Usual shape of the lines in a NMR spectrum, characterized by a central peak with long tails; proportional to 1/[(1/T2)2 + (f - fo)2], where f is frequency and fo is the frequency of the peak (i.e., central resonance frequency). A Lorentzian function is the Fourier transformation of a decaying exponential.

A mathematical function used for signal fitting (filtering) of raw data. Other commonly used line shapes are the Gaussian line shape or the super-Lorentzian line shape.

Magnitude calculation e.g. cuts the amplitude information, or can be used to obtain pure absorption Lorentzian lineshapes in spectroscopy.

Distribution of the relative strength of resonance as a function of frequency, which establishes a particular spectral line. Common line shapes are Lorentzian and Gaussian.

Multiplication of the time-dependent signal data by an exponential function, exp(t/TC), where t is time and TC is a parameter called the time constant (in spectroscopy). The time constant can be chosen to either improve the signal to noise ratio (with a negative TC) or decrease the effective spectral line width (with a positive TC) in the resulting spectrum. The use of a negative TC to improve SNR is equivalent to line broadening by convolving the spectrum with a Lorentzian function of corresponding reciprocal width.