An optical analog computer has been demonstrated which is capable of obtaining quantitative estimates of transfer functions of systems from finite records of input and response data and power spectra of the input and response. The inputx(t)and responsez(t)are recorded as amplitude-transmission variations on a photographic plate. To compute the power spectrum ofx(t), the Fourier transformX(omega)ofx(t)is formed by illuminatingx(t)with light from a He-Ne laser and focusing the resulting diffraction pattern with a lens to formX(omega). This diffraction pattern, when read out with a properly-shaped light-gathering probe connected to a photomultiplier, will yield an estimate of the power spectrum ofx(t). In a similar manner, the power spectrum ofz(t)is estimated. To estimate the transfer functionH(omega), a hologram ofX*(omega)is made. From the hologram, a transparency is made whose amplitude transmission is proportional to1/ X*(omega)X(omega). When the hologram is illuminated byZ(omega), the resulting diffraction pattern will containX*(omega)Z(omega).X*(omega)Z(omega)is then imaged onto the transparency whose amplitude transmission is1/X*(omega)X(omega)formingH(omega) = X*(omega)Z (omega)/ X*(omega)X(omega). Experimental results are presented which indicate that good estimates of power spectra and transfer functions can be obtained by this method.