An automated measurement system was developed to characterize the spatial gradient, linearity of the spatial gradient, bandwidth and transverse uniformity of a linear variable filter (LVF). To demonstrate this, the LVF fabricated in our group has been measured and analyzed. Simulations for beam spot size effects on measurements were performed for various LVF spectral peak profiles with results indicting significant averaging effect due to beam spot size and this is consistent with experiment results. Moreover, to fit the peak profile more accurately, a modified Pearson VII function was proposed and demonstrated high capability to express complex shapes of peaks mathematically. This provides a methodology for deconvoluting the original LVF peak profile from a measured averaged peak profile and has been verified using actual measured data.