User`s guide

Parametric Fitting
3-19
Rationals
Rational models are defined as ratios of polynomials and are given by
where n is the degree of the numerator polynomial and , while m is the
degree of the denominator polynomial and . Note that the coefficient
associated with is always 1. This makes the numerator and denominator
unique when the polynomial degrees are the same.
In this guide, rationals are described in terms of the degree of the
numerator/the degree of the denominator. For example, a quadratic/cubic
rational equation is given by
Like polynomials, rationals are often used when a simple empirical model is
required. The main advantage of rationals is their flexibility with data that has
complicated structure. The main disadvantage is that they become unstable
when the denominator is around zero. For an example that uses rational
polynomials of various degrees, refer to “Example: Rational Fit” on page 3-41.
Sum of Sines
The sum of sines model is used for fitting periodic functions, and is given by the
equation
where a is the amplitude, b is the frequency, and c is the phase constant for
each sine wave term. n is the number of terms in the series and . This
equation is closely related to the Fourier series described previously. The main
y
p
i
x
n 1 i–+
i 1=
n 1+
∑
x
m
q
i
x
mi–
i 1=
m
∑
+
--------------------------------------------=
0 n 5≤≤
1 m 5≤≤
x
m
y
p
1
x
2
p
2
xp
3
++
x
3
q
1
x
2
q
2
xq
3
+++
-----------------------------------------------------=
ya
i
b
i
xc
i
+()sin
i 1=
n
∑
=
1 n 8≤≤