Channeled spectropolarimetry measures the complete polarization state of light, using a single spectrum, by amplitude modulating the Stokes parameters onto spectral carrier frequencies. However, spectral features that are not band limited in the Fourier transform domain, such as narrow-band atomic absorption lines, can generate false polarimetric signatures. We present a false-signature (aliasing) reduction technique that reduces the error induced by these non-band-limited features. Additionally, the spectral resolution of the S0 Stokes parameter is improved, up to the maximum resolution offered by the spectrometer. A theoretical model for implementing the technique on a Fourier transform infrared spectrometer is presented, including an enhanced model that accounts for dichroism within the crystal. The approach is experimentally demonstrated in the middle-wavelength infrared (3-5 µm) with the use of two multiple-order yttrium vanadate retarders. Additional results demonstrating the technique for wavelengths spanning 2.5-15 µm are obtained using cadmium sulfide retarders. Reconstructions are compared to conventional channeled spectropolarimetric reconstructions from the same system.