omega[n_,m_]:=4*Pi*Sin[m*Pi/(2*(n+1))];
xi[c_,t_]:=Module[{m},
            n=Length[c];
            Return[Table[c[[m]]*Cos[omega[n,m]*t],{m,1,n}]];
]
p[c_,t_]:=FourierDST[xi[c,t],1];
c={1,0,0,0,0,0,0,0,0,0}
n=Length[c];
w1=omega[n,1];
T1=2*Pi/w1;

ListPlot[{p[c,0],p[c,T1*0.25],p[c,T1*0.5],p[c,T1*0.75]},PlotRange->{{0,n+1},{-1,1}},AxesLabel->{"k","pk"}]
c={1,0.8,0.7,0.5,0,0.3,0,0.1,0,0}
ListPlot[Table[p[c,T1*t/100],{t,0,10}],PlotRange->{{0,n+1},{-1,1}},AxesLabel->{"k","pk"}]
