We use an analytical calculation based on the Fourier-transform method to study the transmission spectra of multilayer dielectric optical structures as a function of the relative widths of the layers that constitute the unit cell. We can select which harmonics of the fundamental design frequency are transmitted. The results of this Fourier-transform approach are compared with the exact transmission calculated by means of the transfer matrix method and provide a more intuitive understanding of the transmission spectrum. A simple phasor diagram is derived from this Fourier-transform analysis for this purpose. Inasmuch as it is difficult for us to perform experiments in the optical region, we fabricate rf analogs of these structures, using coaxial cables that have different impedances. Experimental results agree with theory.