Rendering System

Description

Embodiments relate to a rendering system and a method for operating the same. Some embodiments relate to a source-specific system identification.

Applications, such as Acoustic Echo Cancellation (AEC) or Listening Room Equalization (LRE) require the identification of acoustic Multiple-Input/Multiple-Output (MIMO) systems. In practice, multichannel acoustic system identification suffers from the strongly cross-correlated loudspeaker signals typically occurring when rendering virtual acoustic scenes with more than one loudspeaker: the computational complexity grows with at least the number of acoustical paths through the MIMO system, which is N_{L}-N_{M} for N_{L} loudspeakers and N_{M} microphones. Robust fast-converging algorithms for multichannel filter adaptation, such as the Generalized Frequency Domain Adaptive Filtering [GFDAF] [BBK05] even have a complexity of N_{L}^{3} when robustly solving the involved linear systems of equations for cross-correlated loudspeaker signals by a Cholesky decomposition [GVL96]. Even more, if the number of loudspeakers is larger than the number of virtual sources N_{s} (i.e. the number of spatially separated sources with independent signals), the acoustic paths from the loudspeakers to the microphones of the LEMS cannot be determined uniquely. As this so-called non-uniqueness problem [BMS98] is inevitable in practice, an infinitely large set of possible solutions for the LEMS exists, from which only one corresponds to the true LEMS.

In the past decades, nonlinear [MHB01] or time-variant [HBK07, SHK13] pre-processing of the loudspeaker signals has been proposed to address the non-uniqueness problem while even slightly increasing the computational burden. On the other hand, the concept of WDAF alleviates both the computational complexity and the non-uniqueness problem [SK14] and is optimum for uniform, concentric, circular loudspeaker and microphone arrays. To this end, WDAF employs a spatial transform which decomposes sound fields into elementary solutions of the acoustic wave equation and allows approximate models and sophisticated regularization in the spatial transform domain [SK14]. Another approach known as Source-Domain Adaptive Filtering (SDAF) [HBSIO] performs a data-driven spatio-temporal transform on the loudspeaker and microphone signals in order to allow an effective modeling of acoustic echo paths in the resulting highly time-varying transform domain. Yet, the identified system does not represent the LEMS, but is a signal dependent approximation. Another adaptation scheme is cailed Eigenspace Adaptive Filtering (EAF), which is actually approximated by WDAF [SB R06]. In the aforementioned approach, an N 2-channel acoustic MIMO system with N_{L} = N_{M} - N would correspond to exactly N paths after transformation of the signals into the system's eigenspace. The method of [HB13] describes an iterative approach for estimating the required eigenspaces of the LEMS. None of these approaches employs side information from an object-based rendering system. Even WDAF only exploits prior knowledge about a transform-domain LEMS, while assuming special transducer placements (uniform circular concentric loudspeaker and microphone arrays).

Therefore, it is the object of the present invention to reduce a computational complexity for identifying a loudspeaker-enclosure-microphone system.

This object is solved by the independent claims.

Advantageous implementations are addressed by the dependent claims.

Embodiments of the present invention provide a rendering system comprising a plurality of loudspeakers, at least one microphone and a signal processing unit. The signal processing unit is configured to determine at least some components of a loudspeaker-enclosure-microphone transfer function matrix estimate describing acoustic paths between the plurality of loudspeakers and the at least one microphone using a rendering filters transfer function matrix using which a number of virtual sources is reproduced with the plurality of loudspeakers.

Further embodiments provide a rendering system comprising a plurality of loudspeakers, at least one microphone and a signal processing unit. The signal processing unit is configured to estimate at least some components of a source-specific transfer function matrix (HS) describing acoustic paths between a number of virtual sources, which are reproduced with the plurality of loudspeakers, and the at least one microphone, and to determine at least some components of a loudspeaker-enclosure-microphone transfer function matrix estimate describing acoustic paths between the plurality of loudspeakers and the at least one microphone using the source-specific transfer function matrix.

According to the concept of the present invention, the computational complexity for identifying a loudspeaker-enclosure-microphone system which can be described by a loudspeaker-enclosure-microphone transfer function matrix can be reduced by using a rendering filters transfer function matrix when determining an estimate of the loudspeaker-enclosure-microphone transfer function matrix. The rendering filters transfer function matrix is available to the rendering system and used by the same for reproducing a number of virtual sources with the plurality of loudspeakers. In addition, instead of directly estimating the loudspeaker-enclosure-microphone transfer function matrix at least some components of a source-specific transfer function matrix describing acoustic paths between the number of virtual sources and the at least one microphone can be estimated and used in connection with the rendering filters transfer function matrix for determining the estimate of the loudspeaker-enclosure-microphone transfer function matrix.

In embodiments, the signal processing unit can be configured to determine the components (or only those components) of the loudspeaker-enclosure-microphone transfer function matrix estimate which are sensitive to a column space of the rendering filters transfer function matrix.

Thereby, the computational complexity for determining the loudspeaker-enclosure-microphone transfer function matrix estimate can further be reduced.

In embodiments, the signal processing unit can be configured to determine at least some components of the loudspeaker-enclosure-microphone transfer function matrix estimate based on the equation

H = H_{s}Hp

wherein H represents the loudspeaker-enclosure-microphone transfer function matrix estimate, wherein H_{s} represents the estimated source-specific transfer function matrix, wherein H_{D} represents the rendering filters transfer function matrix, and wherein Hp represents an approximate inverse of the rendering filters' transfer function matrix H_{D}.

In embodiments, the signal processing unit can be configured to update, in response to a change of at least one out of a number of virtual sources or a position of at least one of the virtual sources, at least some components of the loudspeaker-enclosure-microphone

transfer function matrix estimate using a rende ng filters transfer function matrix corresponding to the changed virtual sources.

For example, the signal processing unit can be configured to update at least some components of the loudspeaker-enclosure-microphone transfer function matrix estimate based on the equation

wherein κ - 1 denotes a previous time interval, wherein κ denotes a current time interval, wherein between the previous time interval and the current time interval at least one out of a number of virtual sources and a position of at least one of the virtual sources is changed, wherein Η(κ\κ represents a loudspeaker-enclosure-microphone transfer function matrix estimate, Η (κ\κ - 1) represents components of the loudspeaker-enclosure-microphone transfer function matrix estimate which are not sensitive to the column space of the rendering filters transfer function matrix,

represents an estimated source-specific transfer function matrix, and wherein Η£(κ) represents an inverse rendering filters transfer function matrix.

Further, the signal processing unit can be configured to update at least some components of the loudspeaker-enclosure-microphone transfer function matrix estimate based on the equation

- 1)) H£ (K)

wherein κ - 1 denotes a previous time interval, wherein κ denotes a current time interval, wherein between the current time interval and the previous time interval at least one out of a number of virtual sources and a position of at least one of the virtual sources is changed, wherein Η(κ\κ) represents a loudspeaker-enclosure-microphone transfer function matrix estimate, wherein Η{κ\κ - 1) represents a loudspeaker-enclosure-microphone transfer function matrix estimate,

represents an estimated source-specific transfer function matrix, wherein Η(κ\κ - 1) represents a loudspeaker-enclosure-microphone transfer function matrix estimate, and wherein represents an inverse rendering filters transfer function matrix.

Therewith, an average load of the signal processing unit can be reduced which can be advantageous for computationally powerful devices which have limited electrical power resources, such as multicore smartphones or tablets, or devices which have to perform other, less time-critical tasks in addition to the signal processing.

Further, the signal processing unit can be configured to update at least some components of the loudspeaker-enclosure-microphone transfer function matrix estimate based on the distributedly evaluated equation

H (K

- 2) + Hg(K ~ 1)Η (κ - 1)

as part of an initialization of a following interval's estimated source-specific transfer function matrix by

H_{S}(K + 1

wherein κ - 2 denotes a second previous time interval, wherein κ - 1 denotes a previous time interval, wherein κ denotes a current time interval, wherein κ + 1 denotes a following time interval, wherein between the time intervals at least one out of a number of virtual sources and a position of at least one of the virtual sources is changed, wherein /Ο - Ι) represents a loudspeaker-enclosure-microphone transfer function matrix estimate, H_{S}(K + 1

represents an estimated source-specific transfer function matrix, wherein R(K - 1\κ - 2) represents a loudspeaker-enclosure-microphone transfer function matrix estimate, wherein (κ - 1) represents an update of an estimated source-specific transfer function matrix, H^ {K - 1) represents an inverse rendering filters transfer function matrix, H_{D} (K + 1) represents a rendering filters transfer function matrix, (κ) represents an update of an estimated source-specific transfer function matrix, and wherein H^'^{K+ >} represents a transition transform matrix which describes an update of an estimated source-specific transfer function matrix of the current time interval to the following time interval, such that only a contribution of

is computed between two time intervals.

This is advantageous for the identification of very large systems, in case of computationally less powerful processing devices, or when sharing one processing device

with other time-critical applications (e.g., head units of a car), the peak load produced by the signal processing application is to be reduced.

Different to all common approaches, embodiments employ prior information from an object-based rendering system (e.g., statistically independent source signals and the corresponding rendering filters) in order to reduce the computational complexity and, although the LEMS cannot be determined uniquely, to allow for a unique solution of the involved adaptive filtering problem. Even more, some embodiments provide a flexible concept allowing either a minimization of the peak or the average computational complexity.

Further embodiments provide a method comprising a step of determining a loudspeaker-enclosure-microphone transfer function matrix describing acoustic paths between a plurality of loudspeakers and at least one microphone using a rendering filters transfer function matrix using which a number of source signals is reproduced with the plurality of loudspeakers.

Further embodiments provide a method comprising a step of estimating at least some components of a source-specific transfer function matrix describing acoustic paths between a number of virtual sources, which are reproduced with a plurality of loudspeakers, and at least one microphone, and a step of determining at least some components of a loudspeaker-enclosure-microphone transfer function matrix estimate describing acoustic paths between the plurality of loudspeakers and the at least one microphone using the source-specific transfer function matrix.

Embodiments of the present invention are described herein making reference to the appended drawings:

Fig. 1 shows a schematic block diagram of a rendering system, according to an embodiment of the present invention;

Fig. 2 shows a schematic diagram of a comparison of paths to be modeled by a classical loudspeaker-enclosure-microphone systems identification and by a source-specific system identification according to an embodiment;

Fig. 3 shows a schematic block diagram of signal paths conventionally used for estimating the loudspeaker-enclosure-microphone transfer function matrix (LEMS H);

Fig. 4 shows a schematic block diagram of signal paths used for estimating the source-specific transfer function matrix (source-specific system H_{s}), according to an embodiment;

Fig. 5 shows a schematic diagram of an example for efficient identification of an

LEMS by identifying source-specific systems during intervals of constant source configuration and knowledge transfer between different intervals by means of a background model of the LEMS, where the identified system components accumulate;

Fig. 6 shows a schematic block diagram of signal paths used for an average-load- optimized system identification, according to an embodiment;

Fig. 7 shows a schematic block diagram of signal paths used for a peak-load- optimized system identification, according to an embodiment;

Fig. 8 shows a schematic block diagram of a spatial arrangement of a rendering system with 48 loudspeakers and one microphone, according to an embodiment;

Fig. 9a shows a schematic block diagram of a spatial arrangement of a rendering system with 48 loudspeakers and one microphone, according to an embodiment;

Fig. 9b shows in a diagram a normalized residual error signal at the microphone of the rendering system of Fig. 9a from a direct estimation of the low- dimensional, source specific system and from the estimation of the high- dimensional LEMS;

shows a schematic block diagram of a spatial arrangement of a rendering system with 48 loudspeakers and one microphone, according to an embodiment;

Fig. 10b shows in a diagram a system error norm achievable by transforming the low-dimensional source-specific system into an LEMS estimate in comparison to a direct LEMS update;

Fig. 1 1 shows a flowchart of a method for operating a rendering system, according to an embodiment of the present invention; and

Fig. 12 shows a flowchart of a method for operating a rendering system, according to an embodiment of the present invention.

Equal or equivalent elements or elements with equal or equivalent functionality are denoted in the following description by equal or equivalent reference numerals.

In the following description, a plurality of details are set forth to provide a more thorough explanation of embodiments of the present invention. However, it will be apparent to one skilled in the art that embodiments of the present invention may be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form rather than in detail in order to avoid obscuring embodiments of the present invention. In addition, features of the different embodiments described hereinafter may be combined with each other unless specifically noted otherwise.

Fig. 1 shows a schematic block diagram of a rendering system 100 according to an embodiment of the present invention. The rendering system 100 comprises a plurality of loudspeakers 102, at least one microphone 104 and a signal processing unit 106. The signal processing unit 106 is configured to determine at least some components of a loudspeaker-enclosure-microphone transfer function matrix estimate H describing acoustic paths 1 10 between the plurality of loudspeakers 102 and the at least one microphone 104 using a rendering filters transfer function matrix H_{D} using which a number of virtual sources 108 is reproduced with the plurality of loudspeakers 102.

In embodiments, the signal processing unit 106 can be configured to use the rendering filters transfer function matrix H_{D} for calculating individual loudspeaker signals (or signals that are to be reproduced by the individual loudspeakers 102) from source signals associated with the virtual sources 108. Thereby, normally, more than one of the loudspeakers 102 is used for reproducing one of the source signals associated with the

virtual sources 108. The signal processing unit 106 can be, for example, implemented by means of a stationary or mobile computer, smartphone, tablet or as dedicated signal processing unit.

The rendering system can comprise up to N_{L} Loudspeakers 102, wherein N_{L} is a natural number greater than or equal to two, N_{L}≥ 2. Further, the rendering system can comprise up to N_{M} microphones, wherein N_{M} is a natural number greater than or equal to one, N_{M}≥ 1 . The number N_{s} of virtual sources may be equal to or greater than one, N_{s} > 1 . Thereby, the number N_{s} of virtual sources is smaller than the number N_{L} of loudspeakers, N_{S} < N_{L}.

In embodiments, the signal processing unit 106 can be further configured to estimate at least some components of a source-specific transfer function matrix H_{s} describing acoustic paths 1 12 between the number of virtual sources 108 and the at least one microphone 104, to obtain a source-specific transfer function matrix estimate H_{S}- Thereby, the processing unit 106 can be configured to determine the loudspeaker-enclosure-microphone transfer function matrix estimate H using the source-specific signal transfer function matrix estimate H_{s}.

In the following, embodiments of the present invention will be described in further detail. Thereby, the idea of estimating the source-specific transfer function matrix (HS) and using the same for determining the loudspeaker-enclosure-microphone transfer function matrix estimate R will be referred to as source-specific system identification.

In other words, subsequently embodiments of the source-specific system identification (SSSysid) and embodiments allowing either a minimization of the peak or the average computational complexity, based on embodiments of the source-specific system identification, will be described. While embodiments of the source-specific system identification allow a unique and efficient filter adaptation and provide the mathematical foundation for deriving a valid LEMS estimate from the identified filters, embodiments of average- and peak-load-optimized systems allows a flexible, application-specific use of processing resources.

Consider an object- based rendering system, i.e. WFS [SRA08], which renders N_{s} statistically independent virtual sound sources (e.g., point sources, plane-wave sources) employing an array of N_{L} loudspeakers. To allow for a voice control of an entertainment system or an additional use of the reproduction system as hands-free front-end in a communication scenario, a set of N_{M} microphones for sound acquisition and an AEC unit may be used. The acoustic paths between the loudspeakers and N_{M} microphones of interest can be described as linear systems with discrete-time Fourier transform (DTFT) domain transfer function matrices H e^{ja}) e £^{N}M^{XN}L with the normalized angular frequency Ω. For the sake of brevity of notation, the argument Ω will be neglected for all signal vectors and transfer function matrices, which means that H stands for H(e^{j} ). This notation is employed in Fig. 2, which depicts the vector of DTFT-domain source signals s E C^{NS} , the rendering filters' transfer function matrix H_{D} e c^{WiXWs}, the loudspeaker signals x_{L} = H_{D}s e C^{Wl} , the LEMS transfer function matrix H, and the microphone signal vector

xjviic = H L = HHn is,

where the cascade of the rendering filters with the LEMS will be referred to as source-specific system

Both for recording near-end sources only (requiring an AEC unit) and for room equalization, the LEMS H can be identified adaptively. This can be done by minimizing a quadratic cost function derived from the difference e_{Mic} between the recorded microphone signals χ_{Μκ} and the microphone signal estimates obtained with the LEMS estimate ?, as depicted in Fig. 3. Thereby, in Fig. 3, the number of squares symbolizes the number of filter coefficients to estimate.

As mentioned before, multichannel acoustic system identification suffers from the strongly cross-correlated loudspeaker signals typically occurring when rendering acoustic scenes with more than one loudspeaker: for more loudspeakers than virtual sources (N_{L} > N_{s}), the acoustic paths of the LEMS H cannot be determined uniquely ('non-unique ness problem' [BMS98]). This means that an infinitely large set of possible solutions for H exists, from which only one corresponds to the true LEMS H .

As opposed to this, the paths from each virtual source to each microphone can be described as an N_{s} x N_{M} MIMO system H_{s} (marked in Fig. 2 by the curly brace) which can be determined uniquely for the given set of statistically independent virtual sources (the assumption of statistical independence even holds if the sources are instruments or persons performing the same song). Due to the statistical independence of the virtual sources, the computational complexity of the system identification with a GFDAF algorithm increases only linearly with N_{s} instead of cubically with N_{L}, as the covariance matrices to invert become diagonal. Furthermore, the number of acoustic paths to be modeled is reduced by a factor of N_{s} / N_{L}. Hence, an estimate for H_{s} can be obtained as depicted in Fig. 4 very accurately and with less effort than an estimate for H according to Fig. 3. Thereby, in Fig. 3, the number of squares symbolizes the number of filter coefficients to estimate. The systems to be identified and the respective estimates are indicated in Fig. 2 above the block diagrams.

Although H is not determined uniquely by H_{s} in general, the non-uniqueness of this mapping is exactly the same as the non-uniqueness problem for determining H directly and finding one of the systems H is easily possible by approximating an inverse rendering system Hp and pre-filtering the source-specific system H_{s} to obtain one particular

= I I S H j )- ^2)

Hence, a statistically optimal estimate H, which also could have been the result from adapting H directly, can be obtained by identifying H_{s} by an H_{s} with very low effort and without non-uniqueness problem and transforming H_{s} into an estimate of H in a systematic way. This can be seen as exploiting non-uniqueness rather than seeing it as a problem: if it is impossible to infer the true system anyway, the effort for finding one of the solutions should be minimized.

Subsequently, determining an LEMS estimate from a Source-Specific System Estimate will be described. In other words, a suitable mapping from a source-specific system to an LEMS corresponding to the source-specific system will be described. For given source-specific transfer function estimates H_{s}, the concatenation of the driving filters with the

LEMS estimate H should fulfill HH_{D} _H_{S}, analogously to Eq. (1 ). For the typical case of less synthesized sources than loudspeakers (N_{s} < N_{L}), this linear system of equations does not allow a unique solution for H - an inverse H_{Q} ^{1} does not exist. However, the minimum-norm solution can be obtained by the Moore-Penrose pseudoinverse [Str09]. Note that the rendering system's driving filters and their inverses are determined during the production of the audio material and can be calculated at the production stage as already. Hence, the LEMS estimate can then be computed from the source-specific transfer functions according to Eq. (2) by pre-filtering H_{s}. For a driver matrix H_{D} with pseudoinverse Hp ,

HDH_{D}

(I - P)

are known as the projectors into the column space of H_{D} and into the left null space of H_{D}, respectively [Str09], These two matrices decompose the A/ dimensional space into two orthogonal subspaces. With this, the LEMS H can be expressed as sum of two orthogonal components

HH_{D}Hj + H(I

H_{s}Hi + Ή^{1}.

(3)

where H ^{L} = H_{S}HD is a filtered version of the source-specific system H_{S} and H^{1} lies in the left null space of H_{D} and is not excited by the latter. Therefore, H^{1} is not observable at the microphones and represents the ambiguity of the solutions for H (non-uniqueness problem). Whenever is employed to map a source-specific system back to an LEMS estimate, the estimate's rows will lie in the column space of H_{D} and all components in the left null space of H_{D}, namely H^{1}, are implied to be zero (0).

Hence, only the LEMS components sensitive to the column space of H_{D} can and should be estimated from a particular H_{s}. This idea will be employed in the following to extend source-specific system identification for time-varying virtual acoustic scenes.

In practice, the number and the positions of virtual acoustic sources may change over time. Thus, the rendering task can be divided into a sequence of intervals with different, but internally constant virtual source configuration. These intervals can be indexed by the interval index JC, where JC is an integer number. At the beginning of an interval JC, an initial source-specific system estimate

can be computed from the information available from observing the interval JC - 1, namely the initial LEMS estimate Η(κ\κ - 1) = Η(κ - 1\κ - 1) can be obtained from interval c - 1, and the current interval's rendering filters H_{d}(K) . After adapting only the source-specific system H_{S} during interval JC, a final source-specific system estimate H_{s}(K \ K) is available at the end of interval JC. Embodying the idea to update only H" and keep H (K \ K - 1) =

- 1)(7 - H_{D} (K)HD (K)) unaltered during a particular interval JC, this can be formulated as

H ( J ) = H^{1}- (K I K - 1 ) 4- H (/ ) H+ (K) .

This can be shown to correspond to a minimum-norm update

ή^{Δ} («) = ή (κ|«) - Η («|« - 1)

= HS ( ^{.}|K) - H_{S} («|« - 1 )

(5)

the smallest update which leads to H_{s}(K \ K) . AS this procedure leaves H^{L} unaltered (Η^{χ}(κ\κ) = Η^{λ}(κ\κ - 1)), information about the true LEMS can accumulate over all intervals, allowing a continuous refinement of // in case of time-varying acoustic scenes.

Fig. 5 outlines this idea for a typical situation. To this end, two time Intervals 1 and 2 are considered, within which the virtual source configurations do not change. But, the virtual source configurations of both intervals are different. Furthermore, the whole system is switched on at the beginning of Interval 1 . This is also depicted in the time line (left) in Fig. 5. The transition from Interval 1 to 2 is indicated at the time line by the label "Transition". To the right of the time line, the adaptive system identification process during Intervals 1 and 2 is illustrated at the top and bottom, respectively. In between, the operations performed during the source-configuration change are visualized. Each of the squares in the system blocks represents a subsystem of fixed size. Consequently, the number of squares is proportional to the size of the linear system itself. In the following, the intervals will be explained in chronological order.

First, interval 1 . At the beginning of interval 1 ("Start" in Fig. 5), the estimate H for the LEMS H is still all zero (indicated by white squares) and it remains like this for the whole interval. On the other hand, after obtaining an initial source-specific system ?_{s}(0|0) via Eq. (4), the source-specific system H_{s} is continuously adapted during this interval, leading to the final estimate H (l| l).

Second, the transition between intervals 1 and 2. At the transition between intervals 1 and 2 (center part of Fig. 5), the virtual source configuration changes. Thus, the driving system is exchanged to allow rendering a different virtual scene (H_{D}(1) is replaced by H_{D}(2)) and information from H_{s} is transferred to H. For this knowledge transfer, the pseudoinverse H_{p} l) of the driving system H_{D}(1) is employed. From the updated LEMS estimate #(2 | 1) = H(l| l) and the new driving filters H_{D}(2), an initialization/^ 211) for H_{s} for the Interval 2 is obtained via Eq. (4).

Third, interval 2. Analogously to interval 1 , only a small source-specific system is adapted within Interval 2 (bottom). Yet, an estimate H is available in the background (system components contributed by interval 1 are gray now). In case of another scene change (exceeds time line in Fig. 5), ¾(2 | 2) can then refine the LEMS estimate H again, leading to an even better initialization for the subsequent interval's source-specific system. Thereby, all intervals with different source configurations contribute to the estimation of the LEMS and support the initialization of the adaptive source-specific systems in case of previously observed and unobserved source configurations.

In the following, embodiments which reduce (or even minimize) a peak computational load or an average computational load for system identification will be described.

Thinking about computationally powerful devices with limited electrical power resources (e.g., multicore tablets or smartphones) or devices which have to perform other, less time-critical tasks in addition to the signal processing, a minimization of the average

computational load for the adaptive filtering is desirable. On the other hand, for the identification of very large systems, in case of computationally less powerful processing devices, or when sharing one processing device with other time-critical applications (e.g., head units of a car), the peak load produced by signal processing application is to be reduced. Thus, the idea of a generic concept allowing either average load or peak load minimization is combined with the idea of source-specific system identification in the following.

In order to reduce the average load, the update can directly be computed as described above with respect to the time-varying virtual acoustic scenes, which leads to an efficient update equation

Η (/φ,·) - Η ( - 1) + (Η_{δ} ( | .) - Η_{3} ( / ,·. - 1)) Η+ (Λ·)

' ■ (6)

for which the operations on an LEMS estimate are outlined in Fig. 6. Thereby, in Fig. 6, the lines represent coefficients of MIMO systems and rounded boxes symbolize pre-filtering the connected incoming coefficients with the MIMO system in the box. Note that the average load is very low due to the low-dimensional adaptation, but the peak load at the scene change is increased due to transformations between source-specific systems and LEMS representations.

A peak-load optimization can be obtained by the idea of splitting the SSSysId update into a component directly originating from the most recent interval's source specific system (to be computed at the scene change) and another component which solely depends on information available one scene change before (pre-computable).

Doing so after inserting the above described update (Eq. (6)) in Eq. (4) leads to

H_{S} (K + 1|K) =

^ ^

H(K|K.- 1)

= H i 1|K - 2) + H£ I) H+ (K 1) HD (K + 1)

(8)

with the transition transform from matrix Η^'*^{"1" 1}-^{1} = HJ(K)H_{d}(K + 1) which maps the update of a source-specific system of interval κ to an update for a source-specific system in interval κ + 1. The benefit of this formulation is becomes obvious from the adaptation scheme depicted in Fig. 7. In Fig. 7, operations performed on and with system estimates in an interval κ of constant virtual source configuration are shown. Thereby, the lines represent coefficients of Ml MO systems and rounded boxes symbolize pre-filtering the connected incoming coefficients with the MIMO system in the box.

Further, in Fig. 7, the parts 130 are time-critical and need to be computed in a particular frame (adaptation of the source-specific system and computation of the contribution from Η_{5}(κ|κ) to H_{s}(/c + while the parts 132 (employing H(K: - 1|K - 2) and H (K - 1) determine Ε(κ\κ - 1) and computation of the contribution from Η(κ(κ - 1) to H_{S} (K + 1 \κ ) can be computed in a distributed way during the complete interval κ. Afterwards, Η(κ\κ -1), H (K, K - 1), and H_{s}(K + 1|κ) are handed over to the next interval.

Note that both the peak-load optimized and the average-load optimized SSSysld mathematically lead to identical LEMS estimates (up to the machine precision). The total computational overhead of the peak-load optimized scheme with respect to the average-load optimized is caused by the additional transform by E^ '^{K+1} which is negligible for long time intervals with constant virtual source configuration.

The lack of side information (virtual source signals and rendering filters or rendering filter computation strategy from other side information) when deploying audio material for a particular rendering system precludes the use of this approach. If the side information cannot be excluded to be available during system identification, a strong evidence for the use of this method can be obtained from the computational load of the system identification process in an AEC application: rendering a single virtual source for a very long time, the computational load caused by the adaptive filtering becomes very low and independent of the number of loudspeakers, which contradicts classical system identification approaches. If this holds, distinguishing between SSSysld and SDAF is necessary. To this end, a static virtual scene with more than one virtual source with independently time-varying spectral content can be synthesized: while SSSysld produces constant computational load, the computational load of SDAF will peak repeatedly due to the purely data-driven trans- forms for signals and systems. Another approach for distinguishing SSSysld from SDAF would

be to alternate between signals with orthogonal loudspeaker-excitation pattern (e.g. virtual point sources at the positions of different physical loudspeakers): the Echo-Return Loss Enhancement (ERLE) can be expected to break down similarly for every scene change for SDAF, while SSSysld exhibits a significantly lowered breakdown when performing a previously observed scene-change again. However, these tests require at least access to the load statistics of a processor running the aforementioned rendering tasks.

In the following, a verification and evaluation of the basic properties of the SSSysld adaptation scheme are provided by simulating a WFS scenario with a linear sound bar of N_{h} = 48 loudspeakers in front of a single microphone (the use of just a single microphone is sufficient for general analyses of the behavior of the adaptation concept as filter adaptation is performed independently for each microphone, anyway) under free-field conditions, as depicted in Fig. 8. In detail, Fig. 8 shows a transducer setup common for the simulation of a prototype with N_{L} = 48 loudspeakers 102 and N_{M} = 1 microphone.

The WFS system synthesizes at a sampling rate of 8 kHz one or more simultaneously active virtual point sources radiating statistically independent white noise signals. Besides, high-quality microphones are assumed by introducing additive white Gaussian noise at a level of -60 dB to the microphones. The system identification is performed by a GFDAF algorithm. The rendering systems' inverses are approximated in the Discrete Fourier Transform (DFT) domain and a causal time-domain inverse system is obtained by applying a linear phase shift, an inverse DFT, and subsequent windowing.

For numerical stability, the pseudoinverse is approximated in the DFT domain by a Tikhonov regularized inverse Hj^{Tik} = (H H_{D} + λΐ) ^{X}H" with a regularization constant λ = 0.005, thereby offering a trade-off between the accuracy of the inversion (small X) and the filter coefficient norm for ill-conditioned H_{D}. To evaluate the simulations, the normalized residual error signal

Where _{M}i_{c} ^{E} C^{Wm} denotes the vector of microphone samples for the discrete-time sample index k and e(/c) £ C^{NM} denotes the corresponding vector of error signals, assesses how well the actual microphone signals can be modeled (this corresponds to

the inverse of the commonly used ERLE measure in AEC). In order to measure how well the LEMS is identified, we employ the normalized system error norm

Where Η_{μ} and Η_{μ}(κ\κ) are DFT-domain transfer function matrices of the estimated and the true LEMS, μ e {0, ... , L - 1} is the DFT bin index, and L is the DFT order.

In the following, two different experiments will be described.

According to a first experiment, 24 s of the microphone signal are synthesized, which are divided into three intervals of length 8 s with different, but internally constant virtual source configurations. The three interval's groups of virtual sources are depicted in Fig. 9a. In detail, in Fig. 9a a schematic block diagram of a setup of N_{L} = 48 loudspeakers 102 (arrows), N_{M} = 1 microphone (cross), and 3 randomly chosen groups 140,142, 144 of 4 virtual sources 108 are shown. Their positions are marked by dots and are connected by a line to symbolize their simultaneous activity. Further, each virtual source 108 is marked by a filled circle and the sources belonging to the same interval of constant source configuration are connected by lines of the same type, i.e., a straight line 140, a dashed line 142 of a first type and a dashed line 144 of a second type.

Fig. 9b shows a diagram of a normalized residual error signal at the microphone 104 resulting during the first experiment from a direct estimation of the low-dimensional, source-specific system (curve 150) and from the estimation of the high-dimensional LEMS (curve 512).

Obviously, the normalized residual error depicted in Fig. 9b quickly drops more uniform by SSSysld, where a unique solution of the adaptive filters can be found, up to the noise floor. Both SSSysld and a direct LEMS update reveal a very similar performance breakdown in case of scene changes. This shows the applicability of SSSysld for AEC.

According to a second experiment, a study of the long-term stability of the proposed adaptation scheme is performed. To this end, 100 different virtual source positions are

drawn with coordinates x_{s} = [x, y, 0]^{T}, x e [0,5, 4.5], 6 [-5.1, -1.1] and each source is exclusively active in its own interval of length 1 s. The resulting scene is depicted in Figure 10a and corresponds to 99 source configuration changes. In detail, Fig. 10a shows a setup of N_{L} = 48 loudspeakers 102 (arrows), N_{M} = 1 microphone 104 (cross), and 100 randomly chosen virtual source positions 08.

The adaptation of source-specific systems and the direct adaptation of the LEMS will be compared in terms of the normalized system error norms. These are depicted in Figure 10b for each of the 100 intervals (determined at the respective intervals' ends). Thereby, Fig. 10b shows a system error norm achievable during the second experiment by transforming the low-dimensional source-specific system into an LEMS estimate (curve 160) in comparison to a direct LEMS update (curve 162).

Obviously, the less complex source-specific updates (curve 160) lead to a completely stable adaptation and similar performance as updating the LEMS directly (curve 162), also in case of repeatedly changing virtual source configurations and for excitation with just a single virtual source. Thereby, the computational complexity is reduced by an order of magnitude. However, a slightly increased normalized system error norm is the result of the repeated transforms with regularized rendering inverse filters and the truncation of the convolution results to the modeled filter lengths.

Embodiments provide a method for identifying a MIMO system employing side information (statistically independent virtual source signals, rendering filters) from an object-based rendering system (e.g., WFS or hands-free communication using a multi-loudspeaker front-end). This method does not make any assumptions about loudspeaker and microphone positions and allows system identification optimized to have minimum peak load or average load. As opposed to state-of-the-art methods, this approach has predictably low computational complexity, independent of the spectral or spatial characteristics of the N_{s} virtual sources and the positions of the transducers (N_{h} loudspeakers and N_{M} microphones). For long intervals of constant virtual source configuration, a reduction of the complexity by a factor of about N_{L}/N_{S} is possible. A prototype has been simulated in order to verify the concept exemplarily for the identification of an LEMS for WFS with a linear sound bar.

Fig. 1 1 shows a flowchart of a method 200 for operating a rendering system, according to an embodiment of the present invention. The method 200 comprises a step 202 of

determining a loudspeaker-enclosure-microphone transfer function matrix describing acoustic paths between a plurality of loudspeakers and at least one microphone using a rendering filters transfer function matrix using which a number of source signals is reproduced with the plurality of loudspeakers.

Fig. 12 shows a flowchart of a method 2 0 for operating a rendering system, according to an embodiment of the present invention. The method 210 comprising a step 212 of estimating at least some components of a source-specific transfer function matrix describing acoustic paths between a number of virtual sources, which are reproduced with a plurality of loudspeakers, and at least one microphone, and a step 214 of determining at least some components of a loudspeaker-enclosure-microphone transfer function matrix estimate describing acoustic paths between the plurality of loudspeakers and the at least one microphone using the source-specific transfer function matrix.

Many applications require the identification of a Loudspeaker-Enclosure-Microphone System (LEMS) with multiple inputs (loudspeakers) and multiple outputs (microphones). The required computational complexity typically grows at least proportionally along the number of acoustic paths, which is the product of the number of loudspeakers and the number of microphones. Furthermore, typical loudspeaker signals are highly correlated and preclude an exact identification of the LEMS (^{'}non-uniqueness problem^{'}). A state-of-the art method for multichannel system identification known as Wave-Domain Adaptive Filtering (WDAF) employs the inherent nature of acoustic sound fields for complexity reduction and alleviates the non-uniqueness problem for special transducer arrangements. On the other hand, embodiments do not make any assumption about the actual transducer placement, but employs side-information available in an object-based rendering system (e.g., Wave Field Synthesis (WFS)) for which the number of virtual sources is lower than the number of loudspeakers to reduce the computational complexity. In embodiments, (only) a source-specific system from each virtual source to each microphone can be identified adaptively and uniquely. This estimate for a source-specific system then can be transformed into an LEMS estimate. This idea can be further extended to the identification of an LEMS for the case of different virtual source configurations in different time intervals. For this general case, the idea of a peak-load-optimized and an average-load-optimized structure are presented, where the peak-load-optimized is well suited for less powerful systems and the average-load-optimized structure for powerful but portable systems which have to minimize the average consumption of electrical power.

Although some aspects have been described in the context of an apparatus, it is clear that these aspects also represent a description of the corresponding method, where a block or device corresponds to a method step or a feature of a method step. Analogously, aspects described in the context of a method step also represent a description of a corresponding block or item or feature of a corresponding apparatus. Some or all of the method steps may be executed by (or using) a hardware apparatus, like for example, a microprocessor, a programmable computer or an electronic circuit. In some embodiments, one or more of the most important method steps may be executed by such an apparatus.

Depending on certain implementation requirements, embodiments of the invention can be implemented in hardware or in software. The implementation can be performed using a digital storage medium, for example a floppy disk, a DVD, a Blu-Ray, a CD, a ROM, a

PROM, an EPROM, an EEPROM or a FLASH memory, having electronically readable control signals stored thereon, which cooperate (or are capable of cooperating) with a programmable computer system such that the respective method is performed. Therefore, the digital storage medium may be computer readable.

Some embodiments according to the invention comprise a data carrier having electronically readable control signals, which are capable of cooperating with a programmable computer system, such that one of the methods described herein is performed.

Generally, embodiments of the present invention can be implemented as a computer program product with a program code, the program code being operative for performing one of the methods when the computer program product runs on a computer. The program code may for example be stored on a machine readable carrier.

Other embodiments comprise the computer program for performing one of the methods described herein, stored on a machine readable carrier.

In other words, an embodiment of the inventive method is, therefore, a computer program having a program code for performing one of the methods described herein, when the computer program runs on a computer.

/

A further embodiment of the inventive methods is, therefore, a data carrier (or a digital storage medium, or a computer-readable medium) comprising, recorded thereon, the computer program for performing one of the methods described herein. The data carrier, the digital storage medium or the recorded medium are typically tangible and/or non-transitionary.

A further embodiment of the inventive method is, therefore, a data stream or a sequence of signals representing the computer program for performing one of the methods described herein. The data stream or the sequence of signals may for example be configured to be transferred via a data communication connection, for example via the Internet.

A further embodiment comprises a processing means, for example a computer, or a programmable logic device, configured to or adapted to perform one of the methods described herein.

A further embodiment comprises a computer having installed thereon the computer program for performing one of the methods described herein.

A further embodiment according to the invention comprises an apparatus or a system configured to transfer (for example, electronically or optically) a computer program for performing one of the methods described herein to a receiver. The receiver may, for example, be a computer, a mobile device, a memory device or the like. The apparatus or system may, for example, comprise a file server for transferring the computer program to the receiver.

In some embodiments, a programmable logic device (for example a field programmable gate array) may be used to perform some or all of the functionalities of the methods described herein. In some embodiments, a field programmable gate array may cooperate with a microprocessor in order to perform one of the methods described herein. Generally, the methods are preferably performed by any hardware apparatus.

The apparatus described herein may be implemented using a hardware apparatus, or using a computer, or using a combination of a hardware apparatus and a computer.

The methods described herein may be performed using a hardware apparatus, or using a computer, or using a combination of a hardware apparatus and a computer.

The above described embodiments are merely illustrative for the principles of the present invention. It is understood that modifications and variations of the arrangements and the details described herein will be apparent to others skilled in the art. It is the intent, therefore, to be limited only by the scope of the impending patent claims and not by the specific details presented by way of description and explanation of the embodiments herein.

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