I have to find the energy of $y(t)$ $$h(t)=ho\;sinc^3(t/T)\\ x(t)=V_0+V_1\;sin(3\pi\; t/T)\\ y(t)=x*h\;(t) $$ Where "$*$" is the convolution and $sinc(t)=\frac {sin(\pi t)}{\pi t}$
I think that the best way is to use the Fourier transform to find $Y(f)$ and then use the Parseval theorem, but I can't find the $sinc^3$ Fourier transform. My idea is: $$sinc^3(t/T) = sinc^2(t/T)\; sinc(t/T)$$ then $$\mathscr{F}[sinc^3(t/T)]=\{ T\; triangle(f\;T)\}*\{ T\; rect(f\;T)\} $$
But I can't solve this convolution. Can someone solve the entire problem?
Essentially, you want the convolution, as you say, of "triangle" with "rectangle".
In other words, you have the functions $$f(x) = \begin{cases}1,&|x|\le 1\\0,&|x|>0\end{cases}$$ and $$g(x) = \begin{cases}1-x/2,&x\in[0,2]\\1+x/2,&x\in[-2,0]\\0,&|x|>2.\end{cases}$$
Now you need to find their convulution: first of all, it will be zero outside the interval $[-3,3]$, and inside it you can easily find the result - you have nothing but polynomials here. Hint: the piecewise result should be polynomial of the second degree.