Encoding equations
From Ambisonia
This table gives the factor a mono signal should be multiplied by before being added to each channel to give FuMa encoding. The first column of formulae allows calculation from the angles of azimuth and elevation (A and E). The second, allows calculation from the normalized position of the source (remember that +x is forwards, +y is left, and +z is up). The formulae in the second column in terms of direction cosines (so x2+y2+z2=1) were determined from those in the first using trigonometric identities.
| Channel | From Angles | From Direction Cosines |
|---|---|---|
| W | sqrt(1/2)=0.707107 | sqrt(1/2)=0.707107 |
| X | cos(A)cos(E) | x |
| Y | sin(A)cos(E) | y |
| Z | sin(E) | z |
| R | 1.5sin2(E) - 0.5 | 1.5z2-0.5 |
| S | cos(A)sin(2E) | 2zx |
| T | sin(A)sin(2E) | 2yz |
| U | cos(2A)cos2(E) | x2-y2 |
| V | sin(2A)cos2(E) | 2xy |
| K | sin(E)(5sin2(E) - 3)/2 | z(5z2-3)/2 |
| L | sqrt(135/256)cos(A)cos(E)(5sin2(E) - 1) | sqrt(135/256)x(5z2-1) |
| M | sqrt(135/256)sin(A)cos(E)(5sin2(E) - 1) | sqrt(135/256)y(5z2-1) |
| N | sqrt(27/4)cos(2A)sin(E)cos2(E) | sqrt(27/4)z(x2-y2) |
| O | sqrt(27/4)sin(2A)sin(E)cos2(E) | sqrt(27)xyz |
| P | cos(3A)cos3(E) | x(x2-3y2) |
| Q | sin(3A)cos3(E) | y(3x2-y2) |
