Miniaturized spectrometers are advantageous for many applications and can be achieved by what we term the filter-array detector-array (FADA) approach. In this method, each element of an optical filter array filters the light that is transmitted to the matching element of a photodetector array. By providing the outputs of the photodetector array and the filter transmission functions to a reconstruction algorithm, the spectrum of the light illuminating the FADA device can be estimated. Here, we experimentally demonstrate an array of 101 band-pass transmission filters that span the mid- to long-wave infrared (6.2 to 14.2 μm). Each filter comprises a sub-wavelength array of coaxial apertures in a gold film. As a proof-of-principle demonstration of the FADA approach, we use a Fourier transform infrared (FTIR) microscope to record the optical power transmitted through each filter. We provide this information, along with the transmission spectra of the filters, to a recursive least squares (RLS) algorithm that estimates the incident spectrum. We reconstruct the spectrum of the infrared light source of our FTIR and the transmission spectra of three polymer-type materials: polyethylene, cellophane and polyvinyl chloride. Reconstructed spectra are in very good agreement with those obtained via direct measurement by our FTIR system.