I will make sure I translated you code to the correct fromula.
On 2/10/23 11:32 AM, 'Tom van Woudenberg' via sympy wrote:
This is the result in Python (same as in Maple): downloaden (5).png
Op vrijdag 10 februari 2023 om 17:31:50 UTC+1 schreef Tom van Woudenberg:
Hi Brombo,
Thank you for the update. It seems my previous posts didn't show
up. Anyway, you result doesn't match the result in Maple and the
numerical evalution of the integral in Python:
Would be wonderful if we'd find an analytical solution.
Op vrijdag 10 februari 2023 om 01:08:56 UTC+1 schreef brombo:
Attached are latest results (I had calculated the roots of the
quadratic wrong) and a plot -
On 2/8/23 4:24 AM, 'Tom van Woudenberg' via sympy wrote:
Hi Brombo,
Thank you for the extensive working-out. I really appreciate
that!
However, the result doesn't seem to match the result in got
in Maple (below result in Python for N(t):
Schermafbeelding 2023-02-08 094041.jpg
Do you have any ideas on the difference?
Op woensdag 8 februari 2023 om 01:10:05 UTC+1 schreef brombo:
I didn't proof read well enough. Typo in equation 4.
Correction attached
On 2/7/23 3:02 AM, 'Tom van Woudenberg' via sympy wrote:
Thank you brombo, I'll take a closer look at the file
you send me!
Op maandag 6 februari 2023 om 22:29:25 UTC+1 schreef brombo:
I cleaned things up here is what the notebook looks
like (see attached html) -
On 2/6/23 10:36 AM, 'Tom van Woudenberg' via sympy
wrote:
Hi there,
When trying to solve a integral as part of a manual
inverse fourier transform, SymPy return the
unevaluated integral. Does anybody know if SymPy is
able to solve this integral with some help? It
would be good enough if I'd be able to obtain the
result for specific values of t.
import sympy as sp
phi,t = sp.symbols('phi,t',real=True)
sp.I*(1 -
sp.exp(4*sp.I*sp.pi*phi))*sp.exp(-8*sp.I*sp.pi*phi)/(2*sp.pi*phi*(-4*sp.pi**2*phi**2
+ 1.5*sp.I*sp.pi*phi + 4))
solution_numeric = 1 / sp.pi * sp.integrate(sp.re
<http://sp.re>(solution_in_frequency_domain_numeric*sp.exp(sp.I*2*phi*t)),(phi,0,4))
print(solution_numeric)
returns:
(Integral(sin(4*pi*phi)*re(exp(2*I*phi*t)/(-4*pi**2*phi**2*exp(8*I*pi*phi)
+ 1.5*I*pi*phi*exp(8*I*pi*phi) +
4*exp(8*I*pi*phi))), (phi, 0, 4)) +
Integral(cos(4*pi*phi)*im(exp(2*I*phi*t)/(-4*pi**2*phi**2*exp(8*I*pi*phi)
+ 1.5*I*pi*phi*exp(8*I*pi*phi) +
4*exp(8*I*pi*phi))), (phi, 0, 4)) +
Integral(-im(exp(2*I*phi*t)/(-4*pi**2*phi**2*exp(8*I*pi*phi)
+ 1.5*I*pi*phi*exp(8*I*pi*phi) +
4*exp(8*I*pi*phi))), (phi, 0, 4)))/(2*pi**2*phi)
Plotting the result for t,0,15 should give this
result according to Maple:
Schermafbeelding 2023-02-06 163521.jpg
Kind regards,
Tom van Woudenberg
Delft University of Technology
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