Need help with a Fourier transform using its properties

Question

The problem states:

Use two Fourier transform properties to find $X(\omega)$

$$x(t) = \mathrm{sinc}^2 (c(t+a))$$

I understand to use the time shifting property to simplify what's inside the sinc function, but after that I am not sure what to do. We are given a table of transforms and properties but I am unsure of which to use to continue in the problem.

Answer 1

Hint:

• Use the Fourier transform pair number $6$ and the modulation property (number $12$ on the right page) to find the Fourier transform of $\mathrm{sinc}^2(t)$. You should assume $x(t)=m(t)=\mathrm{sinc}(t)$. So the Fourier transform would be convolution of two $\mathrm{rect}$ functions which gives you a triangular function.

• Then use the time shifting and time scaling properties (number $3$ and number $5$ on the right page).