I have the following signal:
$$ f(t) = 60\operatorname{sinc}(24t) + (30\operatorname{sinc}(10t) \cdot \cos(40\pi t) ) $$
and I should apply an ideal low-pass filter with a cutoff frequency of $ 10\mathrm{Hz} $.
Now, by applying the fourier transform to the functions above I get (please guide me if I'm wrong):
$$
\frac{5}{2}\operatorname{rect}\left(\frac{t}{24}\right) + 3\operatorname{rect}\left(\frac{t}{10}\right) \ast \frac{1}{2}[\delta(f - 40) + \delta(f+40)]
$$
At this point what should i do? Multiply by a rect built from the $ 10\mathrm{Hz} $ cutoff frequency?
Thanks,