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A new method of solving first order integral equations is proposed, which enables spectra distorted by the measuring instrument to be reconstructed with some meaning. This method is used for processing the results of measuring the energy spectrum of slow neutrons in a uranium-water lattice.

1. Possibilities have been investigated for restoring by means of the regularization method the signals which have been distorted by receiving devices with different characteristics. 2. Rules for selecting regularizing parameters for restoring signals have been derived and the possibility of a precise signal restoration by the regularization method has been determined for two types of equipment, comprising filters with lumped parameters (in particular, for the case of numerical differentiation) and for devices which attenuate high frequencies exponentially. For the first type of equipment the relative error in restoring the signal is proportional to $$\frac{2}{{_\sigma 2n + 3}}\left( {\frac{{\Delta t}}{z}} \right)\frac{2}{{2n + 3}} - 1_{ [see (28)and(31)].}$$ 3. The results thus obtained provide a new approach to the potentialities of recording equipment and propagation channels in receiving single short-duration signals. Thus, in transmitting signals over a cable its maximum length has been determined for the required signal-restoration precision better than p%. For p=10 this condition is A≤6.3 Δt, where Δt is the characteristic signal-variation time and A is the characteristic time of the transfer impulse function A=l2b21.