wxMaxima + gnuplot = Mathematica-like densitymap with a twist

Question

I would like to plot the frequency-domain response of a filter in a similar manner to how the pole-zero plots are on the Wikipedia's "Chebyshev filter" page: http://en.wikipedia.org/wiki/File:Chebyshev_Type_I_Filter_s-Plane_Response_(8th_Order).svg . In particular, what I would like is to cut the plot in half along the Y axis and to make the cut stand out as representing the frequency response.

So far I have managed to get this:

The maked seam can be seen but it doesn't stand out, as if freshly welded. I hope the meaning gets to you because I can't find a better explanation now.

Now, what I have, so far, with wxMaxima's draw3d() function, is this:

draw3d(logx=false,logy=false,logz=true,
enhanced3d=false,line_width=2,color=red,explicit(cabs(Hs(x+%i*y)),x,-0.01,0,y,-3,3),
enhanced3d=[z**.5,x,y,z],palette=gray,proportional_axes=xy,
/* cbrange=[0.05,100.95], */ view=[0,0],yv_grid=101,xu_grid=101,
explicit(cabs(Hs(x+%i*y)),x,-1,0,y,-3,3))$

where Hs(s) is defined earlier, say:

Hs(s):=0.0248655/((s+0.210329)*(s^2+0.12999*s+0.521695)*(s^2+0.340319*s+0.22661))$

I don't know how to make the frequency response stand out, the order of printing doesn't seem to matter. Does anyone know if it can be done and, if so, how?

Answer 1

I don't know how to achieve that with maxima, but here is a solution with gnuplot only. This uses the + pseudo filename to create the 1D-plot for x=0 with splot. Complex numbers are specified with brackets, {x,y}, i.e. i = {0,1}:

set terminal pngcairo size 1000,800
set output 'chebyshev.png'

N = 501
set isosamples N
set samples N
set pm3d interpolate 3,3

set palette gray
set cbrange [*:10]
set xrange [-1:0]
set yrange [-3:3]

set logscale z
set autoscale zfix

set view 120,278
unset key
set grid

Hs(s) = 0.0248655/((s+0.210329)*(s**2+0.12999*s+0.521695)*(s**2+0.340319*s+0.22661))

splot abs(Hs(x+{0,1}*y)) w pm3d, \
      '+' using (y = ($0/(N-1.0) * 6 - 3), 0):(y):(abs(Hs({0,1}*y))) w l lw 3

The result with 4.6.3 is: