Solution
= Solution
For real $f$, <complex conjugation> commutes with its <absolutely convergent> Fourier <integral>:
$$
[\widetilde f(-\omega)]^*
=\left[\int_{-\infty}^\infty f(t)e^{i\omega t}\,dt\right]^*
=\int_{-\infty}^\infty f(t)e^{-i\omega t}\,dt.
$$
Thus
$$
\boxed{[\widetilde f(-\omega)]^*=\widetilde f(\omega).}
$$
This <Hermitian symmetry> pairs the positive- and negative-frequency components of a real signal; its real part is even and its imaginary part is odd.