Laplace transform not found.
3 次查看(过去 30 天)
显示 更早的评论
I am trying to compute the Laplace transform of a known function. I have replicated the code shown below in Mathematica and it works fine, but I am unsure as to why it is not working in Matlab. The result I get is just laplace (some expression).
clearvars
close all
syms G w0 wc wk tau s C
a(tau) = int(wk^3*exp(-1i*(wk-w0)*tau), wk, 0, wc);
corr(tau) = (G/(w0^3))*(a(tau));
F(s) = laplace(corr(tau),tau,s);
C(s) = solve(s*C-1==-F(tau)*C,C);
2 个评论
Walter Roberson
2020-12-3
编辑:Walter Roberson
2020-12-3
How are you doing the transform in Mathematica? Wolfram Alpha says it is invalid.
https://www.wolframalpha.com/input/?i=laplace+transform&assumption=%7B%22F%22%2C+%22LaplaceTransformCalculator%22%2C+%22transformfunction%22%7D+-%3E%22%28G*%28%286*exp%28tau*w0*sqrt%28-1%29%29%29%2Ftau%5E4+%2B+%28exp%28tau*w0*sqrt%28-1%29%29*exp%28-tau*wc*sqrt%28-1%29%29*%28tau%5E3*wc%5E3*sqrt%28-1%29+%2B+3*tau%5E2*wc%5E2+-+tau*wc*6*sqrt%28-1%29+-+6%29%29%2Ftau%5E4%29%29%2Fw0%5E3%22&assumption=%7B%22F%22%2C+%22LaplaceTransformCalculator%22%2C+%22variable1%22%7D+-%3E%22tau%22&assumption=%7B%22C%22%2C+%22laplace+transform%22%7D+-%3E+%7B%22Calculator%22%7D&assumption=%7B%22F%22%2C+%22LaplaceTransformCalculator%22%2C+%22variable2%22%7D+-%3E%22s%22
回答(1 个)
Walter Roberson
2020-12-3
The wk^3*exp(x*tau) is getting integrated to include a /tau^4 term -- the general pattern wk^n*exp(...*tau) integrates to something that divides by tau^(n+1)
And that is leading to a problem with the laplace. You do not have compensating tau^4 in your numerator, and
syms t s
laplace(1/t, t, s)
which is to say that the laplace transform of division by the variable being transformed is not being processed. That is because the transform does not exist.
另请参阅
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!