Signal processing in quasi-holographic system as an inverse problem

A quasi-holographic system is defined formally as a system executing the processing of signals in the case of the solution of inverse problems described by Fredholm equations of the first kind with finite difference kernels whose effective width decreases as their spectrum width when a certain function of the integral equation is determined on a bounded interval. A regularized solution to the system of integral equations is obtained. The concept of the specific number of operations required in obtaining this solution is defined, and the existence of a minimum value of the specific number of operations required during multistep processing is demonstrated. Particular consideration is given to the minimization of the number of operations when using the direct method and the convolution method based on the FFT to calculate weighted sums in the case of a linear-FM signal.