Peakshapes Lorentzian

The Lorentzian peakshape corresponds to a statistical function called the Cauchy distribution. It is less common but often arises in certain types of spectroscopy such as NMR. A simplified equation for a Lorentzian is... 

Gaussian and Lorentzian peakshapes of equal half-heights... 

The main difference between Gaussian and Lorentzian peakshapes is that the latter has a bigger tail, as illustrated in Figure 3.2 for two peaks with identical half-widths and heights. 

Asymmetric peakshapes often described by a Gaussian/Lorentzian model, (a) Tailing left is Gaussian and right Lorentzian. (b) Fronting left is Lorentzian and right Gaussian... 

The peakshape in the frequency domain relates to the decay curve (or mechanism) in the time domain. The time domain equivalent of a Lorentzian peak is... 

In die Fourier transform of a real time series, die peakshapes in the real and imaginary halves of die spectrum differ. Ideally, the real spectrum corresponds to an absorption lineshape, and die imaginary spectrum to a dispersion lineshape, as illustrated in Figure 3.20. The absorption lineshape is equivalent to a pure peakshape such as a Lorentzian or Gaussian, whereas die dispersion lineshape is a little like a derivative. 

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