Almost‐Periodic Response Determination for Models of the Basilar Membrane

I. W. Sandberg, J. B. Allen

Research output: Contribution to journalArticlepeer-review


Electrical networks consisting of linear passive elements and many nonlinear resistors are often used to model the basilar membrane. The inputs to these networks are typically a sum of sinusoids switched on at t = 0, and the resulting quantities of interest because of their interpretation as analogs of experimental observables are the steady‐state response components of a certain current and of certain voltages. In this paper, recently obtained mathematical results concerning the input‐output representation of nonlinear systems are used to give, for the first time, a locally convergent expansion for all of the steady‐state quantities of interest. Also given is a good deal of information concerning general properties of the expansion, and this establishes important properties of the nonlinear network's response. Of particular practical interest is a term in the expansion that contains a component whose frequency is (2f1 — f2) when the network's input consists of a sum of two sinusoids, with frequencies f1 and f2. One of our main results is an explicit expression for this (2f1 — f2) component.

Original languageEnglish (US)
Pages (from-to)1775-1786
Number of pages12
JournalAT&T Technical Journal
Issue number8
StatePublished - Oct 1985
Externally publishedYes

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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