Let the sampling frequencies along both the directions be 32 cycles per sample. Is there aliasing or not in the image $x(m, n)$ ? If so, what are the impersonated frequencies?
*(i)
$$
x(m, n)=\cos \left(\frac{2 \pi}{32} 28 m+\frac{2 \pi}{32} 30 n-\frac{\pi}{6}\right)
$$
(ii)
$$
x(m, n)=\cos \left(\frac{2 \pi}{32} 15 m+\frac{2 \pi}{32} 14 n+\frac{\pi}{2}\right)
$$
(iii)
$$
x(m, n)=\cos \left(\frac{2 \pi}{32} 27 m+\frac{2 \pi}{32} 22 n-\frac{\pi}{3}\right)
$$
(iv)
$$
x(m, n)=\cos \left(\frac{2 \pi}{32} 3 m+\frac{2 \pi}{32} 3 n+\frac{\pi}{2}\right)
$$
(v)
$$
x(m, n)=\cos \left(\frac{2 \pi}{32} 32 m+\frac{2 \pi}{32} 32 n+\frac{\pi}{4}\right)
$$
(vi)
$$
x(m, n)=\cos \left(\frac{2 \pi}{32} 17 m+\frac{2 \pi}{32} 11 n-\frac{\pi}{3}\right)
$$