In this paper, a hybrid optical-digital system, consisting of a holographic mask, two Fourier lenses, a CCD detector and a microcomputer, is presented for computing a superposition integral, which is expressed as the integral of input data and impulse response or point-spread -function. In principle, the system can be used for performing an arbitrary linear transform and multiplication of matrices, as well as extracting the features of a pattern. In this system all the spacings between the input, lens, mask and output planes are equal to the focal length of the Fourier lens, The point-spread function is represented by the process of lightwave propagating through the optical system and modulating in the mask. The mask is produced by using computer-generated-hologram techniques. In experimental research, the system is tested by Walsh-Hadamard transform, matrix multiplication and geometric moment integral. The experimental results show that, the measured values of the above integrals are in agreement with the theoretical calculations.