Good morning, i had a question regarding the Nyquist rate : Let's say i have a signal $x(t)$ with Nyquist Rate $w_0$. I need to find the Nyquist rate of the following two signals : $$(x * z)(t) \text{ where } z(t) = \sin(\omega_0/3 t)$$ $$(x * z)(t) \text{ where } z(t) = \cos(\omega_0 t)$$

If i understand, it means $x(t)$ is band limited at $\omega_0/2$. I also know that convolution in the time domain is multiplication in the frequency domain. But I am unsure how to conclude on those questions. I hope you can help ! Thanks a lot