The effective use of complex fenestration systems in buildings requires knowledge of their optical spectral and directional properties. While the directional properties are commonly assessed by the measurement of bidirectional transmission or reflection distribution functions, the addition of spectral information would significantly aid in the design and analysis of such systems. This paper describes the development of a spectral estimation method that reconstructs reflectance and transmittance spectra of unknown complex fenestration samples in the Heliodome, an innovative video-goniophotometer. The estimation method relies on the digital output of a tri-chromatic charge-coupled device camera in eight filterbands to reconstruct a sample's spectrum using the truncated generalised singular value decomposition. This method is validated by comparing estimated spectra with documented reflectance and transmittance spectra of reference samples. In most spectrally selective materials, the method achieved average improvements of 50% over the Heliodome's previous quasi-spectral assessment method.