Fourier transform of tent signal

[Neutronium]

Hello, I'm having an issue with a given problem.

Homework Statement

Using Parseval's Equation find the energy of the signal $$z(t)=\frac{4}{4+t^{2}}$$

Homework Equations

The book solves that problem by using the tent signal CTFT and duality property (i.e ). However that properly isn't in the formula sheet, and the book derives it inversely!

The Attempt at a Solution

I tried to develop it by plugging $$z(t)$$ into the CTFT analysis equation, but it becomes a serious mess with integration by parts.

So what should I do? Take the tent property as it is and apply it to the question?

Thank you.

 

[MATLABdude]

Hello, I'm having an issue with a given problem.

Homework Statement

Using Parseval's Equation find the energy of the signal $$z(t)=\frac{4}{4+t^{2}}$$

Homework Equations

The book solves that problem by using the tent signal CTFT and duality property (i.e ). However that properly isn't in the formula sheet, and the book derives it inversely!

The Attempt at a Solution

I tried to develop it by plugging $$z(t)$$ into the CTFT analysis equation, but it becomes a serious mess with integration by parts.

So what should I do? Take the tent property as it is and apply it to the question?

Thank you.

I would suggest you try doing a partial fraction decomposition on z(t). That should simplify things a little (also keep in mind the time shifting property of the convolution). I believe this works, but I haven't done a Fourier transform in a few years...

EDIT: And welcome to PhysicsForums!