Consider weighted spherical windowing (matrix form)

[joslloand]

Kronlachner's spherical cap windowing model proposes what is equivalent to a rectangular window over a portion of the sphere.

We've seen two artifacts when using this approach:

1. ripples in the directional response due to the window's sharp edges
2. reduced rV vector magnitude (after degree truncation)

It is expected that smoother windowing equivalent to the Tukey window, Planck-taper window, Kaiser window or other adjustable windows will offer similar directional control, but suppress the ripples seen in the response of the rectangular (spherical cap) window.

NOTE: there is a question as to whether rV lengths will be reduced given alternative windows.

[joslloand]

• Beam weights for spherical cap in sc-lang can be found here.
• Function to apply these weights in order can be found here.
• Creating an instance of HoaMatrixXformer from the returned matrix can be found here.

[joslloand]

The Zotter-Butterworth window is also a good candidate for spherical windowing.

[joslloand]

Another example of windowing, along with an accompanying visualisation, can be found here: weightedWindow.scd