Package edu.cnu.mdi.splot.example

Class LorentzianExample

java.lang.Object
java.awt.Component
java.awt.Container
java.awt.Window
java.awt.Frame
javax.swing.JFrame
edu.cnu.mdi.splot.example.AExample
edu.cnu.mdi.splot.example.LorentzianExample
All Implemented Interfaces:
PlotChangeListener, ImageObserver, MenuContainer, Serializable, EventListener, Accessible, RootPaneContainer, WindowConstants
public class LorentzianExample extends AExample
Example demonstrating the Lorentzian (Breit-Wigner / Cauchy) fit: 
 y(x) = A·(Γ/2)² / [(x−x&sub0;)² + (Γ/2)²] + B

Synthetic data is generated from a known resonance peak, Gaussian noise is added, and the built-in CurveDrawingMethod.LORENTZIAN fitting method is applied. The Lorentzian has heavier tails than a Gaussian of the same FWHM — this example generates both for direct visual comparison so the difference is immediately apparent.

The true parameters of the Lorentzian are:

  • A = 12.0 (peak height above baseline)
  • x₀ = 5.0 (resonance center)
  • Γ = 1.6 (FWHM; the half-width at half-maximum is Γ/2 = 0.8)
  • B = 0.5 (flat background)

A Lorentzian arises in physics wherever a damped harmonic oscillator describes the response: nuclear/particle resonances (Breit-Wigner), atomic spectral lines, Q-factor of mechanical and electrical resonators, and natural line widths.

See Also:

  • Constructor Details

    • LorentzianExample

      public LorentzianExample(boolean headless)
      Creates the example, optionally without showing a window.
      Parameters:
      headless - if true the window is not displayed

  • Method Details