1. Determine whether the system q(x, y) = f(x, - 1) + f(0, y) is
(a) Linear
(b) Shift-invariant
2. Consider the 1-D system whose input-output equation is given by
g(x) = f(x) * f(x) where * denotes convolution
(a) Write an integral expression that gives g(x) as a function of f(x)
(b) Determine whether the system is linear
(c) Determine whether the system is Shift-invariant
3. Consider two continuous signals f(x, y) and g(x, y) that are separable, show that their convolution is also separable.
4. Show that the 2-D Fourier transform of the rect function is the sinc function.