At present time have been developed methods to improve the signal bandwidth of fiber-optical transmission systems (FOTS). A special case of such methods is considered in earlier works of the author. The essence of the proposed methods is to transfer more than one bit of information in one clock interval. The fundamental complexity of the implementation of such methods is the need to form a low-frequency component (envelope) of an optical signal of a given shape. A solution to this problem is proposed using a single laser pulse. In this case, the laser pulse is fed to the inputs of optical amplifiers, and from their outputs - to the inputs of delay lines with a precision step. As a result of the summation of the signals from the outputs of the delay lines, an approximant of a given optical signal is formed. This article assumes that the laser pulse has the form of a hyperbolic secant. A proof of the convergence of the corresponding approximants to functions of a given type is given. A numerical analysis confirming the solutions has been also performed. It is shown that the rate of convergence is of the order of 1/N, where N is the number of approximating pulses (the number of delay lines). It is shown that the proposed solutions are consistent with the characteristics of modern FOTS and can be implemented at the existing technological level of manufacturing optical components.