Activation measurements are utilized to determine approximate representations of neutron spectra in the form of orthonormal expansions. Two different methods, the Gram-Schmidt and least-squares expansions, are examined. The sensitivity of these methods to experimental error in the neutron cross sections is explored. The least-squares method proves generally superior to the Gram-Schmidt method in this application. The present computations imply that more accurate spectral information can be obtained from orthonormal expansions which employ fewer cross sections of high precision as opposed to many cross sections of moderate precision.