The　discrete　Fourier　transform(DFT)　is　used　for　fractional　Brownian　motion(FBM)　surface　synthesis　in　tribology(i.e.,　contact,　sliding,　and　sealing,　etc).　However,　the　relationship　between　fractal　parameters(fractal　dimension　and　scale　factor)　and　traditional　parameters,　the　influence　of　fractal　parameters　on　surface　appearance,　have　not　been　deeply　discussed　yet.　These　lead　to　some　kind　of　difficulty　to　ensure　the　synthesized　surfaces　with　ideal　fractal　characteristic,　required　traditional　parameters　and　geometric　appearance.　A　quantitative　relationship　between　fractal　parameters　and　the　root　mean　square　deviation　of　surface　(Sq)　is　derived　based　on　the　energy　conservation　property　between　the　space　and　frequency　domain　of　DFT.　Under　the　stability　assumption,　the　power　spectrum　of　a　FBM　surface　is　composed　of　concentric　circles　strictly,　a　series　of　FBM　surfaces　with　prescribed　Sq　could　be　synthesized　with　given　fractal　dimension,　scale　factor,　and　sampling　numbers,　but　the　ten-point　height(Sz),　the　skewness(Ssk)　and　the　kurtosis(Sku)　are　still　in　random,　where　the　probability　distributions　of　Sz　and　Ssk　are　approximately　normal　distribution.　Furthermore,　by　iterative　searching,　a　surface　with　desired　Abbott-Firestone　curve　could　be　obtained　among　those　surfaces.　An　intuitive　explanation　for　the　influence　of　fractal　dimension　and　scale　factor　on　surface　appearance　is　obtained　by　discussing　the　effects　on　the　ratio　of　energy　between　high　and　low　frequency　components.　Based　on　the　relationship　between　Sq　and　surface　energy,　a　filtering　method　of　surface　with　controllable　Sq　is　proposed.　The　proposed　research　ensures　the　synthesized　surfaces　possess　ideal　FBM　properties　with　prescribed　Sq,　offers　a　method　for　selecting　desired　Abbott-Firestone　curve　of　synthesized　fractal　surfaces,　and　makes　it　possible　to　control　the　Sq　of　surfaces　after　filtering.　©　Chinese　Mechanical　Engineering　Society　and　Springer-Verlag　Berlin　Heidelberg　2013.