The fast Fourier transform (FFT) method of spectral analysis converts a time domain signal to a more easily visualized frequency domain spectrum but does not distinguish between signal and noise and produces spectral artifacts (e.g., "Gibb's oscillations") for a truncated and/or improperly sampled time domain signal. For example, FFT cannot resolve two signals if the sampling duration is less than one cycle of the frequency difference between the two signals. Here, linear prediction Cholesky decomposition spectral analysis is applied to ion cyclotron resonance mass spectrometry. The algorithm is robust and capable of extracting spectral parameters (frequency, time domain exponential damping constant, magnitude, and phase) from a signal consisting of multiple exponentially damped noisy sinusoids. Compared to FFT data reduction, linear prediction can offer significantly increased sensitivity (for signals at or below the rms noise level), elimination of Gibb's oscillations, and increased spectral resolving power for a time domain signal that either is truncated or has damped to the rms noise level before the end of the acquisition period. The present analysis can handle up to 8K time domain data sets with 2.5 h PC computation time.