I would like to compute the minimum sampling frequency for the signal $x(t)$ given below:
$x(t)= sinc ^3(300t) * sinc ^5(600t)$ and $ *$ stands for convolution.
where the sinc function is defined as $sinc (w t) = sin (\pi wt)/(\pi wt)$.
I have tried like this : $sinc^3(300t)$ will correspond convolution of 3 rectangular functions in frequency domain which results in a frequency limited function to 3 times 150 Hz ie 450 Hz. And the other function corresponding to maximum of frequency 5 times 300 Hz which is 1500 Hz. Now finally convolution operator get transformed to multiplication in frequency domain , is the maximum frequency content limited to 450 Hz and minimum sampling frequency 900 Hz?
It would be helpful if someone shows me the derivation of fourier transform of sinc function for this purpose.