User`s guide

3 Fitting Data

3-16

Library Models

The parametric library models provided by the Curve Fitting Toolbox are

described below.

Exponentials

The toolbox provides a one-term and a two-term exponential model.

Exponentials are often used when the rate of change of a quantity is

proportional to the initial amount of the quantity. If the coefficient associated

with e is negative, y represents exponential decay. If the coefficient is positive,

y represents exponential growth.

For example, a single radioactive decay mode of a nuclide is described by a

one-term exponential. a is interpreted as the initial number of nuclei, b is the

decay constant, x is time, and y is the number of remaining nuclei after a

specific amount of time passes. If two decay modes exist, then you must use the

two-term exponential model. For each additional decay mode, you add another

exponential term to the model.

Examples of exponential growth include contagious diseases for which a cure

is unavailable, and biological populations whose growth is uninhibited by

predation, environmental factors, and so on.

Fourier Series

The Fourier series is a sum of sine and cosine functions that is used to describe

a periodic signal. It is represented in either the trigonometric form or the

exponential form. The toolbox provides the trigonometric Fourier series form

shown below,

where a

models any DC offset in the signal and is associated with the i = 0

cosine term, w is the fundamental frequency of the signal, n is the number of

terms (harmonics) in the series, and .

ya= e

nwx()b

nwx()sin+cos

i 1=

∑

1 n 8≤≤