Sampling signals with finite set of apertures
The article discusses the issue of sampling continuous signals using a finite set of apertures. Using the apparatus of generalized functions, an analytical form of sampling is obtained for ideal sampling, for sampling a limited signal and for sampling a signal using a limited set of apertures. It is shown that the signal spectrum is the product of the signal spectrum at ideal sampling by some known factor, the influence of which can be eliminated. The type of this factor can be obtained if the type of aperture is known. The type of analytical expression differs from those known in the literature on image sampling. The use of an analytical expression for sampling can be used to reconstruct the original image from the image obtained with different sets of apertures. For this it is necessary to divide the Fourier spectrum of the sampled image by a factor depending on the selected aperture. Having received the inverse Fourier transform from it, you can get the original one.