Continuous Angles of Arrival

Quantized angles-of-arrival do not suffice when sources move over time. Also, continuous angles-of-arrival allow a less quantized ``source width'' parameter for each source--as if the source were coming from a distant solid-angle region (like a nebula) instead of one point (star).

There are various methods for continuously variable fractional-delay filtering (Smith, 2010). Perhaps the simplest is by means of Lagrange interpolation (Franck, 2008; Smith, 2010; Välimäki, 1995; Franck, 2011).

The case of first-order Lagrange interpolation is especially simple, being simple linear interpolation. Thus, one can linearly ``cross-fade'' in amplitude from one source angle to the next to implement a moving source. Distributed sources can be formed as a linear combination of adjacent source angles.