n=256; h=2π/n;

SD=Table[5Sin[x]+10 Sin[4 x],{x,0,2π-h,h}];

Dimensions[SD]

plotData=ListPlot[SD,Joined->True]

FSD = Im[Fourier[SD]];

ListPlot[FSD[[1;;32]],Joined->True,PlotRange->All,PlotStyle->RGBColor[1,0,0]]

u[x_]:=2Sum[FSD[[i+1]] Sin[ i h x],{i,1,5}] /(Sqrt[n])

fPlot=Plot[u[x],{x,0,256},PlotStyle->RGBColor[1,0,0],PlotRange->All]

Show[{fPlot,plotData},PlotRange->All]

?Fourier