order and degree

The order and degree parameters appear in audioBlockFormat only for the 'HOA' typeDefinition.

The meaning of order and degree values is based on the following definition of real-valued spherical harmonics:

$$Y_n^m(\theta,\phi) = N_n^{|m|}P_n^{|m|}\cos(\theta) \begin{cases} \sqrt{2}\cos(m\phi), & \text{for}\ m > 0\\ 1, & \text{for}\ m = 0\\ -\sqrt{2}\sin(m\phi), & \text{for}\ m < 0 \end{cases}$$

Where:

• $n$ is the order value, $m$ is the degree value, $\phi$ is azimuth, and $\theta$ is elevation
• $N_n^{|m|}$ is the normalization parameter for the given order and degree
• $P_n^{|m|}$ is the associated Legendre function for the given order and degree.

The associated Legendre functions $P_n^m(x)$ are defined as:

$$P_n^m(x) = \left(1-x^2\right)^{\frac{m}{2}} \frac{d^m}{dx^m} P_n(x),\quad m≥0$$

with the Legendre polynomial $P_n(x)$ and without the Condon-Shortley phase term $(-1)^m$.