Fournier Command and Integral Command

Good day,

I would like to ask for your assistance regarding the use of matlab code. The given equation is t/9+t^2. Now, I was able to put in the code in matlab as follows:

Fournier Code:

syms w t

f = t/(9 + t^2)

F = fourier(f)

pretty(F)

However, I need to have an integral command for this example. The answer must be similar in the given picture..

Can you provide me the integral command given the fournier command specified above? Thank you.

Answer 1

[Star Strider]

I hope this is not homework!

syms w t T 
f = t/(9 + t^2) 

f = 

F = int(f*exp(-1j*w*t), t, -T, T)

F = 

F = int(f*exp(-1j*w*t), t, -1, 1)

F = 

F = simplify(f,500)

F = 

[MathWizardry]

Hi,

Can you do it like this sir? The answer is not correct sir.

The answer must be similar in the given picture..

[Star Strider]

I changed the sign of the exponent in the edited version just now (although that is irrelevant, so long as the inverse transform has the opposite sign). The limits of integration can be ±Inf or ±T or ±1 since that makes no difference in the integral, so long as they are symmetrical (in this instance).

EDIT — (27 Apr 2021 at 03:41)

The int function has problems with this, however integrateByParts does not:

syms w t 
f = t/(t+9*t^2)

f = 

F1 = int(f*exp(-1j*w*t), t, -1, 1)

F1 = 

F1 = simplify(F1, 500)

F1 = 

F2 = integrateByParts((t/(t+9*t^2))*exp(-1j*w*t), diff(t))

F2 = 

F2(t) = simplify(F2, 500)

F2(t) = 

IntF2 = F2(1)-F2(-1)

IntF2 = 

IntF2 = simplify(IntF2, 500)

IntF2 = 

.