I was asked this question below.
I have to match i-v to a-j (matching could be one to many or many to one) and i should prove the matchings.
If conjugation is not made, i can assume that $h(n_1,n_2)$ is real.
How can i start solving this question?
Thanks. The question
HINT You have to take the DTFT of each side and match. For example (i) $$ \begin{align} \mathsf{DTFT}\left\{-h^*[n_1,n_2]\right\}&=\sum_{n_1=-\infty}^\infty\sum_{n_2=-\infty}^\infty -h^*[n_1,n_2]\;\mathrm{e}^{-i(n_1\omega_1+n_2\omega_2)}\\ &=-\left[\sum_{n_1=\infty}^\infty\sum_{n_2=-\infty}^\infty h[n_1,n_2]\;\mathrm{e}^{i(n_1\omega_1+n_2\omega_2)}\right]^*\\ &=-\left[\sum_{n_1=\infty}^\infty\sum_{n_2=-\infty}^\infty h[n_1,n_2]\;\mathrm{e}^{-i[n_1(-\omega_1)+n_2(-\omega_2)]}\right]^*\\ &=-[H(-\omega_1,-\omega_2)]^*\\ &=-H^*(-\omega_1,-\omega_2) \end{align} $$ that is (i)-(f).