We employ Maple’s ability to compute symbolic Fourier transforms of continuous curves to extract essential chemical information from interferograms produced with contemporary laboratory instruments. An interferogram is a function in the distance or time domain produced from the interference of waves, of which Fourier transformation into the wavenumber or frequency domain yields a distribution or spectrum that contains precise information about molecular structure and properties. We describe in turn each of four prototypical applications of continuous Fourier transforms – applied to diverse signals from coherent electron scattering, coherent xray scattering, microwave emission and infrared absorption – and then demonstrate how the capabilities of software for computer algebra enable the derivation of information in a chemically meaningful form. We distinguish between Fourier exponential, cosine and sine transforms that yield novel complementary information about molecular properties.