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Nonlinear crosstransformation of amplitude-frequency modulation of quasi-monochromatic acoustic signals
Responsible organisation
1998 (English)In: Acustica, ISSN 0001-7884, Vol. 84, no 3, 414-424 p.Article in journal (Refereed) PublishedAlternative title
Ickelinjär korstranformering av amplitud- och frekvensmodulering av kvasi-monokromatiska akustiska signaler (Swedish)
Abstract [en]

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.

Abstract [sv]

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.

Place, publisher, year, edition, pages
Stuttgart: S. Hirzel Verlag , 1998. Vol. 84, no 3, 414-424 p.
Keyword [en]
Burgers' equation, nonlinear acoustics, nonlinear wave propagation, modulated signals, Cole-Hopf, shock waves
National Category
Signal Processing Mathematics Applied Mechanics
Identifiers
URN: urn:nbn:se:bth-10205ISI: 000074181000002Local ID: oai:bth.se:forskinfo234BA4A7FE9CB409C12568A3002CABC1OAI: oai:DiVA.org:bth-10205DiVA: diva2:838278
Note
S. Gurbatov (University of Nizhny Novgorod)Available from: 2012-09-18 Created: 2000-03-15 Last updated: 2015-06-30Bibliographically approved

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