Non-separable, higher-order generalized cosine windows in 2D for images
The form:

$$w(x, y) = \sum_{j = -K}^{K}\sum_{k = -K}^{K} a_{|j|,|k|}\; \cos(\pi jx + \pi ky),$$

where:

$$a_{j,k} = a_{k,j},\\
\sum_{j = -K}^{K}\sum_{k = -K}^{K} a_{|j|,|k|} = 1,\\
x \in -1..1,\\
y \in -1..1$$

yields window functions that are 2D similar. Window functions of that form are not generally separable, but some of them are, for example:

$$w(x, y) = \frac{\cos(\pi x - \pi y)}{8} + \frac{\cos(\pi x + \pi y)}{8} + \frac{\cos(\pi x)}{4} + \frac{\cos(\pi y)}{4} + \frac{1}{4}\\
= \left(\frac{\cos\left(\pi x\right)}{2} + \frac{1}{2}\right)\left(\frac{\cos\left(\pi y\right)}{2} + \frac{1}{2}\right)$$



For this window function, if the balance between the zero-frequency term and the higher terms is altered (as in going from Hann to Hamming), separability breaks.