Built-in fit functions

Line

This function is used to fit a curve which has a linear shape.

The results will be given in the Log panel:

Polynomial

This function is used to fit a polynomial to data which has a curvilinear shape. It opens the Polynomial Fit Options dialog, allowing you to choose the curve to fit, the order of the polynomial function to use, the number of points of the resulting curve and the abscissa limits for the fit.

The results of the fit are displayed in the Log panel.

ExpDecay1

This is the first order exponential decay function and is defined as: y = y₀ + Ae^-x/t, where A is the amplitude, t is the time constant or e-folding time and y₀ is the Y offset.

ExpDecay2

This is the second order exponential decay function and is defined as: y = y₀ + A₁e^-x/t₁ + A₂e^-x/t₂, where A₁ and A₂ are the amplitudes, t₁ and t₂ are the decay times and y₀ is the Y offset.

ExpDecay3

This is the third order exponential decay function and is defined as: y = y₀ + A₁e^-x/t₁ + A₂e^-x/t₂ + A₃e^-x/t₃, where A₁, A₂ and A₃ are the amplitudes, t₁, t₂ and t₃ are the decay times and y₀ is the Y offset.

ExpGrowth

This is the first order exponential growth function and is defined as: y = y₀ + Ae^x/t, where A is the amplitude, t is the time constant and y₀ is the Y offset.

ExpLin

This function is defined as: y = e^-b₁x/(b₂ + b₃*x).

ExpSaturation

The exponential saturation function is defined as: y = b₁(1 - e^-b₂x).

PlanckWavelength

The Planck wavelength function is defined as: y = a/(x⁵(e^b/x - 1)).

Boltzmann

This function is used to fit a curve which has a sigmoidal shape. The formula used is:

in which A₁ is the low Y limit, A₂ is the high Y limit, x₀ is the inflexion (half amplitude) point and dx is the width.

Logistic

This function can be used to fit a curve which has a sigmoidal shape. The formula used is:

where A₁ is the initial Y value, A₂ is the final Y value, x₀ is the inflexion point (center) and p is the power.

Gauss

This function can be used to fit a curve which has a bell shape. It depends on four parameters: A (the area below the curve), w (the width), x_C (the center of the bell shaped curve) and y₀ (the offset along the Y-axis). The formula used in QtiPlot is described in the image below:

The full width at half maximum (FWHM) is the width of a spectrum curve measured between those points on the Y-axis which are half the maximum amplitude. It is calculated by QtiPlot after a Gauss fit operation from the width w parameter.

GaussAmp

This function is used to fit a curve which has a bell shape. The formula used is:

where A is the amplitude, w is the width, x_C is the center and y₀ is the Y-values offset.

Lorentz

This function is used to fit a curve which has a bell shape. The formula used is:

in which A is the area, w is the width, x_c is the center and y₀ is the Y-values offset.

PsdVoigt1

This function is a linear combination of Gaussian and Lorentzian functions:

The parameters of the PsdVoigt1 function have the following meaning: y₀ is the Y-values offset, A is the area, w is the width (FWHM), x_c is the center and m_u is a profile shape factor.

PsdVoigt2

This function is a linear combination of Gaussian and Lorentzian functions with different FWHM:

The parameters of the PsdVoigt2 function have the following meaning: y₀ is the Y-values offset, A is the area, w_G is the Gaussian FWHM, w_L is the Lorentzian FWHM, x_c is the center and m_u is a profile shape factor.

Rational0

This rational function is defined as: y = (b + cx)/(1 + ax).

Rational1

This rational function is defined as: y = (1 + cx)/(a + bx).

Rational2

This rational function is defined as: y = (a + bx)/(1 + cx + dx²).

Reciprocal

This is the two parameter linear reciprocal function, defined as: y = 1/(a + bx).

Sine

This function can be used to fit a curve which has a waveform shape. The formula used is: y = y₀ + Asin[π(x - x_C)/w], where y₀ is the offset, A is the amplitude, x_C is the phase shift and w is the period (w > 0).

SineSqr

This function can be used to fit a curve which has a waveform shape. The formula used is: y = y₀ + Asin²[π(x - x_C)/w]

where y₀ is the offset, A is the amplitude, x_C is the phase shift and w is the period (w > 0).