Fourier's transformation on sinc function 3

Question

So I have function

$$f(t)=\frac{sin(7t)}{\pi t}+\frac{\sin(\pi t)}{7t}$$

and I figured I should turn it into

$$f(t)=\frac{7t}{\pi t}sinc(7t)+\frac{\pi t}{7t}sinc(\pi t)$$

But I'm not quite sure how the fourier transformation/integration acts with sinc.

Answer 1

Alright, this is not the perfect answer, but how sinc basicly works here is:

$$f(t)=\frac{sin(7t)}{\pi t}+\frac{\sin(\pi t)}{7t}$$

$$F(w)=7rect_7(w)+\frac{pi^2}{7}rect_7(w)$$

The exact answer might be wrong, but the logic here is:

$$f(t)=sinc(t)$$

$$F(w)=\pi rect_1(w)$$

and

$$f(t)=sinc(at)$$

$$F(w)=\frac{1}{|a|}F(\frac{w}{a})$$