Efficient computation of spectral line shapes

A method for computing spectral line shapes based on the Fourier representation of the Voigt profile is presented. The linearity of Fourier transforms is used to eliminate the need to evaluate the Voigt function repeatedly. Instead, the method requires computing only sines, cosines, and exponentials for each line and two Fourier transforms for the entire frequency range. The method is shown to be computationally more efficient than previous approaches for a wide variety of problems, particularly when there are many overlapping lines. In contrast to other approximations which have fixed error bounds, the accuracy of the transform method can be controlled by varying the frequency interval and number of points. A part of the R-band of molecular oxygen at 13,160 cm^-1 (7620Å) is computed to demonstrate the advantages of the transform method.