Ah yes, thanks for this. Will the Sympy include these symbolic fourier transform results?
The last two: -1/t^2 and 2/t^3 can be solved using the time differentiation and the 'duality' property of Fourier transform. In matlab this can be done by syms t w fourier(-1/t^2) I used Maple but it does not work either, only for sin and cos which is just 0.5 amplitude dirac delta pulses. On Wednesday, April 21, 2021 at 5:29:50 PM UTC+1 emanuel.c...@gmail.com wrote: > Le mardi 20 avril 2021 à 13:01:13 UTC+2, jks...@gmail.com a écrit : > >> Fourier transform is currently implemented in SymPy only for integrable >> functions. None of those functions is integrable >> > > I beg your pardon ? > > >>> from sympy import fourier_transform, exp, cos, sin, integrate > >>> from sympy.abc import t,w,o > >>> integrate(sin(o*t),t) > Piecewise((-cos(o*t)/o, Ne(o, 0)), (0, True)) > >>> integrate(cos(o*t),t) > Piecewise((sin(o*t)/o, Ne(o, 0)), (t, True)) > >>> integrate(1/t**2,t) > -1/t > >>> integrate(2/t**3,t) > -1/t**2 > > so SymPy cannot be used find the transform. >> > Please… > > >>> from sympy import fourier_transform, exp, cos, sin, integrate, I, pi, oo, > >>> latex > >>> from sympy.abc import t,w,o > >>> integrate(sin(o*t)*exp(-2*I*pi*w*t),(t,-oo,oo)) > Piecewise((o/(4*pi**2*w**2*(-o**2/(4*pi**2*w**2) + 1)) + 1/(o*(1 - > 4*pi**2*w**2/o**2)), Eq(2*Abs(arg(o)), 0) & (Abs(2*arg(w) + pi) < pi) & > (Abs(2*arg(w) - pi) < pi)), (Integral(exp(-2*I*pi*t*w)*sin(o*t), (t, -oo, > oo)), True)) > >>> integrate(cos(o*t)*exp(-2*I*pi*w*t),(t,-oo,oo)) > Piecewise((I/(2*pi*w*(-o**2/(4*pi**2*w**2) + 1)) + 2*I*pi*w/(o**2*(1 - > 4*pi**2*w**2/o**2)), Eq(2*Abs(arg(o)), 0) & (Abs(2*arg(w) + pi) < pi) & > (Abs(2*arg(w) - pi) < pi)), (Integral(exp(-2*I*pi*t*w)*cos(o*t), (t, -oo, > oo)), True)) > >>> integrate(1/(t**2)*exp(-2*I*pi*w*t),(t,-oo,oo)) > Integral(exp(-2*I*pi*t*w)/t**2, (t, -oo, oo)) > >>> integrate(2/(t**3)*exp(-2*I*pi*w*t),(t,-oo,oo)) > 2*Integral(exp(-2*I*pi*t*w)/t**3, (t, -oo, oo)) > > So sympy *can* compute at least the first two, but not via > fourier_transform. > > BTW, according to Wolfram Alpha, > > - sin(o*t) has transform -I*sqrt(1/2)*sqrt(pi)*(dirac_delta(o + w) - > dirac_delta(-o + w)) > - cos(o*t) has transform sqrt(1/2)*sqrt(pi)*(dirac_delta(o + w) + > dirac_delta(-o + w)) > - t^(-2) has transform sqrt(1/2)*sqrt(pi)*w*sgn(w) > - 2/t^3 has transform -I*sqrt(1/2)*sqrt(pi)*w^2*sgn(w) > > > HTH, > > >> Kalevi Suominen >> >> On Tuesday, April 20, 2021 at 11:38:08 AM UTC+3 aTPer wrote: >> >>> I am trying to compute the integral fourier transform of >>> sin(t),cos(t),-1/t^2 and 2/t^3(look at screenshot). This for checking >>> answers for maths homework/tutorials. >>> So, I went to the Sympy documentation page and learned the code from >>> there to compute the FTs of the functions defined above but none of it >>> actually works. Then, I tried using the noconds=False This is my code: >>> >>> from sympy import fourier_transform, exp, cos, sin >>> from sympy.abc import t,w,o >>> fourier_transform(sin(o*t), t, w, noconds=False) >>> fourier_transform(cos(o*t), t, w, noconds=False) >>> fourier_transform(-1/t**2, t, w, noconds=False) >>> fourier_transform(2/t**3, t, w, noconds=False) >>> >>> https://i.stack.imgur.com/90eo8.png >>> >> -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/0bf1de58-5c9a-48b2-8a44-70b456586e6bn%40googlegroups.com.
