  The product processor output has recently been introduced as a spatial power
spectral density estimate, unifying product arrays such as coprime arrays,
nested arrays, and standard uniform line arrays. The expected value and
covariance function of this estimate for a white Gaussian process was derived
in previous work over these various array configurations. However, this prior
work used a uniform taper in all cases. In this paper, we show that when
product arrays are windowed with non-uniform tapers, the expected value of the
product processor output is the convolution of the true spatial power spectral
density with the spatial Fourier transform of the difference coarray. This
expected value makes a Fourier transform pair with a spatial autocorrelation
estimate obtained by windowing the true autocorrelation function. We also
derive the covariance function of the product processor output with non-uniform
tapers, and compare these derived statistics for the aforementioned array
geometries. Also, in prior work, the moments were provided only for linear
arrays; this paper extends the estimation results to multidimensional arrays.
