Infrared (IR) spectra from 1200 to 1800 cm(-1) of the pure alpha-helix and beta-sheet secondary structures have been extracted using a covariant least-squares procedure which relates a library of 40 infrared (IR) solution protein spectra from the work of Dong, Carpenter, and Caughey and amino acid fractions of the proteins based on assignments by STRIDE (secondary structure identification) of Eisenhaber and Argos. The excitonic splitting of the beta-sheet structures is determined for this library of solution proteins. The method is extended to find a set of spectral basis functions that analyze IR spectra of protein samples for alpha-helix and beta-sheet content. A rigorous error analysis including covariance, the correlations between the input library spectra, was used to justify the results and avoid less meaningful results. The utility of the results on alpha-helix and beta-sheet regions is demonstrated by detecting protein changes due to cancer in imaging Fourier transform IR (FTIR) spectra of liver tissue slices. This work ends with a method to extract IR spectra of less prominent torsional angle distributions.