usually the folded and unfolded forms, owing to spatial structure differences, can be expected to have different chemical shifts at one or more sites and differences in IR absorption band position and intensities.

Not sure about IR, but in NMR amide chemical shifts can tell you quite a bit about the folded state of a protein. When chemical shifts have poor dispersion in the proton dimension and are localized around ~8.6 ppm, this is a sign that the protein is disordered/unfolded. Whereas, if you get a spectra of well-dispersed peaks, it is a sign of secondary and/or tertiary structure in the protein. I think you can also make some rough assumptions of secondary structure from amide chemical shifts, but if you have the remaining backbone (Ca, Cb & C') chemical shifts, you can get very accurate predictions of the protein's secondary structure.

Stephen gave you a very good answer. I would add that with NMR spectra of protein amides (the most common spectra called 15N1H-HSQC); you can follow NH-peak moving upon thermal/chemical denaturation and in that way get the overall and local folding features of your protein. Beside this there are various NMR experiments by which you can measure solvent exposure of your protein residues just observing intensity changes in your amides (deuterium-exchange experiments, CLEANEX-PM and silmilar). Many other things you can get only form NH peaks: flexibility of protein regions (15N-relaxation experiments), interaction with ligands (perturbation of protein amide peaks upon addition of ligand or protein binding parner) and so on.