τ) Fourier Transform mass spectrometry signal parameters from the acquired Fourier Transform mass spectrometry data using as a time-domain model an exponentially decaying sinusoid that has been truncated white Gaussian noise or its equivalent representation as a complex-valued discrete Fourier transform, wherein the Fourier Transform mass spectrometry data is represented either as a time-series of measurements or equivalently as a complex-valued discrete Fourier transform.