Method and apparatus for generating a mixed spatial / coefficient domain representation of an HOA signal from a coefficient domain representation of the HOA signal

Abstract

To provide a method and an apparatus for generating a mixed spatial / coefficient domain representation capable of varying the number of HOA signals from a coefficient domain representation in an HOA (Higher Order Ambisonics) representation in which two representations of a spatial domain and a coefficient domain exist.SOLUTION: The HOA encoder 20 separates the vector d of coefficient domain signals into a vector d1 of coefficient domain signals having a fixed number of HOA coefficients and a vector d2 of coefficient domain signals having a varying number of HOA coefficients. A vector d1 of a certain number of HOA coefficients is transformed into a vector of corresponding spatial domain signals w1. To facilitate high quality encoding without introducing signal discontinuities, a vector of a variable number of HOA coefficients of the coefficient domain signal is adaptively normalized and multiplexed with a vector of the spatial domain signal.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a method and apparatus for generating a mixed spatial / coefficient domain representation of an HOA signal from a coefficient domain representation of the HOA signal, where the number of HOA signals can be variable. [Background technology]

[0002] Higher-Order Ambisonics (HOA) is a mathematical description of a two- or three-dimensional sound field. The sound field can be captured by a microphone array, designed from a synthetic source, or a combination of both. HOA can be used as a transmission format for two- or three-dimensional surround sound. In contrast to loudspeaker-based surround sound representations, the advantage of HOA is that it reproduces sound fields with a variety of loudspeaker configurations. This makes HOA suitable for a universal audio format.

[0003] The spatial resolution of an HOA is determined by its order, which determines the number of HOA signals that describe the sound field. There are two representations of an HOA: the spatial domain and the coefficient domain. In most cases, an HOA is originally represented in the coefficient domain and then transformed into the spatial domain by matrix multiplication (or transformation) (as described in EP 2469742). The spatial domain contains the same number of signals as the coefficient domain. However, in the spatial domain, each signal is associated with a direction, and the directions are uniformly distributed on a unit sphere. This makes it easier to analyze the spatial distribution of the HOA representation. The coefficient domain representation is a time domain representation, just like the spatial domain representation. Summary of the Invention

[0004] In the following description, the aim is basically to use the spatial domain as much as possible for the PCM transmission of the HOA representation in order to provide the same dynamic range for each direction. This means that the PCM samples of the HOA signal in the spatial domain must be normalized to a predefined range of values. However, the drawback of such normalization is that the dynamic range of the HOA signal in the spatial domain is smaller than in the coefficient domain. This is caused by the transformation matrix that generates the spatial domain signal from the coefficient domain signal.

[0005] In some applications, the HOA signals are transmitted in the coefficient domain. For example, in the process described in EP 13305558, all signals are transmitted in the coefficient domain, since a constant HOA signal and a variable number of additional HOA signals are transmitted. However, as discussed above and shown in EP 2469742, transmission in the coefficient domain is not advantageous.

[0006] As a solution, a constant number of HOA signals can be transmitted in the spatial domain, and only a variable number of additional HOA signals are transmitted in the coefficient domain. Transmitting the additional HOA signals in the spatial domain is not possible because if the number of HOA signals changes over time, the transformation matrix from the coefficient domain to the spatial domain will change over time, which may result in discontinuities in all spatial domain signals that are not optimal for the subsequent perceptual coding process.

[0007] In order to be able to transmit this additional HOA signal without exceeding a predetermined range of values, a reversible normalization process can be used that is designed to avoid discontinuities in such signals and achieves efficient transmission of the inverted parameters.

[0008] Regarding the dynamic range of the two HOA representations and the normalization of the HOA signal for PCM coding, we derive below whether such normalization should be performed in the coefficient domain or the spatial domain.

[0009] In the coefficient time domain, the HOA representation is expressed as N coefficient signals

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[0010] This coefficient signal is expressed as a vector

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[0011] The transformation into the spatial domain is performed using the following NxN transformation matrix:

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[0012] spatial domain vector

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[0013] The inverse transformation from the spatial domain to the coefficient domain is performed by the following equation: d(k)=Ψw(k) (2) Once the range of sample values ​​is defined in one domain, the transformation matrix Ψ automatically defines the range of values ​​in the other domain. In the following description, the term (k) for the kth sample is omitted.

[0014] Since the HOA representation is actually reproduced in the spatial domain, the range of values, loudness, and dynamic range are defined in the spatial domain. The dynamic range is defined by the bit resolution of the PCM encoding. In this application, "PCM encoding" refers to the conversion of floating-point representation samples to integer representation samples in fixed-point notation.

[0015] For PCM coding of the HOA representation, N spatial domain signals are coded with the largest PCM value W max and rounded to a fixed-point integer PCM representation, -1 ≤ w n It must be normalized to a value range of <1.

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[0016] The range of values ​​of the samples in the coefficient domain is determined by the infinity norm of the matrix Ψ defined by equation (4) and

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[0017] Conversely,

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[0018] The problem solved by the present invention is how to transmit in the coefficient domain those parts of an HOA signal for which spatial domain normalization is desired, without reducing the dynamic range in the coefficient domain. Furthermore, the normalized signal must not contain discontinuous changes in signal level in order to perform perceptual coding without the quality degradation caused by discontinuous changes in signal level. This problem is solved by the method disclosed in claims 1 and 6. Apparatuses using this method are disclosed in claims 2 and 7, respectively.

[0019] In principle, the method of the invention is suitable for generating a mixed spatial / coefficient domain representation of an HOA signal from a coefficient domain representation of said HOA signal, the number of said HOA signals being variable over time within successive coefficient frames. - separating the vector of HOA coefficient domain signals into a first vector of coefficient domain signals having a constant number of HOA coefficients and a second vector of coefficient domain signals having a variable number of HOA coefficients over time; - transforming said first vector of coefficient domain signals into a corresponding vector of spatial domain signals by multiplying said first vector of coefficient domain signals with the inverse of a transformation matrix; - PCM-encoding said vector of spatial domain signals to obtain a vector of PCM-encoded spatial domain signals; - normalizing the second vector of coefficient domain signals by a normalization factor, the normalization being adaptive to the current range of values ​​of the HOA coefficients of the second vector of coefficient domain signals, such that the range of values ​​available for the HOA coefficients of the vector is not exceeded during the normalization, and a uniformly continuous transition function is applied to the coefficients of the current second vector in order to continuously change the gains in the vector from the gains in the previous second vector to the gains in the subsequent second vector, the normalization providing side information for a corresponding decoder-side denormalization; - PCM-encoding said vector of normalized coefficient domain signals to obtain a vector of PCM-encoded normalized coefficient domain signals; - multiplexing said vector of PCM-encoded spatial domain signals with said vector of PCM-encoded normalized coefficient domain signals.

[0020] In principle, the inventive generating device is suitable for generating a mixed spatial / coefficient domain representation of an HOA signal from a coefficient domain representation of said HOA signal, the number of said HOA signals being variable over time within successive coefficient frames. means configured to separate a vector of HOA coefficient domain signals into a first vector of coefficient domain signals having a constant number of HOA coefficients and a second vector of coefficient domain signals having a variable number of HOA coefficients over time; - means configured to transform said first vector of coefficient domain signals into a corresponding vector of spatial domain signals by multiplying said first vector of coefficient domain signals by the inverse of a transformation matrix; - means configured to PCM-encode said vector of spatial domain signals to obtain a vector of PCM-encoded spatial domain signals; - means configured to normalize the second vector of coefficient domain signals by a normalization factor, the normalization being adaptive to a current range of values ​​of the HOA coefficients of the second vector of coefficient domain signals, in such a way that the range of values ​​available for the HOA coefficients of the vector is not exceeded during the normalization, and in such a way that a uniformly continuous transition function is applied to the coefficients of the current second vector in order to continuously change the gains in the vector from the gains in the previous second vector to the gains in the subsequent second vector, the normalization providing side information for a corresponding decoder-side denormalization; - means configured to PCM-encode said vector of normalized coefficient domain signals to obtain a vector of PCM-encoded normalized coefficient domain signals; means adapted to multiplex said vector of PCM-encoded spatial domain signals and said vector of PCM-encoded normalized coefficient domain signals.

[0021] In principle, the inventive decoding method is suitable for decoding a mixed spatial / coefficient domain representation of an encoded HOA signal, the number of which can be time-varying within successive coefficient frames, said mixed spatial / coefficient domain representation of an encoded HOA signal having been generated according to the inventive generation method described above, said decoding method comprising: - demultiplexing said multiplexed vectors of PCM-encoded spatial domain signals and PCM-encoded normalized coefficient domain signals; - transforming said vectors of PCM-encoded spatial domain signals into corresponding vectors of coefficient domain signals by multiplying said vectors of PCM-encoded spatial domain signals with said transformation matrix; - denormalizing said vector of PCM-encoded normalized coefficient domain signals, said denormalizing comprising: --The corresponding exponent e of the above received sub-information n (j-1) and the recursively calculated gain value g n (j-2) to find the transition vector hn (j-1) for the corresponding processing of the subsequent vector of the PCM-encoded normalized coefficient domain signal being processed. n Calculating the transition vector (j-1) where j is the running index of the input matrix of HOA signal vectors; applying a corresponding inverse gain value (the inverse of the gain value) to a current vector of PCM-encoded normalized signals to obtain a corresponding vector of said PCM-encoded denormalized signals; the denormalizing step including: - combining said vector of coefficient domain signals and the denormalized coefficient domain vector to obtain a combined vector of HOA coefficient domain signals, which may have a variable number of HOA coefficients.

[0022] In principle, the decoding device of the present invention is suitable for decoding a mixed spatial / coefficient domain representation of an encoded HOA signal, the number of which can be time-varying within successive coefficient frames, said mixed spatial / coefficient domain representation of an encoded HOA signal having been generated according to the inventive generation method, said decoding device comprising: means configured to demultiplex said multiplexed vector of PCM-encoded spatial domain signals and PCM-encoded normalized coefficient domain signals; means configured to transform said vectors of PCM-encoded spatial domain signals into corresponding vectors of coefficient domain signals by multiplying said vectors of PCM-encoded spatial domain signals with said transformation matrix; means configured to denormalize said vector of PCM-encoded normalized coefficient domain signals, said denormalization comprising: --The corresponding exponent e of the received sub-information n (j-1) and the recursively calculated gain value g n (j-2) to find the transition vector h n(j-1) for the corresponding processing of the subsequent vector of PCM-encoded normalized coefficient domain signals to be processed. n Calculating the transition vector, where (j-1) is held, where j is the successive index of the input matrix of HOA signal vectors; applying a corresponding inverse gain value (the inverse of the gain value) to a current vector of PCM-encoded normalized signals to obtain a corresponding vector of said PCM-encoded denormalized signals; means configured to denormalize, the means comprising: means configured to combine said vector of coefficient domain signals and the denormalized coefficient domain vector to obtain a combined vector of HOA coefficient domain signals, which may have a variable number of HOA coefficients.

[0023] Advantageous further embodiments of the invention are disclosed in the respective dependent claims.

[0024] Exemplary embodiments of the present invention are described with reference to the accompanying drawings. [Brief explanation of the drawings]

[0025] [Figure 1] FIG. 1 illustrates PCM transmission of the original coefficient domain HOA representation in the spatial domain. [Figure 2] FIG. 1 illustrates combined transmission of HOA representations in the coefficient and spatial domains. [Figure 3] FIG. 1 illustrates combined transmission of HOA representations in the coefficient and spatial domains using block-wise adaptive normalization for the signal in the coefficient domain. [Figure 4] FIG. 10 illustrates an adaptive normalization process for an HOA signal xn(j) expressed in the coefficient domain. [Figure 5] FIG. 10 illustrates a transition function used for a smooth transition between two different gain values. [Figure 6] FIG. 1 illustrates an adaptive denormalization process. [Figure 7] FIG. 1 shows the FFT frequency spectrum of the transition function hn(l) using different power exponents en, where the maximum amplitude of each function is normalized to 0 dB. [Figure 8] FIG. 1 illustrates an example transition function for three consecutive signal vectors. DETAILED DESCRIPTION OF THE INVENTION

[0026] Regarding the PCM coding of the HOA representation in the spatial domain, we set -1 ≤ w (in floating-point representation) to allow PCM transmission of the HOA representation as shown in Figure 1. n <1 is assumed to be satisfied. At the input of the HOA encoder, a transform step or stage 11 transforms the coefficient domain signal d of the current input signal frame into a spatial domain signal w using equation (1). A PCM encoding step or stage 12 converts the floating-point samples w into PCM-encoded integer samples w' in fixed-point notation using equation (3). In a multiplexing step or stage 13, the PCM-encoded integer samples w' are multiplexed into the HOA transmission format.

[0027] The HOA decoder demultiplexes from the received HOA transmission format into a signal w' in a demultiplexing step or stage 14, and retransforms the signal w' into a coefficient domain signal d' using equation (2) in step or stage 15. This inverse transform increases the dynamic range of d' because the transformation from the spatial domain to the coefficient domain always involves a format conversion from integer (PCM) to floating point.

[0028] The standard HOA transmission of FIG. 1 fails when the matrix Ψ varies over time. This is the case when the number or index of HOA signals varies over time for successive HOA coefficient sequences, i.e., successive input signal frames. As mentioned above, an example of such a case is the HOA compression process described in European Patent Application No. 13305558, in which a constant number of HOA signals are transmitted continuously and a time-variable number of HOA signals are transmitted in parallel with varying signal indices. All of the signals are transmitted in the coefficient domain, which, as mentioned above, is suboptimal.

[0029] In accordance with the present invention, the process described in connection with FIG. 1 can be extended as shown in FIG.

[0030] In step or stage 20, the HOA encoder separates the HOA vector d into two vectors d1 and d2, where the number of HOA coefficients M for vector d1 is constant and vector d2 contains a variable number K of HOA coefficients. Since the signal index n is time-invariant for vector d1, PCM encoding is performed in the spatial domain in steps or stages 21, 22, 23, 24, and 25 using signals corresponding to w1 and w'1 shown in the lower signal path of Figure 2. This corresponds to steps or stages 11 to 15 in Figure 1. However, multiplexing step / stage 23 obtains an additional input signal d"2, and in the HOA decoder, demultiplexing step / stage 24 provides a different output signal d"2.

[0031] The number or size K of HOA coefficients in vector d2 varies over time, and the index n of the transmitted HOA signal varies over time. This precludes transmission in the spatial domain because a time-varying transformation matrix would be required, which would result in discontinuities in all perceptually coded HOA signals (note that perceptual coding steps or stages are not shown in the figure). However, such signal discontinuities should be avoided, as they would degrade the quality of the perceptual coding of the transmitted signal.

[0032] Therefore, d2 should be transmitted in the coefficient domain. Due to the larger range of values ​​of the signal in the coefficient domain, the signal is further divided into coefficients d1 and d2 before PCM coding is applied in step or stage 27.

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[0033] The output signal d″2 of the demultiplexing step / stage 24 is a factor

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[0034] According to the present invention, the efficiency of PCM coding in the coefficient domain can be improved by using signal-adaptive normalization of the signal. However, such normalization must be invertible and uniformly continuous from sample to sample. The required block-wise adaptive processing is illustrated in Figure 3. The jth input matrix

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[0035] In adaptive normalization in step / stage 36, a uniformly continuous transition function is applied to the samples of the current input coefficient block to continuously change the gain from the last input coefficient block to the gain of the next input coefficient block. This type of processing requires a delay of one block, because the change in normalization gain must be detected in the previous input block. The advantage is that the amplitude modulation introduced is small, so the perceptual coding of the modulated signal has little effect on the denormalized signal.

[0036] The adaptive normalization is performed independently for each HOA signal in D2(j). The signals are represented by the row vector x n T is expressed by

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[0037] 4 shows in more detail the adaptive normalization in step / stage 36. The inputs to this process are: ·Time-smoothed maximum value x n,max,sm (j-2) Gain value g n (j-2), that is, the corresponding signal vector block x n The gain applied to the coefficient immediately preceding (j-2) current block signal vector x n (j) Signal vector x of the previous block n (j-1)

[0038] First block x n When processing (0) begins, the recursive input values ​​are initialized with the given values. n The coefficient of (-1) can be set to zero, and the gain value g n (-2) is best set to "1", x n,max,sm (-2) may be set to a predetermined average amplitude value.

[0039] Then, the immediately preceding block g n The gain value of (j-1), the corresponding value e of the side information vector e(j-1) n (j-1), the time-smoothed maximum value x n,max,sm (j-1), and the normalized signal vector x' n (j-1) is the output of the process.

[0040] The purpose of this process is to process the signal vector x n The gain value applied to (j-1) is g n (j-2) to g n (j-1) to obtain the gain value g n (j-1) is the signal vector x n The purpose is to normalize (j) to a suitable range of values.

[0041] In the first processing step or stage 41, the signal vector

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[0042] In step or stage 43, x n,max This applies temporal smoothing to the previous temporally smoothed maximum value x n,max,sm This is done using a recursive filter that receives the current temporally smoothed maximum value x n,max,sm (j-1). The purpose of such smoothing is to dampen the adaptation of the normalized gain over time, thereby reducing the number of gain changes and thus the amplitude modulation of the signal. n,max Temporal smoothing is applied only if the value x is within a given range of values. n,max If is not within the given range of values, then x n,max,sm (j-1) to x n,max (i.e., leave it as it is and set it to x n,maxThe value of ) is retained. The reason is that the subsequent process has to attenuate the actual value of x n,max within a predetermined value range. Therefore, the time smoothing process operates only when the normalization gain is constant or when the signal x n (j) is amplified without exceeding the value range.

[0043] In step / stage 43, x n,max,sm (j - 1) is calculated as follows. [Equation] Here, 0 < a ≤ 1 is the attenuation constant.

[0044] To reduce the bit rate for the transmission of vector e, the normalization gain is calculated from the current time-smoothed maximum value x n,max,sm (j - 1) and transmitted as a power exponent with base "2". Therefore, [Equation] should be satisfied, and in step or stage 44, the quantized power exponent e n (j - 1) is obtained from the following formula [Equation]

[0045] During the period when the signal is amplified again (i.e., the value of the total gain increases over time) to utilize the resolution available for efficient PCM coding, the power exponent e n(j) (and thus the gain difference between successive blocks) may be limited to a small maximum value, e.g., '1'. This has two advantageous effects: first, a small gain difference between successive blocks results in only a small amplitude modulation through the transition function, resulting in reduced crosstalk between adjacent subbands in the FFT spectrum (see the related discussion on the influence of transition functions on perceptual coding in relation to Fig. 7); second, the bit rate for coding the exponent is reduced by limiting its value range.

[0046] Total maximum amplification value

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[0047] In step or stage 45, the exponent value e n (j-1) is applied to the transition function to obtain the current payoff value g n (j-1) to obtain the gain value g n (j-2) to the gain value g n For successive transitions to (j-1), we use the function shown in Figure 5. The operation rules of the function are as follows:

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[0048] At step or stage 46, the signal vector x n The (j-1) sample is calculated by the transition vector h n It is weighted by the gain value of (j-1).

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[0049] More specifically, the transition vector

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[0050] The adaptive denormalization process at the decoder or receiver side is shown in Figure 6. The input value is the PCM coded normalized signal x" n (j-1), the appropriate exponent e n (j-1), and the gain value of the previous block g n (j-2). The gain value of the previous block g n (j-2) is calculated recursively. Here, g n (j-2) must be initialized with a predetermined value used in the encoder. The output is the gain value g from step / stage 61. n (j-1) and the denormalized signal from step / stage 62

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[0051] In step or stage 61, a power is applied to the transition function x n To recover the range of values ​​of (j-1), equation (11) is used to calculate the received exponent en (j-1) and the recursively calculated payoff g n (j-2) to transition vector h n (j-1) to calculate the gain g for the next block processing. n (j-1) is h n It is set to (L-1).

[0052] In step or stage 62, the inverse gain (the inverse of the gain) is applied. The amplitude modulation applied in the normalization process is

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[0053] Regarding the side information transmission, the exponent e n For (j-1) transmissions, the probability cannot be assumed to be uniform, since the normalization gain applied to successive blocks of the same value range will be constant. Therefore, entropy coding can be applied to the exponent values ​​to reduce the required data rate, similar to, for example, Huffman coding.

[0054] One drawback of the above process is that the gain value g n It would be a recursive calculation of (j-2), so the denormalization process can only start from the beginning of the HOA stream.

[0055] One solution to this problem is to n The solution is to add an access unit to the HOA format to provide information for regularly calculating (j-2). In this case, the access unit is

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[0056] Normalized signal x' n The effect of (j-1) on perceptual coding is h n (l) Frequency response

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[0057] Figure 7 shows the magnitude-normalized (to 0 dB) FFT spectrum H to clarify the spectral distortion introduced by amplitude modulation. n (u) indicates |H n The decay of (u)| is relatively rapid for small exponents and flattens out for larger exponents.

[0058] h in the time domain n (l) by x n The amplitude modulation of (j-1) is H in the frequency domain. n (u) is equivalent to convolution with the frequency response H n The rapid decay of (u) causes x' n The crosstalk between adjacent subbands in the FFT spectrum of (j-1) is reduced. n(j-1) is highly relevant for the subsequent perceptual coding process because subband crosstalk affects the estimated perceptual characteristics of the signal. n For the attenuation of (u), the denormalized signal x n For (j-1), x' n The assumption of a perceptual coding process for (j-1) is valid.

[0059] This means that for small exponents, x' n The perceptual coding process of (j-1) is almost x n It is shown that the perceptual coding process of normalized signals is equivalent to that of (j-1), and furthermore, that the perceptual coding process of normalized signals has little effect on non-normalized signals as long as the magnitude of the exponent is small.

[0060] The processing of the present invention may be performed by a single processor or electronic circuit at the sending and receiving ends, or may be performed by several processors or electronic circuits operating in parallel and / or operating on different parts of the processing of the present invention.

[0061] Several aspects will be described. [Aspect 1] 1. A method for decoding an HOA representation, the method comprising: transforming the vector of PCM-encoded spatial domain signals in the HOA representation into a corresponding vector of coefficient domain signals by multiplying the vector of PCM-encoded spatial domain signals by a transform matrix; denormalizing the vector of PCM-encoded normalized coefficient domain signals of the HOA representation, wherein the denormalizing comprises: determining a transition vector, each element of the transition vector being determined as a recursively calculated gain value multiplied by a base value raised to a corresponding power, the corresponding power being provided as side information, and the corresponding power and the gain value being based on successive indices of an input row of an HOA signal vector; applying the corresponding inverse gain value to the vector of PCM-encoded normalized coefficient domain signals to determine a corresponding vector of PCM-encoded denormalized signals; denormalizing, including combining said vector of coefficient domain signals with said vector of unnormalized coefficient domain signals to determine a combined vector of HOA coefficient domain signals, which may have a variable number of HOA coefficients; A method comprising: [Aspect 2] 1. An apparatus for decoding an HOA expression, the apparatus comprising: means configured to transform a vector of PCM-encoded spatial domain signals in said HOA representation into a corresponding vector of coefficient domain signals by multiplying said vector of PCM-encoded spatial domain signals by a transformation matrix; means configured to denormalize the vector of PCM-encoded normalized coefficient domain signals of the HOA representation, the means configured to denormalize comprising: means configured to determine a transition vector, each element of the transition vector being determined as a recursively calculated gain value multiplied by a base value raised to a corresponding power, the corresponding power being provided as side information, and the corresponding power and the gain value being based on successive indices of an input row of an HOA signal vector; means configured to apply said corresponding inverse gain value to said vector of PCM encoded normalized coefficient domain signals to determine a corresponding vector of PCM encoded denormalized signals; means configured to denormalize, the means comprising: means configured to combine said vector of coefficient domain signals with said vector of unnormalized coefficient domain signals to determine a combined vector of HOA coefficient domain signals, which may have a variable number of HOA coefficients; 1. An apparatus comprising: Aspect 3 A computer program product for causing a computer to execute the method according to aspect 1.

Claims

1. 1. A method for decoding a Higher Order Ambisonics (HOA) representation, the method comprising: perceptually decoding the plurality of PCM-encoded coefficient domain signals to determine normalized coefficient domain signals; For each normalized coefficient domain signal: Receive index side information; the exponent side information, a gain value, and f(l)=0.25cos(πl / (L-1))+0.75, where l = 0, 1, 2, …, L-1 determining a transition vector based on a function f(l) based on determining an output denormalized vector by multiplying the transition vector by the normalized coefficient domain signal; outputting the output denormalized vector. method.

2. 2. The method of claim 1, wherein the transition vector is determined based on multiplication of the previous gain value and the value of the function f(l) raised to a first value, the first value being determined based on the exponent side information.

3. 2. The method of claim 1, further comprising entropy decoding entropy coded exponent side information from the coded bitstream to determine the exponent side information.

4. The method of claim 1 , wherein the encoded bitstream comprises a sequence of frames.

5. A non-transitory storage medium containing, storing or recording a digital audio signal decoded according to claim 1.

6. A non-transitory computer-readable storage medium storing executable instructions that cause a computer to perform the method of claim 1.

7. 1. An apparatus for decoding a Higher Order Ambisonics (HOA) representation, the apparatus comprising: a first processing unit for perceptually decoding the plurality of PCM-encoded coefficient domain signals to determine normalized coefficient domain signals; For each normalized coefficient domain signal: Receive exponent side information; the exponent side information, a gain value, and f(l)=0.25cos(πl / (L-1))+0.75, where l = 0, 1, 2, …, L-1 determining a transition vector based on a function f(l) based on determining an output denormalized vector by multiplying the transition vector by the normalized coefficient domain signal; Output the output denormalized vector and a second processing unit configured to Device.

8. 8. The apparatus of claim 7, wherein the second processing unit is configured to determine the transition vector based on multiplication of the previous gain value and the value of the function f(l) raised to a first value, the first value being determined based on the exponent side information.

9. 8. The apparatus of claim 7, wherein the second processing unit is further configured to entropy decode entropy coded exponent side information from the coded bitstream to determine the exponent side information.

10. The apparatus of claim 7 , wherein the encoded bitstream comprises a sequence of frames.

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