Measurement of nonlinear vibration by signal compression method

The signal compression method [Aoshima, J. Acoust. Soc. Am. 69, 1484–1488 (1981); Aoshima, J. Acoust. Soc. Jpn. (E) 3, 105–109 (1982)] is shown to be useful for analyzing nonlinear systems as well as linear systems. If a nonlinear system can be modeled as a parallel combination of a linear part and elements subject to a power law, such as a squarer, they can be analyzed separately by the signal compression method. As the test signal of the signal compression method has been generated by an ‘‘expanding filter’’ H(ω)=exp(jαω2), the linear response can be detected by a ‘‘compression filter’’ H−1(ω)=exp(−jαω2). Then the nonlinear component generated by the squarer is also compressed by another ‘‘second‐order compression filter’’ H−12(ω)=exp(−jαω2/2). The frequency tripled component, which is generated by a third power nonlinear element, is compressed by the ‘‘third‐order compression filter’’ H−13(ω)=exp(−jαω2/3). Results of model experiments by an analog squarer and a numerical nonlinear processing are exempl...