Coded HOA data frame representation that includes non-differential gain values associated with channel signals of specific ones of the dataframes of an HOA data frame representation

An apparatus for determining for the compression of an HOA data frame representation (C(k)) a lowest integer number βe of bits for describing representations of non-differential gain values corresponding to amplitude changes as an exponent of two (2e) for channel signals of the HOA data frames,

• wherein each channel signal in each frame comprises a group of sample values and wherein to each channel signal (y1(k−2), . . . ,yI(k−2)) of each one of the HOA data frames a differential gain value is assigned, wherein the differential gain value causes a change of amplitudes of first sample values of a channel signal in a current HOA data frame ((k−2)) with respect to second sample values of a channel signal in a previous HOA data frame ((k−3)), and wherein resulting gain adapted channel signals are encoded in an encoder,
• and wherein the HOA data frame representation (C(k)) was rendered in a spatial domain to O virtual loudspeaker signals wj(t), wherein positions of the virtual loudspeakers are lying on a unit sphere and are targeted to be distributed uniformly on that unit sphere, said rendering being represented by a matrix multiplication w(t)=(Ψ)−1·c(t), wherein w(t) is a vector containing all virtual loudspeaker signals, Ψ is a virtual loudspeaker positions mode matrix, and c(t) is a vector of the corresponding HOA coefficient sequences of the HOA data frame representation,
• and wherein said HOA data frame representation (C(k)) was normalised such that
• 
• w
• ⁡
• (
• t
• )
• 
• ∞
• =
• max
• 1
• ≤
• j
• ≤
• O
• ⁢
• 
• w
• j
• ⁡
• (
• t
• )
• 
• ≤
• 1
• ⁢
• ∀
• t
• ,
• said apparatus including:
• a processor configured to determine the channel signals (y1(k−2), . . . ,yI(k−2)) by:
• a) for representing predominant sound signals (x(t)) in said channel signals, multiplying said vector of HOA coefficient sequences c(t) by a mixing matrix A, wherein mixing matrix A represents a linear combination of coefficient sequences of a normalised HOA data frame representation;
• b) for representing an ambient component cAMB(t) in the channel signals, subtracting the predominant sound signals from the normalised HOA data frame representation, and transforming a resulting minimum ambient component cAMB,MIN(t) by computing wMIN(t)=ΨMIN−1·cAMB,MIN(t), wherein ∥ΨMIN−1∥2<1 and ΨMIN is a mode matrix for said minimum ambient component cAMB,MIN(t);
• c) selecting part of the HOA coefficient sequences c(t) that relate to coefficient sequences of the ambient HOA component to which a spatial transform is applied;
• the processor further configured to determine the integer number βe of bits based on βe=┌log2(┌log2(√{square root over (KMAX)}·O)┐+eMAX+1)┐,
• wherein KMAX=max1≦N≦NMAXK(N,Ω1(N), . . . ,ΩO(N)), N is the order, NMAX is a maximum order of interest, Ω1(N), . . . ,ΩO(N) are directions of said virtual loudspeakers, O=(N+1)2 is the number of HOA coefficient sequences, and K is a ratio between the squared Euclidean norm ∥Ψ∥22 of said mode matrix and O, wherein eMAX>0.