# Nonlinear signal processing using neural networks: Prediction and system modelling

## Abstract

The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing. We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks. The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing. Simulations are presented that document the additional performance achieved by using nonlinear neural networks. First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method. Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics. Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function. It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series. Furthermore, the neural netmore »

- Authors:

- Publication Date:

- OSTI Identifier:
- 5470451

- Report Number(s):
- LA-UR-87-2662; CONF-8706130-4

ON: DE88006479

- DOE Contract Number:
- W-7405-ENG-36

- Resource Type:
- Conference

- Resource Relation:
- Conference: 1. IEEE international conference on neural networks, San Diego, CA, USA, 21 Jun 1987; Other Information: Portions of this document are illegible in microfiche products

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; DATA-FLOW PROCESSING; NETWORK ANALYSIS; ALGORITHMS; DIFFERENTIAL EQUATIONS; LEAST SQUARE FIT; MATHEMATICAL MODELS; NEUROLOGY; NONLINEAR PROBLEMS; SIMULATION; TRANSFER FUNCTIONS; EQUATIONS; FUNCTIONS; MATHEMATICAL LOGIC; MAXIMUM-LIKELIHOOD FIT; MEDICINE; NUMERICAL SOLUTION; PROGRAMMING; 990210* - Supercomputers- (1987-1989); 990230 - Mathematics & Mathematical Models- (1987-1989)

### Citation Formats

```
Lapedes, A, and Farber, R.
```*Nonlinear signal processing using neural networks: Prediction and system modelling*. United States: N. p., 1987.
Web.

```
Lapedes, A, & Farber, R.
```*Nonlinear signal processing using neural networks: Prediction and system modelling*. United States.

```
Lapedes, A, and Farber, R. Mon .
"Nonlinear signal processing using neural networks: Prediction and system modelling". United States. https://www.osti.gov/servlets/purl/5470451.
```

```
@article{osti_5470451,
```

title = {Nonlinear signal processing using neural networks: Prediction and system modelling},

author = {Lapedes, A and Farber, R},

abstractNote = {The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing. We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks. The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing. Simulations are presented that document the additional performance achieved by using nonlinear neural networks. First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method. Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics. Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function. It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series. Furthermore, the neural net seems to be extremely parsimonious in its requirements for data points from the time series. We show that the neural net is able to perform well because it globally approximates the relevant maps by performing a kind of generalized mode decomposition of the maps. 24 refs., 13 figs.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1987},

month = {6}

}