Fourier Transforms of Pulses Containing Exponential Leading and Trailing Profiles

Warshaw, S I

Lawrence Livermore National Laboratory

关键词: Nuclear Explosions;    Electromagnetic Pulses;    Decay;    Amplitudes;    Air;   

DOI  :  10.2172/15002784
RP-ID  :  UCRL-ID-149577
RP-ID  :  W-7405-ENG-48
RP-ID  :  15002784

美国|英语

来源: UNT Digital Library

【 摘 要 】

In this monograph we discuss a class of pulse shapes that have exponential rise and fall profiles, and evaluate their Fourier transforms. Such pulses can be used as models for time-varying processes that produce an initial exponential rise and end with the exponential decay of a specified physical quantity. Unipolar examples of such processes include the voltage record of an increasingly rapid charge followed by a damped discharge of a capacitor bank, and the amplitude of an electromagnetic pulse produced by a nuclear explosion. Bipolar examples include acoustic N waves propagating for long distances in the atmosphere that have resulted from explosions in the air, and sonic booms generated by supersonic aircraft. These bipolar pulses have leading and trailing edges that appear to be exponential in character. To the author's knowledge the Fourier transforms of such pulses are not generally well-known or tabulated in Fourier transform compendia, and it is the purpose of this monograph to derive and present these transforms. These Fourier transforms are related to a definite integral of a ratio of exponential functions, whose evaluation we carry out in considerable detail. From this result we derive the Fourier transforms of other related functions. In all Figures showing plots of calculated curves, the actual numbers used for the function parameter values and dependent variables are arbitrary and non-dimensional, and are not identified with any particular physical phenomenon or model.