The purpose of the present study is to present a new approach to the problem of reconstructing the wave distribution function from observed frequency spectra. A method which does not rely on cold plasma theory is developed. We use numerical methods to solve the dispersion relation for waves in a warm, homogeneous, anisotropic, and multicomponent plasma. This allows us to treat almost any linear wave mode and also to handle a large variety of plasma models, including warm plasma. Doppler effects are taken into account, and reconstruction is performed over a wide frequency range simultaneously. To define a solution to the inverse underdetermined problem occurring in the reconstruction, we use the method of maximum-entropy. As a test of our method, we solve a model problem with simulated data. ¿ American Geophysical Union 1989