X[z_]=(1/5)+(1/(5 (z^4)))+(1/(5 (z^3)))+(1/(5 (z^2)))+(1/(5 z));

a=0.889919+0.646564 I;w=0.886924+0.367376 I;
mag=Abs@DiscreteChirpZTransform[ConstantArray[1/5,5], 31, w, a];
path=N[{Re[#],Im[#]}]&/@Table[a (w^k),{k,0,30}];

Show[{ListPointPlot3D[Flatten/@Thread[{path,mag}] ,Filling->0,FillingStyle->Directive[{Red,Thickness[Large]}],PlotStyle->Directive[{Red,PointSize[Large]}],PlotRange->All, ImageSize->Medium],Graphics3D[{Red,Line[Flatten/@Thread[{path,mag}]]}],Plot3D[Abs[X[x+I y]],{x,-1,1},{y,-1,1}, PlotStyle->Opacity[0.6],Mesh->0,MeshFunctions->{(#1^2+#2^2)&}, PlotRange->{0,30}]}]