RU2823441C2 - Method and apparatus for compressing and reconstructing higher-order ambisonic system representation for sound field - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: invention relates to a method and an apparatus for compressing and reconstructing a higher-order Ambisonic system representation for a sound field. HOA representation is analysed for the presence of dominant sound sources and their directions are evaluated. HOA representation is then decomposed into a number of dominant directional signals and a residual component. This residual component is transformed into a discrete spatial domain in order to obtain functions of common plane waves in uniform directions of sampling, which are predicted from dominant directional signals. Finally, the prediction error is converted back to the HOA region and represents a residual surrounding HOA component for which order reduction is performed, followed by perceptual coding of the dominant directional signals and the residual component.

EFFECT: invention improves the HOA sound field representation compression.

2 cl, 8 dwg

Description

The invention relates to a method and apparatus for compressing and restoring a higher order Ambisonics system representation for a sound field.

State of the art

The Higher Order Ambisonics system, referred to as HOA, offers one way to represent three-dimensional sound. Other methods are wavefield synthesis (WFS) or channel-based methods, such as 22.2. Unlike channel-based methods, the HOA representation offers the advantage that it is independent of the specific speaker system. This flexibility, however, comes at the expense of the decoding processing that is required to play the HOA representation on a particular speaker system. Compared to the WFS approach, where the number of loudspeakers required is usually very large, HOA can also be played on systems consisting of only a few loudspeakers. An additional advantage of HOA is that the same representation can also be used without any modification for binaural playback on headphones.

HOA is based on the representation of the spatial density of complex amplitudes of harmonic plane waves through a truncated spherical harmonic (SH) expansion. Each expansion coefficient is a function of angular frequency, which can be equivalently represented by a time domain function. Therefore, without loss of generality, it can be assumed that the complete HOA sound field representation actually consists of time domain functions, where denotes the number of expansion coefficients. These time domain functions will be equivalently referred to as sequences of HOA coefficients in the following.

Spatial resolution of HOA representation improves with increasing maximum order decomposition. Unfortunately, the number of expansion coefficients increases quadratically with order , in particular, . For example, regular HOA views using the order , require coefficients (expansion) of HOA. According to the above considerations, the total bitrate (bit rate) for transmitting the HOA representation, given the required single-channel sampling rate and number of bits per sample, determined by . Passing the HOA view of the order with sampling rate = 48 kHz using bits per sample results in a bitrate of 19.2 Mbps, which is very high for many practical applications such as streaming. Therefore, compression of HOA representations is highly preferable.

Invention

Existing methods that address compression of HOA representations (with ), are quite rare. The most direct approach, followed in E. Hellerud, I. Burnett, A Solvang and UP Svensson, "Encoding Higher Order Ambisonics with AAC", ^124th AES Convention, Amsterdam, 2008, is to directly encode the individual coefficient sequences HOA using Advanced Audio Coding (AAC), which is a perceptual coding algorithm. However, an inherent problem with this approach is the perceptual encoding of signals that are never heard. Reconstructed playback signals are typically obtained by a weighted sum of HOA coefficient sequences, and there is a high likelihood of unmasking perceptual encoding noise when the reconstructed HOA representation is played back on a particular speaker system. A major challenge to unmasking perceptual encoding noise is the high cross-correlations between individual sequences of HOA coefficients. Since the encoding noise signals in individual HOA coefficient sequences are generally uncorrelated with each other, constructive superposition of the perceptual encoding noise can occur while at the same time noise-free HOA coefficient sequences are removed by the superposition. An additional problem is that these cross-correlations lead to reduced efficiency of perceptual coders.

To minimize the extent of both effects, EP 2469742 A2 proposes to transform the HOA representation into an equivalent discrete spatial domain representation prior to perceptual encoding. Formally, this discrete spatial domain is the equivalent of the time domain of the spatial density of the complex amplitudes of harmonic plane waves, sampled in some discrete directions. The discrete spatial domain is thus represented by standard time-domain signals, which can be interpreted as general plane waves colliding from the sampling directions, and correspond to loudspeaker signals if the loudspeakers are located in exactly the same directions as the directions assumed for the spatial domain transform.

Conversion to a discrete spatial domain reduces cross-correlations between individual spatial-domain signals, but these cross-correlations are not completely eliminated. An example for relatively high cross-correlations is a directional signal whose direction falls between adjacent directions covered by the spatial domain signals.

The main disadvantage of both approaches is that the number of perceptually encoded signals is equal to , and the data rate for the compressed HOA representation grows quadratically with the order of the Ambisonics system .

To reduce the number of perceptually encoded signals, patent application EP 2665208 A1 proposes a decomposition of the HOA representation into a given maximum number of dominant directional signals and a residual surround component. Reducing the number of signals to be perceptually encoded is achieved by reducing the order of the residual ambient component. The rationale behind this approach is to maintain high spatial resolution with respect to the dominant directional signals while representing the residual with sufficient accuracy through a lower order HOA representation.

This approach works quite well as long as the sound field assumptions are satisfied, i.e. that it consists of a small number of dominant directional signals (representing general plane wave functions encoded using full order N) and a residual ambient component without any directionality. However, if the subsequent decomposition of the residual ambient component still contains some dominant directional components, the order reduction causes errors that are perceived differently when reproduced after reconstruction. Common examples of HOA representations where the assumptions are violated are general plane waves encoded in order lower than N. Such general plane waves of order lower than N may stem from authoring to make sound sources appear more widely, and can also occur when recording HOA sound field presentations using spherical microphones. In both examples, the sound field is represented by a large number of highly correlated spatial domain signals (see also Ambisonics Higher Order Spatial Resolution for an explanation).

The problem to be solved by the invention is to overcome the disadvantages resulting from the processing described in patent application EP 2665208 A1, thereby also avoiding the above-described disadvantages of the other cited prior art.

This problem is solved by the methods disclosed in claims 1 and 3. Corresponding devices that use these methods are disclosed in claims 2 and 4.

The invention improves on the HOA sound field representation compression processing described in patent application EP 2665208 A1. First, as in EP 2665208 A1, the HOA representation is analyzed for the presence of dominant sound sources, whose directions are evaluated. With knowledge of the directions of the dominant sound sources, the HOA representation is decomposed into a number of dominant directional signals representing common plane waves, and a residual component. However, instead of immediately reducing the order of this HOA residual component, it is converted to a discrete spatial domain to obtain common plane wave functions in uniform sampling directions representing the HOA residual component. These plane wave functions are then predicted from the dominant directional signals. The reason for this operation is that parts of the residual HOA component may be highly correlated with the dominant directional signals.

This prediction may be a simple prediction to produce only a small amount of additional (side) information. In the simplest case, prediction consists of appropriate scaling and delay. Finally, the prediction error is converted back to the HOA region and treated as a residual ambient HOA component for which order reduction is performed. Preferably, the effect of subtracting predictive signals from the residual HOA component is to reduce its total power as well as the remaining magnitude of the dominant directional signals and, in this way, reduce the decomposition error resulting from the reduction in order.

In principle, the new compression method is suitable for compressing a higher order Ambisonics representation, denoted HOA, to a sound field, the method comprising the steps:

- from the current time frame of HOA coefficients, estimation of the directions of the dominant sound sources;

- depending on said HOA coefficients and on said directions of dominant sound sources, decomposing said HOA representation into dominant directional signals in the time domain and a residual HOA component, wherein said residual HOA component is converted into a discrete spatial domain to obtain plane wave functions in uniform sampling directions representing said HOA residual component, and wherein said plane wave functions are predicted from said dominant directional signals, thereby providing parameters describing said prediction, and the corresponding prediction error is converted back to the HOA domain;

- reducing the current order of said residual HOA component to a lower order, resulting in a reduced order residual HOA component;

- decorrelating said reduced order HOA residual component to obtain corresponding time domain signals of the HOA residual component;

- perceptual encoding of said dominant directional signals and said HOA residual component time domain signals to provide compressed dominant directional signals and compressed residual component signals.

In principle, a new compression device is suitable for compressing a higher order Ambisonics representation, referred to as HOA, to a sound field, said device including:

- means that is configured to estimate the directions of the dominant sound sources from the current time frame of the HOA coefficients;

- means that is configured to decompose, depending on said HOA coefficients and on said directions of dominant sound sources, said HOA representation into dominant directional signals in the time domain and a residual HOA component, wherein said residual HOA component is converted into a discrete spatial domain, to obtain plane wave functions in uniform sampling directions representing said HOA residual component, and wherein said plane wave functions are predicted from said dominant directional signals, thereby providing parameters describing said prediction, and the corresponding prediction error is converted back to the HOA domain;

- means that is configured to reduce the current order of said residual HOA component to a lower order, resulting in a reduced order residual HOA component;

- means that is configured to decorrelate said reduced-order HOA residual component to obtain corresponding time domain signals of the HOA residual component;

- means that is configured to perceptually encode said dominant directional signals and said HOA residual component time domain signals to provide compressed dominant directional signals and compressed residual component signals.

In principle, the new recovery method is suitable for recovering a higher order Ambisonics representation compressed according to the compression method described above, wherein said recovery method includes the steps:

- perceptually decoding said compressed dominant directional signals and said compressed residual component signals to provide reconstructed dominant directional signals and reconstructed time domain signals representing the residual HOA component in the spatial domain;

- re-correlating said reconstructed time domain signals to obtain a corresponding reduced order residual HOA component;

- increasing the order of said reduced-order residual HOA component to the original order to provide a corresponding reduced residual HOA component;

- using said recovered dominant directional signals, said recovered residual HOA component of the original order, said estimated directions of dominant sound sources, and said parameters describing said prediction, constructing a corresponding recovered and reconstructed frame of HOA coefficients.

In principle, the new recovery device is suitable for recovering a higher order Ambisonics representation compressed according to the compression method described above, said recovery device including:

- means that is configured to perceptually decode said compressed dominant directional signals and said compressed residual component signals to provide reconstructed dominant directional signals and reconstructed time domain signals representing the residual HOA component in the spatial domain;

- means that is configured to re-correlate said reconstructed time domain signals to obtain a corresponding reduced order residual HOA component;

- means that is configured to increase the order of said residual HOA component of the reduced order to the original order to provide a corresponding restored residual HOA component;

- means that is configured to construct a corresponding recovered and reconstructed frame of HOA coefficients by using said reconstructed dominant directional signals, said reconstructed residual HOA component of the original order, said estimated directions of dominant sound sources, and said parameters describing said prediction.

Preferred further embodiments of the invention are disclosed in the respective dependent claims.

Blueprints

Exemplary embodiments of the invention are described with reference to the accompanying drawings, which show:

Fig. 1a - compression stage 1: decomposition of the HOA signal into a number of dominant directional signals, a residual HOA surround component and additional information;

Fig. 1b - compression stage 2: order reduction and decorrelation for the surrounding HOA component and perceptual encoding of both components;

Fig. 2a - stage 1 recovery: perceptual decoding of time domain signals, re-correlation of signals representing the residual ambient HOA component, and order enhancement;

Fig. 2b - recovery stage 2: construction of a complete HOA representation;

Fig. 3 - HOA decomposition;

Fig. 4 - HOA design;

Fig. 5 - spherical coordinate system.

Exemplary Embodiments

Compression processing

The compression processing according to the invention includes two successive steps illustrated in FIG. 1a and fig. 1b, respectively. The exact definitions of the individual signals are described in the section Detailed Description of HOA Decomposition and Reconstruction. Uses frame-by-frame processing for compression with non-overlapping input frames sequences of HOA coefficients of length , where k denotes the frame index. Frames are defined with respect to the sequences of HOA coefficients defined in equation (42) as

(1)

Where denotes the sampling period.

In fig. 1a, frame The sequences of HOA coefficients are input to a dominant sound source direction estimation step or stage 11, which analyzes the HOA representation for the presence of dominant directional signals whose directions are being estimated. The direction estimation can be performed, for example, by means of the processing described in patent application EP 2665208 A1. The assessed directions are indicated by , Where denotes the maximum number of direction ratings. They are assumed to be located in a matrix How

(2).

It is implicitly assumed that the direction estimates are appropriately ordered by assigning them to the direction estimates from previous frames. Therefore, the time sequence of an individual's direction estimation is assumed to describe the directional trajectory of the dominant sound source. In particular, if it is assumed that the d-th dominant sound source is not active, it is possible to indicate this by assigning an invalid value to . Then, using the estimated directions in , the HOA representation is decomposed at stage or stage 12 of decomposition into some quantity at most dominant directional signals , some parameters , describing the spatial domain signal prediction of the residual HOA component from the dominant directional signals, and the surrounding HOA component , representing the prediction error. A detailed description of this decomposition is provided in the section HOA Decomposition.

In fig. Figure 1b shows perceptual coding of directional signals. and residual ambient HOA components . Directional signals are standard time domain signals that can be individually compressed using any existing perceptual compression technique. Compressing the surrounding HOA area performed in two successive steps or stages. In step or stage 13 of order reduction, the reduction is performed to the order of the Ambisonics system , where, for example, , which results in the surrounding HOA component . This order reduction is accomplished by holding in only HOA coefficients and discarding others. On the decoder side, as described below, the corresponding zero values are added for omitted values.

It should be noted that, compared to the approach in patent application EP 2665208 A1, the reduced order can, in general, be selected smaller, since the total power as well as the remaining directivity value of the residual ambient HOA component is smaller. Therefore, reducing the order causes smaller errors compared to EP 2665208 A1.

In a subsequent stage or decorrelation stage 14, sequences of HOA coefficients representing the surrounding HOA component with reduced order, decorrelated to obtain time domain signals , which are input to (a set of) parallel perceptual encoders or compression modules 15 operating according to any known perceptual compression method. Decorrelation is performed to avoid unmasking the perceptual encoding noise when reproducing the HOA representation following its reconstruction (see patent application EP 12305860.4 for an explanation). Approximate decorrelation can be achieved by transforming V equivalent signals in the spatial domain by applying spherical harmonic transformation as described in EP 2469742 A2.

Alternatively, an adaptive spherical harmonic transform can be used, as proposed in patent application EP 12305861.2, where the grid of sampling directions is rotated to achieve the best possible decorrelation effect. An additional alternative decorrelation method is the Karhunen-Loeve transform (KLT), described in patent application EP 12305860.4. It should be noted that for the latter two types of decorrelation, some type of additional information must be provided, indicated by , to allow decorrelation to be reversed during the HOA recovery stage.

In one embodiment, perceptual compression of all time domain signals And performed jointly to improve coding efficiency.

The output of perceptual encoding is compressed directional signals and compressed ambient time domain signals .

Recovery Processing

The recovery processing is shown in FIG. 2a and fig. 2b. Like compression, it consists of two successive stages. In fig. 2a perceptual recovery of directional signals and time domain signals , representing the residual ambient HOA component, is performed in a perceptual decoding or reconstruction step or stage 21. Resulting perceptually reconstructed time domain signals re-correlated in a re-correlation step or stage 22 to provide an HOA representation of the residual component order . Optionally, re-correlation may be performed in the reverse manner as described for the two alternative treatments described for step/step 14 using passed or stored parameters depending on the decorrelation method used. After this, from the appropriate HOA submission is evaluated order in a step or step 23 of increasing the order by increasing the order. Increasing the order is achieved by adding corresponding rows of 'null values' to , thus it is assumed that the HOA coefficients with respect to higher orders have zero values.

In fig. 2b, a complete HOA representation is reconstructed in the construction step or stage 24 from the reconstructed dominant directional signals. along with relevant directions and prediction parameters , as well as from the residual ambient HOA component , which results in a restored and reconstructed frame HOA coefficients.

In the case where the perceptual compression of all time domain signals And performed jointly to improve encoding efficiency, perceptual recovery of compressed directional signals and compressed time domain signals is also performed jointly in an appropriate manner.

A detailed description of the reconstruction is provided in the HOA Reconstruction section.

HOA decomposition

A flow chart illustrating the operations performed for HOA decomposition is given in FIG. 3. Brief description of the operation: First, smooth the dominant directional signals are calculated and output for perceptual compression. Next, the remainder between the HOA submission dominant directional signals and the original HOA representation represented by a certain amount directional signals , which can be considered as general plane waves from uniformly distributed directions. These directional signals are predicted from the dominant directional signals , where the prediction parameters are displayed . Finally, the remainder is calculated and displayed between the original HOA representation and HOA submission dominant directional signals along with HOA representation predicted directional signals from uniformly distributed directions.

Before going into detail, it should be mentioned that changes in directions between successive frames can lead to disruption of the continuity of all calculated signals during construction. Therefore, instantaneous estimates of the corresponding signals for overlapping frames are computed first, which have a length of 2B. Second, the results of successive overlapping frames are smoothed using an appropriate windowing function. Each anti-aliasing, however, introduces single-frame delay.

Calculation of instantaneous dominant directional signals

Calculation of the instantaneous dominant directional signals at stage or stage 30 from the estimated directions of sound sources in for the current frame HOA coefficient sequences are based on mode mapping as described in M.A. Poletti, “Three-Dimensional Surround Sound Systems Based on Spherical Harmonics,” J. Audio Eng. Soc., 53(11), pages 1004-1025, 2005. In particular, those directional signals are sought whose HOA representation results in the best approximation of the given HOA signal.

Additionally, without loss of generality, it is assumed that each direction estimate active dominant sound source can be uniquely determined by a vector having an inclination angle and azimuth angle (see Fig. 5 for illustration) according to

(3).

First, the mode matrix based on the directional estimates of the active sound sources is calculated according to

(4).

,

Where

(5).

.

In equation (4), denotes the number of active directions for the kth frame and , shows their indexes. denotes real-valued spherical harmonics, which are defined in the section Definition of real-valued spherical harmonics.

Secondly, the matrix is calculated , containing instantaneous estimates of all dominant directional signals for the (k-1)th and kth frames, defined as

, (6)

Where

, (7).

This is done in two stages. In the first stage, the directional signal samples in the rows corresponding to inactive directions are set to zero, i.e.

, If , (8)

Where shows a set of active directions. In the second step, directional signal samples corresponding to active directions are obtained by first arranging them in a matrix according to

(9).

This matrix is then calculated to minimize the Euclidean error rate

(10).

The solution is given by

(eleven).

Temporal smoothing

For stage or stage 31, smoothing is described only for directional signals , since smoothing of other types of signals can be performed in a completely similar way. Directional Signal Estimates , , whose samples are contained in the matrix according to equation (6), are subject to windowing through the corresponding window function :

(12).

This window function must satisfy the condition that it produces a '1' when added to its shifted version (assuming a shift of B samples) in the overlap region:

(13).

An example for such a window function is given by the periodic Hann window defined by

For (14).

The smoothed directional signals for the (k-1)th frame are calculated by an appropriate superposition of the windowed instantaneous estimates according to

(15).

Samples of all smoothed directional signals for the (k-1)th frame are located in the matrix

(16).

,

Where

(17).

It is assumed that the smoothed dominant directional signals are continuous signals that are sequentially input to perceptual encoders.

Computing the HOA representation of smoothed dominant directional signals

From And , the HOA representation of the smoothed dominant directional signals at stage or stage 32 is calculated depending on the continuous signals , to simulate the same operations that would be performed to construct an HOA. Since changes in direction estimates between successive frames can lead to discontinuity once the instantaneous HOA representations of overlapping frames of length are computed again and the results of successive overlapping frames are smoothed by using an appropriate windowing function. Therefore, the HOA representation obtained through

, (18)

Where

(19)

And

(20)

HOA Residual Representation via Directed Signals on a Regular Grid

From And (those. , delayed by a delay of 381 frames), the residual representation of the HOA by means of directional signals on a regular grid is calculated in step or stage 33. The purpose of this operation is to obtain directional signals (i.e., functions of general plane waves) colliding from some fixed , almost uniformly distributed directions , (also referred to as grid directions) to represent the remainder .

First, with respect to the grid directions, the mode matrix calculated as

, (21)

Where

(22).

Since the mesh directions are fixed throughout the compression procedure, the mode matrix must be evaluated only once.

The directional signals on the corresponding grid are obtained as

(23)

.

Predicting directional signals on a regular grid of dominant directional signals

From And , directional signals on a regular grid are predicted in step or step 34. Predicting directional signals on a regular grid consisting of grid directions , from directional signals, is based on two consecutive frames for smoothing purposes, i.e. enlarged frame of grid signals (lengths ) predicted from an enlarged frame of smoothed dominant directional signals

(24).

First, every grid signal , contained in , is assigned to the dominant directional signal , contained in . The assignment may be based on the calculation of a normalized cross-correlation function between the grid signal and all dominant directional signals. Specifically, this dominant directional signal is assigned to the grid signal that provides the highest value of the normalized cross-correlation function. The assignment result can be formulated using the assignment function , appointing th grid signal -th dominant directional signal.

Secondly, each grid signal predicted from the assigned dominant directional signal .

Predicted grid signal calculated by delay and scaling from the assigned dominant directional signal How

, (25)

Where denotes the scaling factor and shows the sampling delay. These parameters are chosen to minimize the prediction error.

If the power of the prediction error is greater than the power of the grid signal itself, the prediction is assumed to have failed. Then, the corresponding prediction parameters can be set to any invalid value.

It should be noted that other types of prediction are also possible. For example, instead of calculating the full range scaling factor, it is also reasonable to determine the scaling factors for perceptually oriented frequency ranges. However, this operation improves the prediction due to the increased amount of additional information.

All prediction parameters can be located in the parameter matrix as

(26).

It is assumed that all predicted signals , , are located in the matrix .

Computing the HOA representation of predicted directional signals on a regular grid

The HOA representation of the predicted grid signals is calculated at step or stage 35 of according to

(27).

Computing the HOA representation of the residual component of the ambient sound field

From , which is the time-smoothed version (at stage/stage 36) for , from , which is a two-frame delayed version (delays 381 and 383) for , and from , which is a one-frame delayed version (delay 382) for , the HOA representation of the residual component of the ambient sound field is calculated in step or step 37 by

(28).

HOA reconstruction

Before describing in detail the processing of individual steps or stages in FIG. 4 in detail, a brief description is provided.

Directional signals with respect to uniformly distributed directions are predicted from the decoded dominant directional signals using prediction parameters . Next up is the full HOA view. constructed from the HOA representation dominant directional signals, HOA representations predicted directional signals and residual ambient HOA components .

Computing the HOA representation of dominant directional signals

And are input to step or stage 41 to determine the HOA representation of the dominant directional signals. After calculating the mode matrices And from direction estimates And , based on estimates of the directions of active sound sources for the k-th and (k-1)-th frames, the HOA representation of the dominant directional signals obtained through

(29)

Where

(thirty)

And

(31)

Predicting directional signals on a regular grid of dominant directional signals

And are introduced into step or stage 43 to predict directional signals on a regular grid of dominant directional signals. An enlarged frame of predicted directional signals on a regular grid consists of elements according to

, (32)

which are predicted from the dominant directional signals by

(33).

Computing the HOA representation of predicted directional signals on a regular grid

In step or step 44 to calculate the HOA representation of the predicted directional signals on a regular grid, the HOA representation of the predicted directional signals of the grid is obtained by

, (34)

Where denotes the mode matrix with respect to predefined mesh directions (see equation (21) for definition).

Constructing the HOA Sound Field Representation

From (those. , delayed by 42 frame delay), (which is the time-smoothed version for at stage/stage 45) and , the complete HOA sound field representation is finally constructed at stage or stage 46 as

(35).

Basics of the Ambisonics system of the highest order

The higher order Ambisonics system is based on the description of the sound field within a compact region of interest, which is assumed to be free of sound sources. In this case, the spatiotemporal behavior of sound pressure at time t and position x inside the region of interest is physically completely determined by the homogeneous wave equation. The following is based on a spherical coordinate system, as shown in FIG. 5. The x-axis points to the forward position, the y-axis points to the left, and the z-axis points to the up. Position in space represented by a radius (i.e. distance to the origin), tilt angle , measured from the polar z-axis, and the azimuthal angle , measured counterclockwise in the xy plane from the x axis. denotes transposition.

It can be shown (see E. G. Williams, "Fourier Acoustics", volume 93 of Applied Mathematical Sciences, Academic Press, 1999) that the Fourier transform of sound pressure with respect to time, denoted by , i.e.

, (36)

Where denotes the angular frequency and i denotes the imaginary unit, can be expanded into a series of spherical harmonics according to

, (37)

Where denotes the speed of sound and k denotes the angular index of the mode, which is related to the angular frequency How , denotes spherical Bessel functions of the first kind, and denotes real-valued spherical harmonics of order n and degree m, which are defined in the section Definition of real-valued spherical harmonics. Expansion coefficients depend only on the angular index of the mode k. Note that the sound pressure is implicitly assumed to be spatially limited in range. Thus, the series is truncated with respect to the order index n at the upper limit of N, which is called the HOA presentation order.

If the sound field is represented by the superposition of an infinite number of harmonic plane waves of different angular frequencies and comes from all possible directions defined by a tuple of angles , it can be shown (see B. Rafaely, "Plane-wave Decomposition of the Sound Field on a Sphere by Spherical Convolution", J. Acoust. Soc. Am., 4(116), pages 2149-2157, 2004) that the corresponding plane wave complex amplitude function can be expressed through spherical harmonic expansion

, (38)

where are the expansion coefficients refer to expansion coefficients How

(39).

Assuming that the individual coefficients are functions of angular frequency , applying the inverse Fourier transform (denoted as ) provides time domain functions

(40)

for each order n and degree m that can be collected in a single vector

(41)

.

Time domain function position index inside a vector given through .

The latest Ambisonics system format provides a sampled version using sampling rate How

, (42)

Where denotes the sampling period. Elements are referred to as Ambisonics coefficients. Note that time domain signals and, therefore, the coefficients of the Ambisonics system are real-valued.

Definition of real-valued spherical harmonics

Real-valued spherical harmonics are given through

, (43)

Where

. (44)

Associated functions of Legendre are defined as

(45)

with Legendre polynomial and, unlike the above E.G. Williams tutorial, without the Condon-Shortley phase term .

Higher-order spatial resolution of the Ambisonics system

General plane wave function , arriving from direction , is submitted to the HOA via

(46).

Corresponding spatial density of plane wave amplitudes given through

(47)

(48).

It can be seen from equation (48) that it is the product of the general plane wave function and spatial dispersion functions , for which it can be shown that it depends only on the angle between And , having the property

(49).

As expected, in the limit of infinite order, i.e. , the spatial dispersion function transforms into the Dirac delta function , i.e.

(50).

However, in the case of finite order N, the contribution of the general plane wave from the direction blurs into adjacent directions, where the degree of blur decreases with increasing order. Graph of normalized function for different values of N is shown in Fig. 6. It should be noted that any direction The behavior of the time domain of the spatial amplitude density of a plane wave is a multiple of its behavior in any other direction. In particular, the functions And for some fixed directions And are highly correlated with each other with respect to time t.

Discrete spatial domain

If the spatial density of plane wave amplitudes is sampled at a certain amount spatial directions , , which are almost uniformly distributed on the unit sphere, are obtained directional signals . Collecting these signals into a vector

, (51)

can be verified by using equation (47) that this vector can be calculated from the continuous representation of the Ambisonics system , defined in equation (41), by simple matrix multiplication as

, (52)

Where denotes the combined transposition and conjugation, and denotes the mode matrix defined by

, (53)

Where

. (54)

Since the directions are almost uniformly distributed on the unit sphere, the regime matrix is, in general, invertible. Therefore, a continuous representation of the Ambisonics system can be calculated from the directional signals through

(55).

Both equations constitute a transformation and inverse transformation between the Ambisonics representation and the spatial domain. In this application these transformations are called spherical harmonic transformation and inverse spherical harmonic transformation.

Since the directions are almost uniformly distributed on the unit sphere,

, (56)

what justifies the use instead of in equation (52). Preferably, all of the relationships mentioned are valid for the discrete time domain, as well.

On the encoding side as well as on the decoding side, the new processing may be performed by a single processor or electronic circuit, or by several processors or electronic circuits operating in parallel and/or operating in different parts of the new processing.

The invention can be used to process corresponding audio signals that may be reproduced or played on a speaker arrangement in a home environment or on a speaker arrangement in a movie theater.

Claims (13)

1. A method for reconstructing a compressed representation of a higher order Ambisonics system (denoted HOA), the method comprising: perceptually decoding the compressed dominant directional signals and the compressed residual component signals to provide reconstructed dominant directional signals and reconstructed time domain signals representing the residual HOA component in the spatial domain; re-correlating the reconstructed time domain signals to obtain a corresponding reduced-order residual HOA component; determining a restored residual HOA component based on a corresponding reduced-order residual HOA component; determining predicted directional signals based on at least a parameter; determining a HOA sound field representation based on the reconstructed dominant directional signals, the predicted directional signals, and the reconstructed HOA residual component, and wherein the parameter refers to the number of active directional signals in the current frame. 2. A device for restoring a higher order representation of the Ambisonics system (denoted HOA), the device comprising: a decoder that performs perceptual decoding of the compressed dominant directional signals and the compressed residual component signals to provide reconstructed dominant directional signals and reconstructed time domain signals representing the residual HOA component in the spatial domain; re-correlation means that re-correlate the reconstructed time domain signals to obtain a corresponding reduced-order residual HOA component; a processor configured to determine a reconstructed residual HOA component based on a corresponding reduced-order residual HOA component, the processor further configured to determine predicted directional signals based on at least a parameter; wherein the processor is further configured to determine a HOA sound field representation based on the reconstructed dominant directional signals, the predicted directional signals, and the reconstructed residual HOA component, and wherein the parameter refers to the number of active directional signals in the current frame.

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