How do I find the Energy Density Function of $g(t)$ if i am not given an input or impulse response? $$g(t)=\frac{12a}{t^2+a^2}$$
I need to find the Energy Density Function of the signal, but everywhere I look has an input and an impulse response. Does anyone know how to solve this. Would I just take the absolute value of it, square it and then integrate it?
If you're referring to energy spectral density, then you need to compute the squared magnitude of the Fourier transform of $g(t)$:
$$\big|G(\omega)\big|^2=\left|\int_{-\infty}^{\infty}g(t)e^{-j\omega t}dt\right|^2\tag{1}$$