The 37-residue human islet amyloid polypeptide (hIAPP or amylin) self-assembles into fibers, the assembly of which has been associated with the disease mechanism of type II diabetes. Infrared spectroscopy in conjunction with isotope labeling is proving to be a powerful tool for studying the aggregation process of hIAPP and other amyloid forming proteins with residue specific structure and kinetic information, but the relationship between the spectroscopic observables and the structure is not fully established. We report a detailed analysis of the linear and 2D IR spectra of hIAPP fibers isotope labeled at seven different residue positions. The features of the 2D IR spectra, including the frequencies, linewidths, intensities, and polarization dependence of the diagonal and cross-peaks, rely heavily on the position of the isotope labeled residue. In order to understand how these measured parameters depend on fiber secondary and tertiary structure, we have simulated 1D and 2D IR spectra utilizing idealized structural models in addition to a recently published solid-state NMR based model of the amyloid fibril. The analysis provides a more rigorous foundation for interpreting the infrared spectra of amyloids. In addition, we demonstrate that 2D IR spectra can be employed to distinguish between residues in beta-sheets versus those in turn regions, and that transitional residues between secondary structures can be identified by the suppression of their cross-peaks in 2D IR spectra. This latter approach is not limited to amyloid fibrils and will be generally useful in identifying regions of secondary structure in proteins using 2D IR spectroscopy and isotope labeling.