Convolution of Spectra
The spectrum function F'(ω) of a lowresolution spectrum is calculated as a convolution
,
where F(ω') is any highresolution spectrum function described in previous paragrsph, and B(ωω') is the apparatus function, which simulates the effect of the aperture of the device.
Fig. 1. Five apparatus functions B(x) used for convolution of highresolution spectra: 1  rectangular slit function, 2  triangular slit function, 3  Gaussian slit function, 4  dispersion slit function, 5  ideal Michelson interderometer slit function. These functions are normalized to unity; γ is a slit width or an apparatus resolution (AR).
Portal sites deals with different apparatus functions (Fig. 1):

Rectangular slit function
B(x) = 1/γ , if x ≤ γ/2 & B(x) = 0, if x > γ/2 ;

Triangular slit function
B(x) = 1/γ*(1x/γ), if x ≤ γ & B(x) = 0, if x > γ ;

Gaussian slit functionsimilar to the Doppler line shape (see the Line profiles section)
B(x) = sqrt(ln2/π) · exp(ln2·(x/γ)^{2}) ; 
Dispersion slit function similar to the Lorentz line shape considered in Line profiles section
B(x) = π^{1} · (γ/2) · (x^{2} + (γ/2)^{2}) ,but the halfwidth γ here equals the double halfwidth D.

Slit function of the ideal Michelson interferometer
B(x) = sin(2πx/γ)/(πx) if x<>0 & 1 if x=0 ;

Difraction slit function
B(x) = sin(πx/γ)^{2}·γ/(πx)^{2} if x<>0 & 1 if x=0 .
Certainly, to obtain the suitable accuracy of the lowresolution spectrum, the interval of the highresolution spectrum should be larger than the interval of the lowresolution spectrum by, at least, a double wing of slit function. The system provides such increase of the range on lowresolution spectrum simulation by default.