This uses the Chebychev design technique from the text to fit a 4 element array to a (Subscript[T, 3]) function, and visualize it with polar plots.  This includes a Manipulate to visualize the variation with d.

(* http://mathematica.stackexchange.com/questions/77910/is-there-a-plot-style-for-polarplot-to-look-like-matlab-polar *)
ClearAll[f, max, t,dv, m, r, z0, th, zv]

dv = {1/8,1/4,1/2};
r = 20 ;
m = 3 ;
z0 := Cosh[(1/m) ArcCosh[ 10^(#/20)]] // N &;
zv = z0[20] ;
f := (4 #3^3 Cos[Pi #2 Cos[#1]]^3 - 3 #3 Cos[ Pi #2 Cos[#1]])^2 & ;
(*max = NMaximize[ f[th, z0], {th, 0, Pi}] [[1]] ;*)
max = ((NMaximize[ {f[t, #, zv], t < 2 Pi, t > 0}, {t}] &/@ dv) // Transpose) [[1]] // Max ;


p = PolarPlot[f[t, #, zv] &/@ dv // Evaluate,{t, 0, 2 Pi},(*PlotStyle->Directive[Thickness[Large],Red,Dashed],*)(*PolarAxesOrigin->{Pi/2,1},*)
PolarAxesOrigin->{0,max},
PolarGridLines->Automatic,PolarAxes->True,PolarTicks->{Table[{N[Pi/6 i],ToString[30 i]<>"°"},{i,-5,6}],Automatic}
,
PlotLegends->Placed[Row[{"d/λ = ", #}] &/@ dv,{Left, Bottom}]]

q = PolarPlot[10 Log10[f[t, #, zv] ]&/@ dv // Evaluate,{t, 0, 2 Pi},(*PlotStyle->Directive[Thickness[Large],Red,Dashed],*)(*PolarAxesOrigin->{Pi/2,1},*)
PolarAxesOrigin->{0,10 Log10[max]},
PolarGridLines->Automatic,PolarAxes->True,PolarTicks->{Table[{N[Pi/6 i],ToString[30 i]<>"°"},{i,-5,6}],Automatic},
PlotLegends->Placed[Row[{"d/λ = ", #}] &/@ dv,{Left, Bottom}]]

Manipulate[
Module[{m,z0, f, max},
m = 3 ;
z0 = Cosh[(1/m) ArcCosh[ 10^(r/20)]] // N;
f := (4 z0^3 Cos[Pi d Cos[#]]^3 - 3 z0 Cos[ Pi d Cos[#]])^2 & ;
max = NMaximize[ f[th], {th, 0, 2 Pi}] [[1]] ;
PolarPlot[f[t],{t, 0, 2 Pi},PlotStyle->Directive[Thickness[Large],Red,Dashed],(*PolarAxesOrigin->{Pi/2,1},*)
PolarAxesOrigin->{0,max},
PolarGridLines->Automatic,PolarAxes->True,PolarTicks->{Table[{N[Pi/6 i],ToString[30 i]<>"°"},{i,-5,6}],Automatic}]
]
,
{{d, 1/4, "d/λ"}, 0.01, 5, Appearance -> "Labeled"},
{{r, 20, "power gain (dB)"}, 20, 40, Appearance -> "Labeled"}
]

(*PolarPlot[10 Log10[Cos[t]^2],{t, 0, 2 Pi},PlotStyle->Directive[Thickness[Large],Red,Dashed],(*PolarAxesOrigin->{Pi/2,1},*)
PolarAxesOrigin->{0,1},
PolarGridLines->Automatic,PolarAxes->True,PolarTicks->{Table[{N[Pi/6 i],ToString[30 i]<>"°"},{i,-5,6}],Automatic}]*)

(*Plot[10 Log10[Cos[t]^2], {t, 0, 2 Pi}]*)

<<peeters` ;
(*peeters`setGitDir[ "notes\\blogit" ] *)
peeters`setGitDir[ "figures\\ece1229" ]

peeters`exportForLatex["ChebychevT3FittingFig3", p]
peeters`exportForLatex["ChebychevT3FittingDbFig4", q]