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The most common form of input current pulses used in magnetostrictive displacement transducers are rectangular pulses. Since, in addition to this form, it is possible to use other forms other than rectangular, the article investigates the output signal of a magnetostrictive displacement transducer under the influence of exponential current pulses. Formulas, expressions and mathematical models of the processes of formation of ultrasonic waves, as well as their translation in the medium of the waveguide and readout by an inductive element are considered. The expression is investigated by which the numerical characteristics of the measuring signal in devices fixing angular and linear displacement based on the magnetostrictive effect are determined. The measuring signal is generated by the combined action of the field of a permanent magnet and a magnetic field created under the influence of current pulses in the form of an exponential. The data obtained in computational experiments, theoretical and practical studies gave grounds to conclude that it is possible to use linear and angular displacements of input current pulses of exponential form in magnetostrictive converters. The results obtained in this work are of practical importance and must be taken into account when developing magnetostrictive devices and devices. [ABSTRACT FROM AUTHOR]