In order to clarify the spatial statistics calculation of road roughness and find out the relations among several important power spectral densities (PSD), Parseval’s theorem and the Wiener-Khintchine theorem are employed. Based on these theorems, the calculation formulas of spatial autocorrelation and PSD functions can be obtained, and a detailed derivation of the conversion relationships among spatial displacement, velocity and acceleration PSD is given. The relationships between spatial frequency PSD and angular frequency PSD can be obtained according to different Fourier transform patterns. Moreover, due to the lack of strictly theoretical analysis of PSD discretization for road irregularity modeling, it is thoroughly analyzed based on the frequency domain convolution theorem and the principles of six kinds of Fourier transform. In addition, the irrationality of the PSD verifying method in the literature is pointed out. It is also proved that Welch’s spectrum estimation method produces different kinds of road PSD depending on different parameters, such as spatial or temporal sampling frequency. Results show that the analysis and derivation are accurate and can be applied to road irregularity modeling and vehicle ride comfort analysis.