How can I plot laplace transformed functions?

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Murloc50 on 28 Nov 2021
Commented: Star Strider on 29 Nov 2021
How can I plot laplace transformed functions? Since the function should be imaginary I can not use fplot, can I? For example, how would I plot this:
syms x
f = sin(x);
l = laplace(f);
Thanks in advance.
Murloc50 on 29 Nov 2021
I think a 3D Plot would be best since it is a function with a complex and real part, wouldnt it? Since I am no expert, what kind of plot would you recommend? Or does this depend on the function laplace() returns?

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Accepted Answer

Star Strider
Star Strider on 29 Nov 2021
It might be easier to do this outside the Symbolic Math Toolbox.
That aside, try this —
syms x s js rs sigma omega
f = sin(x);
l = laplace(f)
l = 
lc(sigma,omega) = subs(l,{s},{sigma+1j*omega}) % Define As Complex, With Complex Arguments
lc(sigma, omega) = 
fsurf(lc, [ -0.1 0 -2*pi 2*pi ], 'MeshDensity',125)
set(gca, 'YTick',[-2*pi : pi/2 : 2*pi], 'YTickLabel',compose('%.1f\\pi',(-2:0.5:2)))
axis([-0.1 0.1 -2*pi 2*pi])
Plotting it in two dimensions is of course an option, however the function has three dimensions (,amplitude) so a three-dimensional plot is appropriate. The two complex-conjugate poles at are clearly visible.
Not perfect, however the best fsurf can do here with this function!

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