1. An apparatus for performing spectral analysis, the apparatus comprising: a. a data acquisition system configured to measure a signal emitted from a sample in response to excitation energy applied thereto, and to average the measured signal over a plurality of measurements to generate an averaged signal; b. a data processing system including: a noise-reduction pre-processor configured to create a vector space from said averaged signal, and to generate the singular values and corresponding eigenvectors of a correlation matrix constructed within said vector space, said vector space containing a noisefree signal subspace and a noise subspace, said singular values including noisefree singular values associated with said noisefree signal subspace, and noise singular values associated with said noise subspace; and c. a control system configured to identify a gap between a noisefree singular value and an adjacent noise singular value, so as to request the data acquisition system to perform additional measurements if no such separation can be identified, and to prevent further measurements from being made by the data acquisition system if the appearance and stability of said gap can be established.