I have a signal $x(t)$ with bandwidth $B_x$, and I am taking its cosine to create $y(t) = cos(x(t))$. After checking the spectrum with FFT, it seems that $y(t)$ is also bandlimited. But, is there a way to prove it? If so, what is the bandwidth?
I have tried applying the integrals from the Fourier series definition, but these integrals have to be evaluated numerically, so they don´t provide a rigorous, analytical proof.
Thanks in advance.