Sensed vibration spectra are compared with theoretically calculated spectra and the peaks in the respective spectra are mutually matched.

Estimates are then made of stretched wavelet spectra from the input spectra.

The spectra may include spectra as described above.

Preferably, the spectroscopic response is selected from infrared spectra or ultraviolet-visible spectra.

The subsequent mass spectra for precursors that are common to previous IDA cycles are summed with spectra for the plurality of mass spectra from previous IDA cycles to obtain summed mass spectra.

Comparative spectra of various samples can be compared to each other and/or to controls or reference spectra and/or comparative spectra to determine a variety of information.

Algorithmic models are developed from the classification spectra; these models are verified with the verification spectra.

The crystal forms can be characterized by X-ray powder diffraction (XRPD) spectra, differential scanning calorimetry (DSC) spectra, infrared absorption spectra and so on.

The spectra are then compared using multivariate analysis to determine diagnostic regions of the spectra.

A destretched wavelet spectra is then obtained.

Spectra are generated by a LIBS instrument from the sample, and are grouped into either classification spectra or verification spectra.

The three spectra are used to determine and remove a mechanically induced signal from EPR spectra to determine radiation-induced spectra.

In a cognitive wireless communication system, a spectrum sensor senses spectra in multiple frequency bands.

A light detecting device (10) detects specific spectra in the dispersed spectra of light substantially simultaneously.

Spectra of the samples are scanned and vigorously compared to known spectra as part of a diagnostic interpretation system (16).