Doppler effect considered as a distortion of time, application to an engineering case

The ground-based listening of aircraft, rockets, or space launchers, and the simulation of recorded acoustic spectra with a view to civilian or military applications, raise the problem of the distortion by the Doppler effect of the spectrum emitted by the sound sources, in addition to other problems related to the sound propagation in atmosphere. We propose a solution to the direct problem—the characteristics of the sound source and its trajectory are known—based on an original time approach to the Doppler effect. This study shows in fact that it is not necessary to distinguish between frequency and sound level variations, both being directly related to the ratio of the emission to the reception durations of a chosen signal sequence. The developed method has a character of generality and can be applied without restriction in most cases (e.g. variable speed of the mobile, curved trajectory, atmosphere with wind and temperature gradients) using an acoustic propagation code, but remains obviously applicable in an isotropic environment to simple or complex cases, for example when the observer is moving.