Wavelength-resolved neutron transmission experiments are useful for characterizing the microstructure of macroscopic specimens with 2D spatial resolution perpendicular to the beam direction. The crystallographic texture can affect the neutron transmission in the thermal neutron energy range, which manifests as changes in the shape and height of Bragg edges as a function of neutron wavelength. Models have been proposed to predict the transmission of textured polycrystalline materials from knowledge of the material texture and have proved to accurately predict the observed transmission data. In recent work, a novel method was described and tested for obtaining texture integral parameters from the combined analysis of transmission data measured along several directions of a specimen in a hexagonal crystal Zr alloy. However, this procedure has limitations when dealing with high-symmetry crystal structures. In this work, a generalization of such a method based on the expansion of the orientation distribution function (ODF) in symmetric generalized spherical harmonics that is applicable to all crystal and sample symmetries is presented. Using this method, the low-order Fourier coefficients of the ODF can be estimated by analyzing transmission data obtained for a reduced set of beam directions. This method was verified using a cubic Cu sample, for which transmission data were available along five different directions. Two sample symmetries were assumed to reduce the number of Fourier coefficients of the ODF. In the case of cylindrical symmetry (fiber-type texture), the results were good; but in the case of orthorhombic symmetry, some bias was observed which was attributed to the reduced number of beam directions used to perform the evaluation.