I think what I have done is correct up to the point of taking the
convolution product. Both G(t) and H(t) are piecewise functions. You
have to be super careful when convolving them. I think that is where I
messed up. I am working on a sympy class to convolve piecewise
functions. Currently it works for some but I hard coded some things in
the class I shouldn't have and am currently fixing that problem.
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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