Nonlinear crosstransformation of amplitude-frequency modulation of quasi-monochromatic acoustic signals

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Author(s): Claes Hedberg, Sergey Gurbatov
Title: Nonlinear crosstransformation of amplitude-frequency modulation of quasi-monochromatic acoustic signals
Translated title: Ickelinjär korstranformering av amplitud- och frekvensmodulering av kvasi-monokromatiska akustiska signaler
Journal: Acustica-Acta Acustica
Year: 1998
Volume: 84
Issue: 3
Pagination: 414-424
ISSN: 0001-7884
Publisher: S. Hirzel Verlag
City: Stuttgart
ISI number: 000074181000002
Organization: Blekinge Institute of Technology
Department: Dept. of Mechanical Engineering (Institutionen för maskinteknik)
Dept. of Mechanical Engineering S-371 79 Karlskrona
+46 455 780 00
Authors e-mail:
Language: English
Abstract: This work is devoted to the investigation of evolution of intense quasi-harmonic signals in the case of infinite acoustic Reynolds numbers. The consideration is based on the zero viscocity limit solution of the Burgers equation, which reduces the Cole-Hopf solution to a "maximum" principle. This limit solution permits an easy way to get the profile of the waves, postition of shocks and their velocities at arbitrary times. The process of transformation of an initial quasi-monochromatic wave into s sawtooth wave is considered. It is shown that the nonlinearity leads to suppression of the initial amplitude modulation and to the transformation of the initial frequency modulation inot a shock amplitude modulation. The amplitude of the low frequency component generated by a quasi-mono-chromatic wave is found. It is shown that the interaction of this component with high frequency waves leads to phase modulation, which increases with distance. The amplitudes of the new components of the spectrum are found. Is is show

n that when the value of phase modulation is small, the amplitudes of the satellites do not depend on the distance or the number of harmonics of the primary wave.
Summary in Swedish: Med hjälp av Burgers ekavation beskrivs starka icke-linjära signalers utveckling. Vid frekvensmodulerade insignaler får efterhand en transformering till skenbart amplitudmodulerade. Och tvärtom, vid amplitudmodulering får frekvensmodulering som resultat. Ett specialfall är när samtidig frekvens och amplitudmodulering gör att stötvågornas läge inte ändras med tiden och signalens form därför för all tid ser likadan ut. Amplituden minskar förstås.
Subject: Mathematics\General
Mechanical Engineering\General
Signal Processing\Hydro-Acoustics
Keywords: Burgers' equation, nonlinear acoustics, nonlinear wave propagation, modulated signals, Cole-Hopf, shock waves
Note: S. Gurbatov (University of Nizhny Novgorod)