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Fourier self-deconvolution is a special high pass FFT filter which synthetically narrows the effective trace bandwidth features. This aids in identifying the principal bands that make up a more complex band with overlapping features. This can be useful for more accurate determination of the number of peaks in a trace region, the band positions, and areas. This technique can also be used to accurately determine starting parameters for applications such as Curve Fit.
This application is based on the method described by P.R. Griffiths and G. Pariente. Two filters are employed in this method. An exponential filter is used to sharpen spectral features; the constant  is varied to change the filter shape. The parameter equals the full width at half hieght (FWHH) of the widest resolvable peak. Realize that the imposed filter is the transform of a Lorentzian line shape.
As Fourier self-deconvolution tends to increase the apparent noise in the data, there is some benefit to be gained by simultaneously applying a low pass smoothing filter. This can effectively reduce the noise, which may be at a higher spatial frequency than the peaks, without losing peak resolution. The forms of the filters are boxcar and Bessel, and are mathematically described below.
The deconvolution filter is a simple exponential filter of the form  where is the deconvolution filter constant and X is the array (i.e., data file) whose X range is normalized between 0 and 1. This function is multiplied by the Fourier transformed trace, and the data is then reverse Fourier transformed to give the result. | 
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