### Abstract

A method is developed for the analysis of nonlinear biological systems based on an input temporal single that consists of a sum of a large number of sinusoids. Nonlinear properties of the system are manifest by responses at harmonics and intermodulation frequencies of the input frequencies. The frequency kernels derived from these nonlinear responses are similar to the Fourier transforms of the Wiener kernels. Guidelines for the choice of useful input frequency sets, and examples satisfying these guidelines, are given. A practical algorithm for varying the relative phases of the input sinusoids to separate high-order interactions is presented. The utility of this technique is demonstrated with data obtained from a cat retinal ganglion cell of the Y type. For a high spatial frequency grating, the entire response is contained in the even-order nonlinear components. Even at low contrast, fourth-order components are detectable. This suggests the presence of an essential nonlinearity in the functional pathway of the Y cell, with its singularity at zero contrast.

Original language | English (US) |
---|---|

Pages (from-to) | 459-483 |

Number of pages | 25 |

Journal | Biophysical Journal |

Volume | 29 |

Issue number | 3 |

State | Published - 1980 |

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### ASJC Scopus subject areas

- Biophysics

### Cite this

*Biophysical Journal*,

*29*(3), 459-483.

**A method of nonlinear analysis in the frequency domain.** / Victor, J.; Shapley, Robert.

Research output: Contribution to journal › Article

*Biophysical Journal*, vol. 29, no. 3, pp. 459-483.

}

TY - JOUR

T1 - A method of nonlinear analysis in the frequency domain

AU - Victor, J.

AU - Shapley, Robert

PY - 1980

Y1 - 1980

N2 - A method is developed for the analysis of nonlinear biological systems based on an input temporal single that consists of a sum of a large number of sinusoids. Nonlinear properties of the system are manifest by responses at harmonics and intermodulation frequencies of the input frequencies. The frequency kernels derived from these nonlinear responses are similar to the Fourier transforms of the Wiener kernels. Guidelines for the choice of useful input frequency sets, and examples satisfying these guidelines, are given. A practical algorithm for varying the relative phases of the input sinusoids to separate high-order interactions is presented. The utility of this technique is demonstrated with data obtained from a cat retinal ganglion cell of the Y type. For a high spatial frequency grating, the entire response is contained in the even-order nonlinear components. Even at low contrast, fourth-order components are detectable. This suggests the presence of an essential nonlinearity in the functional pathway of the Y cell, with its singularity at zero contrast.

AB - A method is developed for the analysis of nonlinear biological systems based on an input temporal single that consists of a sum of a large number of sinusoids. Nonlinear properties of the system are manifest by responses at harmonics and intermodulation frequencies of the input frequencies. The frequency kernels derived from these nonlinear responses are similar to the Fourier transforms of the Wiener kernels. Guidelines for the choice of useful input frequency sets, and examples satisfying these guidelines, are given. A practical algorithm for varying the relative phases of the input sinusoids to separate high-order interactions is presented. The utility of this technique is demonstrated with data obtained from a cat retinal ganglion cell of the Y type. For a high spatial frequency grating, the entire response is contained in the even-order nonlinear components. Even at low contrast, fourth-order components are detectable. This suggests the presence of an essential nonlinearity in the functional pathway of the Y cell, with its singularity at zero contrast.

UR - http://www.scopus.com/inward/record.url?scp=0018861202&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0018861202&partnerID=8YFLogxK

M3 - Article

C2 - 7295867

AN - SCOPUS:0018861202

VL - 29

SP - 459

EP - 483

JO - Biophysical Journal

JF - Biophysical Journal

SN - 0006-3495

IS - 3

ER -