Non-separable, higher-order generalized cosine windows in 2D for images Higher-order generalized cosine windows define a useful parametric family of windows functions, embedding Hamming, Hann, Blackman, Nutall, etc.:
$$w(n) = \sum_{k = 0}^{K} a_k\; \cos\left( \frac{2 \pi k n}{N} \right)$$
Are there non-separable 2D similar forms, i.e. not a tensor product of the 1D form, usable on the standard rectangular lattice (excluding designs such as in Multidimensional windows over arbitrary lattices and their application to FIR filter design)?
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.