EP2189010B1 - Apparatus and method for determining a component signal with great accuracy - Google Patents

Description

The present invention relates to an apparatus and method for detecting high accuracy component signals for a WFS (Wave Field Synthesis) system, and more particularly to an efficient algorithm for delay interpolation for wave field synthesis display systems.

Wave field synthesis is an audio reproduction method developed at TU Delft for the spatial reproduction of complex audio scenes. In contrast to most existing audio reproduction techniques, the spatially correct rendering is not limited to a small area, but extends over a wide viewing area. WFS is based on a well-founded mathematical-physical basis, namely the principle of Huygens and the Kirchhoff-Helmholtz integral.

Typically, a WFS reproduction system consists of a large number of loudspeakers (so-called secondary sources). The loudspeaker signals are formed from delayed and scaled input signals. Since many audio objects (primary sources) are typically used in a WFS scene, many such operations are required to generate the loudspeaker signals. This requires the high computing power required for wave field synthesis.

In addition to the advantages mentioned above, WFS also offers the possibility of realistically mapping moving sources. This feature is used in many WFS systems and is, for example, for the use in the cinema, virtual reality applications or live performances of great importance.

However, the playback of moving sources causes a number of characteristic errors that do not occur in the case of static sources. The signal processing of a WFS playback system has a significant influence on the playback quality.

A primary goal is the development of signal processing algorithms for the playback of moving sources using WFS. The real-time capability of the algorithms is an important condition. The most important criterion for evaluating the algorithms is the objective perceived audio quality.

As I said, WFS is a very expensive audio reproduction process in terms of processing resources. This is mainly due to the large number of speakers in a WFS setup and the often high number of virtual sources used in WFS scenes. For this reason, the efficiency of the algorithms to be developed is of paramount importance.

An important question is what quality improvement should be achieved by the algorithms to be developed. This is especially true considering the other artifacts caused by the WFS, which may be more disruptive depending on the quality of the signal processing algorithms or obscure (mask) the artifacts of the signal processing. Therefore, the focus is on the development of algorithms whose quality can be scaled by various parameters (eg interpolation orders, filter lengths, etc.). This includes, as an extreme case, algorithms whose reproduction errors are below the perception threshold under idealized conditions (elimination of all other artifacts). Depending on the desired quality, the characteristics of the other artifacts as well as the available resources an optimal compromise (tradeoff) can be found.

1. (a) Zulässige Quellgeschwindigkeiten. Generell sind virtuelle Quellen mit beliebigen Quellgeschwindigkeiten zu unterstützen. Jedoch nimmt der Einfluss der Dopplerverschiebung mit zunehmender Geschwindigkeit zu. Zusätzlich gelten viele physikalische Gesetzmäßigkeiten, die auch in der WFS genutzt werden, nur für Geschwindigkeiten unterhalb der Schallgeschwindigkeit. Daher wird folgender als sinnvoll erachteter zulässiger Bereich für die Quellgeschwindigkeit v_src festgesetzt: $$\left|{\mathrm{v}}_{\mathrm{src}}\right|\le \frac{\mathrm{1}}{\mathrm{2}}\mathrm{c}\mathrm{.}$$
   
   
   Dabei ist c die Schallgeschwindigkeit des Mediums. Unter Standardbedingungen beträgt die erlaubte Geschwindigkeit von Quellen somit etwa 172 ^m/s bzw. 619 ^km/h.
2. (b) Frequenzbereiche. Als Wiedergabebereich für die Frequenz f wird der komplette Audio-Frequenzbereich angenommen, d.h. $$\mathrm{20}\mathrm{Hz}\le \mathrm{f}\le \mathrm{20}\mathrm{KHz}$$
   
   
   Es ist zu beachten, dass die Wahl der oberen Grenzfrequenz und der dabei zu erzielenden Güte entscheidenden Einfluss auf den Ressourcenbedarf der Algorithmen hat.
3. (c) Samplingfrequenz. Die Wahl der Abtastrate hat großen Einfluss auf die zu entwerfenden Algorithmen. Zum einen steigt der Fehler der meisten Delay-Interpolationsalgorithmen stark an, je geringer der Abstand des interessierenden Frequenzbereichs zur Nyquist-Frequenz ist. Auch steigt die Länge vieler von Algorithmen benötigter Filter stark an, je schmaler der Bereich zwischen oberer Grenzfrequenz des Audiofrequenzbereiches und der Nyquist-Frequenz ist, da dieser Bereich in vielen Verfahren zum Filterentwurf als sog. don't care-Band verwendet wird.
   Änderungen der Sampling-Frequenz können daher weitgehende Anpassungen der verwendeten Filter und sonstiger Parameter erfordern und somit auch die Performance und die Eignung spezieller Algorithmen maßgeblich beeinflussen.
   Standardmäßig werden Systeme, die in professionellen Audiotechnik üblich sind, mit einer Abtastrate von 48 KHz betrieben. Daher wird diese Samplingfrequenz im Folgenden angenommen.
4. (d) Zielhardware. Obwohl die zu entwickelnden Algorithmen generell unabhängig von der verwendeten Hardware sind, ist eine Festlegung der Zielplattform aus verschiedenen Gründen sinnvoll:
   1. (i) Die Architektur der verwendeten CPUs, z. B. die Unterstützung von Parallelarbeit, hat Einfluss auf das Design der Algorithmen.
   2. (ii) Größe und Architektur des verwendeten Speichers beeinflussen Entwurfsentscheidungen beim Algorithmenentwurf.
   3. (iii) Für die Festsetzung von Performanceforderungen sind Angaben über die Leistungsfähigkeit der Zielhardware notwendig.

A number of criteria and ranges of values can be defined that facilitate the design of the algorithms. These include:

1. (a) Permissible swelling speeds. In general, virtual sources with arbitrary source speeds are to be supported. However, the influence of the Doppler shift increases with increasing speed. In addition, many physical laws that are also used in WFS apply only to speeds below the speed of sound. Therefore, the following permissible range for the source velocity v _src considered useful: $$\left|{\mathrm{v}}_{\mathrm{src}}\right|\le \frac{\mathrm{1}}{\mathrm{2}}\mathrm{c}\mathrm{,}$$
   
   
   Where c is the sound velocity of the medium. Under standard conditions, the permitted speed of sources is thus about 172 ^m / s or 619 ^km / h.
2. (b) frequency ranges. As the playback range for the frequency f, the entire audio frequency range is assumed, ie $$\mathrm{20}\mathrm{Hz}\le \mathrm{f}\le \mathrm{20}\mathrm{KHz}$$
   
   
   It should be noted that the choice of the upper limit frequency and the quality to be achieved has a decisive influence on the resource requirements of the algorithms.
3. (c) sampling frequency. The choice of the sampling rate has a great influence on the algorithms to be designed. First, the error of most delay interpolation algorithms increases sharply the closer the distance of the frequency range of interest to the Nyquist frequency. Also, the length of many filters required by algorithms increases sharply, the narrower the range between Upper cutoff frequency of the audio frequency range and the Nyquist frequency is because this area is used in many methods for filter design as a so-called do not care band.
   Changes in the sampling frequency may therefore require extensive adjustments of the filters and other parameters used and thus also significantly influence the performance and the suitability of special algorithms.
   By default, systems that are common in professional audio technology operate at a sampling rate of 48 kHz. Therefore, this sampling frequency is assumed below.
4. (d) target hardware. Although the algorithms to be developed are generally independent of the hardware used, determining the target platform makes sense for a number of reasons:
   1. (i) The architecture of the CPUs used, e.g. For example, the support of parallel work has an influence on the design of the algorithms.
   2. (ii) Size and architecture of the memory used influence design decisions in algorithm design.
   3. (iii) To determine performance requirements, information about the performance of the target hardware is required.

• Aktuelle Desktop- oder Workstation-Standardkomponenten basierend auf x86-Technik,
• Keine Verwendung von Spezial-Hardware
• Prozessoren mit performanter Floating-Point-Funktionalität,
• Vergleichsweise großer Arbeitsspeicher und
• Typischerweise Unterstützung SIMD-Befehlssätzen (z. B. SSE).

Since systems are currently and for the foreseeable future mostly based on PC technology, the following properties are assumed:

• Current desktop or workstation standard components based on x86 technology,
• No use of special hardware
• Processors with high-performance floating-point functionality,
• Comparatively large memory and
• Typically support SIMD instruction sets (eg SSE).

1. (1) Berechnung der WFS-Parameter. Durch Anwendung des WFS-Synthese-Operators werden für jede Kombination aus Quelle und Lautsprecher ein Skalierungs- und ein Delay-Wert bestimmt. Diese Berechnung erfolgt mit einer relativ geringen Frequenz. Zwischen diesen Stützstellen werden die Scale- und Delay-Werte mittels einfacher Verfahren interpoliert. Daher ist der Einfluss auf die Performance vergleichsweise gering.
2. (2) Filterung. Zur Umsetzung des WFS-Operators ist eine Filterung mit einem Tiefpassfilter mit 3 dB Flankensteilheit erforderlich. Zusätzlich kann eine Quell- und/oder lautsprecherabhängige Anpassung an die Wiedergabeverhältnisse erfolgen. Da die Filter-Operation jedoch jeweils nur einmal pro Eingangs- und/oder Ausgangssignal durchgeführt wird, ist der Performancebedarf im Allgemeinen moderat. Zusätzlich wird diese Operation in aktuellen WFS-Systemen auf dedizierten Recheneinheiten durchgeführt.
3. (3) WFS-Skalierung. Diese, oftmals eigentlich inkorrekt als WFS-Faltung bezeichnete, Operation beaufschlagt die in einer Verzögerungsleitung abgelegten Eingangssignale mit der vom Syntheseoperator berechneten Verzögerung und skaliert dieses Signal mit einer ebenfalls vom Syntheseoperator berechneten Skalierung. Diese Operation wird für jede Kombination aus virtueller Quelle und Lautsprecher durchgeführt. Die Lautsprechersignale werden durch Summation aller skalierten Eingangsignale für den betreffenden Lautsprecher gebildet.

The algorithms in audio signal processing in wave field synthesis can be divided into different categories:

1. (1) Calculation of WFS parameters. Using the WFS Synthesis operator, a scaling and a delay value are determined for each combination of source and speaker. This calculation is done with a relatively low frequency. Between these nodes, the scale and delay values are interpolated using simple procedures. Therefore, the impact on performance is comparatively low.
2. (2) filtering. To implement the WFS operator, filtering with a low-pass filter with 3 dB slope is required. In addition, a source and / or speaker-dependent adaptation to the reproduction conditions can take place. However, since the filter operation is performed only once per input and / or output, the performance requirements are generally moderate. In addition, this operation is performed in current WFS systems on dedicated arithmetic units.
3. (3) WFS scaling. This, often incorrectly referred to as WFS convolution, operates on the input signals stored in a delay line with the delay calculated by the synthesis operator, and scales this signal with one also from the synthesis operator calculated scaling. This operation is performed for each combination of virtual source and speaker. The loudspeaker signals are formed by summing all scaled input signals for the respective loudspeaker.

Because WFS scaling is performed on any combination of virtual source and speaker, as well as on each audio sample, it forms the bulk of the resource requirements of a WFS system, even with very little complexity of the single operation.

1. (A) Kammfiltereffekte (Spatial Aliasing). Das aus der Wiedergabe statischer Quellen bekannte räumliche Aliasing erzeugt oberhalb der Aliasing-Frequenz ein von der Quellposition sowie der Frequenz abhängiges, von Überhöhungen und scharfen Einbrüchen geprägtes Interferenzmuster. Bei Bewegungen der virtuellen Quelle verändert sich dieses Muster dynamisch und erzeugt so für einen ruhenden Betrachter eine zeitabhängige Frequenzverzerrung.
2. (B) Nichtbeachtung der retardierten Zeit. Bei der Berechnung der WFS-Parameter wird die aktuelle Position der Quelle herangezogen. Für eine korrekte Wiedergabe ist jedoch die Position ausschlaggebend, von der der aktuell eintreffende Schall ausgesandt wurde. Dies erzeugt einen systematischen Fehler der Dopplerverschiebung, der jedoch bei moderaten Geschwindigkeiten recht gering ausfällt und in den meisten Anwendungen der WFS sehr wahrscheinlich nicht störend wahrgenommen wird.
3. (C) Doppler-Spreizung. Eine bewegte Quelle führt aufgrund der unterschiedlichen Relativgeschwindigkeiten zu verschiedenen Dopplerfrequenzen in den von den sekundären Quellen abgestrahlten Signalen. Diese äußern sich am Hörort in einer Verbreiterung des Frequenzspektrums der virtuellen Quelle. Dieser Fehler kann nicht mit der WFS-Theorie erklärt werden und ist Gegenstand aktueller Forschungen.
4. (D) Audio-Störungen durch Delay-Interpolation. Zur WFS-Skalierung werden beliebig verzögerte Eingangssignale benötigt, die aus den nur zu beliebigen Zeitpunkten vorlie-genden diskreten Samples berechnet werden. Die dazu verwendeten Algorithmen unterscheiden sich stark in ihrer Qualität und erzeugen oftmals Artefakte, die störend wahrgenommen werden.

In addition to the well-known playback errors (artifacts) of WFS, a number of other characteristic errors occur in moving sources. The following errors can be identified:

1. (A) Spatial aliasing. The spatial aliasing known from the reproduction of static sources generates above the aliasing frequency an interference pattern which is dependent on the source position as well as on the frequency and which is characterized by elevations and sharp dips. As the virtual source moves, this pattern changes dynamically, creating a time-dependent frequency distortion for a dormant viewer.
2. (B) Non-observance of the delayed time. When calculating the WFS parameters, the current position of the source is used. For a correct reproduction, however, the position from which the currently arriving sound was emitted is decisive. This creates a systematic error in the Doppler shift, which, however, is quite low at moderate speeds and is most likely not obtrusive in most WFS applications.
3. (C) Doppler spread. A moving source leads to different due to the different relative speeds Doppler frequencies in the signals radiated from the secondary sources. These express themselves at the auditory location in a widening of the frequency spectrum of the virtual source. This error can not be explained by the WFS theory and is the subject of current research.
4. (D) Audio interference due to delay interpolation. For WFS scaling, any delayed input signals are required, which are calculated from the discrete samples present only at arbitrary times. The algorithms used differ greatly in their quality and often produce artifacts that are perceived as disruptive.

The natural Doppler effect, ie the frequency shift of a moving source, is not considered an artifact here, as it is a property of the primary sound field that is to be reproduced by a WFS system. Nevertheless, this is undesirable in various applications.

The operation of obtaining the value of a time-discrete sampled signal at arbitrary times is referred to as delay interpolation or fractional-delay interpolation.

For this purpose, a large number of algorithms were developed, which differ greatly in complexity and quality of the interpolation. In general, fractional delay algorithms are implemented as discrete filters which have as input a discrete-time signal and as an output an approximation of the delayed signal.

1. (I) Filterstruktur. FD-Filter (FD = fractional delay) können sowohl als FIR- als auch als IIR-Filter implementiert werden (FIR = finite impulse response, IIR = infinite impulse response).
   FIR-Filter benötigen im Allgemeinen eine höhere Zahl von Filterkoeffizienten und damit auch von Rechenoperationen und erzeugen für beliebige fraktionale Delays auch stets Amplitudenfehler. Sie sind jedoch stets stabil und es existieren viele, darunter auch viele geschlossene, nicht iterative, Entwurfsverfahren.
   IIR-Filter können als Allpass-Filter implementiert werden, die einen exakt konstanten und damit für FD-Filter optimalen Amplitudengang besitzen. Jedoch ist es nicht möglich, die Phase eines IIR-Filters so exakt zu beeinflussen wie im Falle eines FIR-Filters. Die meisten Design-Methoden für IIR-FD-Filter sind iterativ und dementsprechend nicht für Echtzeitanwendungen mit veränderlichen Delays geeignet. Die einzige Ausnahme bildet der Thiran-Filter, für den explizite Formeln für die Koeffizienten existieren. Bei der Implementierung von IIR-Filtern ist es stets notwendig, den Wert der vorhergehenden Ausgänge zu speichern. Dies ist für eine Implementierung in einem WFS-Reproduktionssystem ungünstig, da eine Vielzahl früherer Ausgangssignale verwaltet werden müssten. Des Weiteren setzt eine Verwendung interner Zustände die Eignung von IIR-Filtern für veränderliche Delays herab, da der interne Zustand möglicherweise für ein anderes fraktionales Delay als das aktuelle berechnet wurde. Dies führt zu als Transienten bezeichneten Störungen des Ausgangssignals.
   Aus diesen Gründen werden für den Einsatz in WFS-Reproduktionssystemen nur FIR-Filter untersucht.
2. (II) Feste und variable Fractional-Delays. FD-Filter sind, nachdem ihre Koeffizienten entworfen wurden, nur für einen bestimmten Verzögerungswert gültig. Für jeden neuen Wert muss der Entwurfsvorgang erneut durchgeführt werden. Abhängig von den Kosten dieses Entwurfsvorgangs sind Verfahren mehr oder weniger gut für den Echtzeitbetrieb mit veränderlichen Delays geeignet.
   Verfahren für variable fraktionale Delays (oft als Variable Fractional Delay Filters = VFD bezeichnet) kombinieren die Koeffizientenberechnung und die Filterberechnung und sind daher sehr gut für Echtzeit-Veränderungen des Verzögerungswertes geeignet. Sie sind eine Ausprägung variabler digitaler Filter.
3. (III) Asynchrone Abtastratenumsetzung. In der WFS werden kontinuierlich veränderliche Delays benötigt. Bei der Reproduktion einer sich linear zu eine Sekundärquelle bewegenden virtuellen Quelle ist die Verzögerung beispielsweise eine lineare Funktion der Zeit. Diese Operation kann als asynchrone Samplingratenkonvertierung klassifiziert werden. Verfahren zur asynchronen Abtastratenumsetzung werden typischerweise auf Basis von variablen Fractional-Delay-Algorithmen implementiert. Zusätzlich weisen sie jedoch einige zusätzlich zu lösende Probleme auf, z. B. die Notwendigkeit der Unterdrückung von Imaging- und Aliasingartefakten.
4. (IV) Wertebereich des Fractional-Delay-Parameters. Der Bereich des variablen Delay-Parameters d_frac ist abhängig vom verwendeten Verfahren und nicht zwingend der Bereich 0 ≤ d_frac ≤ 1. So liegt er für die meisten FIR-Verfahren im Bereich $\frac{\mathrm{N}-\mathrm{1}}{\mathrm{2}}\le {\mathrm{d}}_{\mathrm{frac}}\le \frac{\mathrm{N}+\mathrm{1}}{\mathrm{2}},$
   
   wobei N die Ordnung des Verfahrens ist. Dadurch wird die Abweichung von einem linearphasigen Verhalten minimiert. Ein exakt linearphasiges Verhalten ist stets nur für spezielle Werte von d_frac möglich.

Fractional delay interpolation algorithms can be classified according to various criteria:

1. (I) Filter structure. FD filters (FD = fractional delay) can be implemented as both FIR and IIR filters (FIR = finite impulse response, IIR = infinite impulse response).
   FIR filters generally require a higher number of filter coefficients and thus also arithmetic operations and always produce amplitude errors for arbitrary fractional delays. However, they are always stable and there are many, including many closed, non-iterative, design techniques.
   IIR filters can be implemented as all-pass filters that have an exactly constant amplitude response that is optimal for FD filters. However, it is not possible to influence the phase of an IIR filter as accurately as in the case of an FIR filter. Most design methods for IIR FD filters are iterative and therefore not suitable for real time applications with variable delays. The only exception is the Thiran filter, which has explicit formulas for the coefficients. When implementing IIR filters, it is always necessary to store the value of the previous outputs. This is inconvenient for implementation in a WFS reproduction system because a lot of earlier output signals would have to be managed. Furthermore, using internal states reduces the suitability of IIR filters for variable delays because the internal state may have been calculated for a different fractional delay than the current one. This leads to disturbances of the output signal, referred to as transients.
   For these reasons, only FIR filters are tested for use in WFS reproduction systems.
2. (II) Fixed and Variable Fractional Delays. FD filters, after their coefficients have been designed, are valid only for a particular delay value. For each new value, the design process must be performed again. Depending on the cost of this design process are procedures more or less suitable for real-time operation with variable delays.
   Variable Fractional Delay methods (often called Variable Fractional Delay Filters = VFD) combine the coefficient calculation and the filter calculation and are therefore very well suited for real-time changes in the delay value. They are an expression of variable digital filters.
3. (III) Asynchronous Sample Rate Conversion. The WFS requires continuously variable delays. For example, in the reproduction of a virtual source moving linearly to a secondary source, the delay is a linear function of time. This operation can be classified as asynchronous sampling rate conversion. Asynchronous sample rate conversion techniques are typically implemented based on variable fractional delay algorithms. In addition, however, they have some additional problems to be solved, e.g. For example, the need to suppress imaging and aliasing artifacts.
4. (IV) Value range of the fractional delay parameter. The range of the variable delay parameter d _frac depends on the method used and not necessarily on the range 0 ≤ d _frac ≤ 1. Thus, it is within the range for most FIR methods $\frac{\mathrm{N}-\mathrm{1}}{\mathrm{2}}\le {\mathrm{d}}_{\mathrm{frac}}\le \frac{\mathrm{N}+\mathrm{1}}{\mathrm{2}}.$
   
   where N is the order of the method. This minimizes the deviation from linear phase behavior. An exact linear-phase behavior is always possible only for special values of d _frac .

By decomposing the desired delay value d into an integer value d _int and a fractional part or fraction d _frac , any delays can be generated with a fractional delay filter. The delay d _int is implemented by an index shift in the input signal.

Adherence to the ideal operating range, however, requires a minimal value of the delay, which must not be undercut to maintain causality. Thus, methods for delay interpolation, especially high-quality FD algorithms with large filter lengths, also increase the system latency. However, this does not exceed an order of magnitude of 20 to 50 samples, even in the case of extremely complex procedures. However, this is generally low compared to other systemic latencies of a typical WFS playback system.

• Bei der Synthese bewegter Schallquellen mittels WFS werden die Verzögerungen, mit denen die Audiosignale beaufschlagt werden, zeitvariant. Die Signalverarbeitung (Rendering) eines WFS-Wiedergabesystems erfolgt zeitdiskret, Quellsignale liegen also nur zu festgelegten Abtastzeitpunkten vor. Die Verzögerung eines zeitdiskreten Signals um ein Vielfaches der Abtastperiode ist effizient möglich und wird durch ein Verschieben des Signalindexes implementiert. Der Zugriff auf einen Wert eines zeitdiskreten Signals, der zwischen zwei Abtastpunkten liegt, wird als Delay-Interpolation bzw. als Fractional Delay bezeichnet. Dazu werden spezielle Algorithmen benötigt, die sich in Qualität und Performance stark unterscheiden. Einen Überblick über Fractional-Delay-Algorithmen liefert.

The need for delay interpolation also results from the following considerations:

• In the synthesis of moving sound sources using WFS, the delays that are applied to the audio signals are time-varying. The signal processing (rendering) of a WFS playback system is time-discrete, so source signals are available only at fixed sampling times. The delay of a time-discrete signal by a multiple of the sampling period is efficiently possible and is implemented by shifting the signal index. The access to a value of a discrete-time signal, which lies between two sampling points, is referred to as delay interpolation or as fractional delay. This requires special algorithms that differ greatly in terms of quality and performance. An overview of fractional delay algorithms is provided.

In moving-center WFS, the required delay times change dynamically and can take any value. For each speaker signal, a different delay value is generally needed. The algorithms used must therefore support any variable delays.

While the rounding of the delay to the nearest multiple of the sampling period yields sufficiently good results for statistical WFS sources, this method leads to significant disturbances in the case of moving sources.

Wave field synthesis requires delay interpolation for each combination of virtual source and loudspeaker. Combined with the complexity of delay interpolation necessary for good rendering quality, good quality real-time implementation is not practical.

In Edwin Verheijen: "Sound reproduction by wave field synthesis", PhD thesis (pages 106-110), Delft University of Technology, 1997 "describes the need for delay interpolation for moving sources, but only simple (standard) delay interpolation techniques are used to implement the algorithms.

In Marije Baalman, Simon Schampijer, Torben Hohn, Thilo Koch, Daniel Plewe and Eddie Mond: "Creating a large scale wave field synthesis system with swonder", in Proc. of the 5th International Linux Audio Conference, Berlin, Germany, March 2007 is pointed out the need for sampling rate conversion for moving virtual sources. An algorithm based on the algorithm of Bresenham is sketched. However, this is an integer-based algorithm of graphic data processing for displaying lines on rastered display devices. Therefore it can be assumed that this is not a true, interpolating sample rate conversion, but a rounding of the sample points to the nearest integer sample index.

WFS renderers implement several simple methods for delay interpolation. The used class hierarchy allows easy exchange of procedures become. In addition to the delay interpolation, the temporal interpolation of the WFS parameters Delay (and Scale) also influences the quality of the sample rate conversion. In the traditional renderer structure, these parameters are updated only in a fixed grid (currently in time with 32 audio samples).

• IntegerDelay. Dies ist der ursprüngliche Algorithmus. Er unterstützt keine Delay-Interpolation, d. h. Verzögerungswerte werden auf das nächstgelegene Vielfache der Abtastperiode gerundet. Das Update der Verzögerungs- und Skalierungsparameter erfolgt in einem Raster von aktuell 32 Samples. Dieser Algorithmus ist in einer optimierten Assembler-Variante implementiert und für das Echtzeit-Rendering kompletter WFS-Szenen geeignet. Trotzdem beansprucht diese Operation den Hauptteil der im Renderer benötigten Rechenlast.
• BufferwiseDelayLinear. Die WFS-Parameter werden in einem groben Raster angepasst (Notation: bufferwise), die verzögerten Signale selbst werden mit einer Delay-Interpolation auf Basis einer linearen Interpolation berechnet. Die Implementierung erfolgt mit Assembler-Unterstützung und ist von der Performance für den Einsatz mit kompletten WFS-Szenen geeignet. Dieser Algorithmus wird derzeit als Default-Einstellung verwendet.
• SamplewiseDelayLinear. Bei diesem Verfahren werden Skalierungs- und Verzögerungswerte für jedes Sample interpoliert (Notation: samplewise). Die Delay-Interpolation erfolgt wieder durch lineare Interpolation (d. h. Lagrange-Interpolation 1. Ordnung). Dieses Verfahren ist deutlich aufwändiger als die vorherigen und liegt zusätzlich nur in einer C++-Referenzimplementation vor. Daher ist es nicht für den Einsatz mit realen, komplexen WFS-Szenen geeignet.
• SamplewiseDelayCubic. Auch hier werden Scale und Delay sample-genau interpoliert. Die Delay-Interpolation erfolgt mit einem Lagrange-Interpolator dritter Ordnung (d. h. kubisch). Auch dieses Verfahren liegt nur als Referenzimplementation vor und ist ausschließlich für kleine Quellanzahlen geeignet.

The following algorithms are implemented:

• Integer Delay. This is the original algorithm. It does not support delay interpolation, ie delay values are rounded to the nearest multiple of the sample period. The update of the delay and scaling parameters takes place in a grid of currently 32 samples. This algorithm is implemented in an optimized assembler variant and is suitable for real-time rendering of complete WFS scenes. Nevertheless, this operation takes up the bulk of the computational load required in the renderer.
• BufferwiseDelayLinear. The WFS parameters are adjusted in a coarse grid (notation: bufferwise ), the delayed signals themselves are calculated using a delay interpolation based on a linear interpolation. The implementation is done with Assembler support and is suitable for use with complete WFS scenes. This algorithm is currently used as the default setting.
• SamplewiseDelayLinear. This method interpolates scaling and delay values for each sample (notation: samplewise). The delay interpolation is done again by linear interpolation (ie 1st order Lagrangian interpolation). This procedure is considerably more complicated than the previous ones and is additionally only available in a C ++ reference implementation. Therefore, it is not suitable for use with real, complex WFS scenes.
• SamplewiseDelayCubic. Again, scale and delay are interpolated sample-accurate. The delay interpolation is done with a third-order Lagrange interpolator (ie cubic). This method is also available only as a reference implementation and is only suitable for small numbers of sources.

The dissertation of E. Verheijen "Sound Reproduction by Wave Field Synthesis", 19.1.1998, pp. 89-112 XP007906700 discloses basic implementations of the concept and implementation of wave field synthesis replication.

The specialist publication " Principles of Fractional Delay Filters ", by V. Valimaki, TILaakso, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'00) Istanbul, Turkey, 5.6.2000 discloses digital fractional delay filters for fine tuning sampling times, ie, to achieve required band-limited interpolations.

The specialist publication " Rendering Moving Sound with the Doppler Effect in Sound Space ", Iwaya et al., Applied Acoustics, Vol. 86, No. 8 also discloses aspects for implementing audio scenes.

DE 103 55 146 A1 discloses aspects for implementing wave field synthesis.

The Msc Thesis, "Focused Wavefields and Moving Virtual Sources by Wavefield Synthesis," G. Jansen, XP00911966, 1997 discloses various aspects for interpolating between samples in a sequence using integer and fractional delay values.

The technical publication Electronics Letters, 29.9.1994, Vol. 30, No. 20, "Implementation of Wideband Integer and Fractional Delay Element", NP Murphy et al ., disclosed different structures for performing a delay implementation.

The U.S. Patent No. 6,600,495 B1 discloses a filter structure that allows the use of a filter as either a continuous-delay Farrow filter or as a selectable-delay polyphase filter.

The AES Convention Paper by Bleda a. a. May 28-31, Barcelona, Spain, "Design and Implementation of a Compatible Wave Field Synthesis Authoring Tool" discloses a user-friendly editing tool having a data acquisition functionality, a virtual source processor, an auralization processor for accommodating room acoustics, a Functionality for estimating auralization filters, and a final mixing stage.

Based on this prior art, the present invention has the object to provide an apparatus and a method which determines component signals for a wave field synthesis system with significantly higher accuracy.
This object is achieved by a device according to claim 1 or 10, a method according to claim 15 or 16, or a computer program according to claim 18.

The gist of the present invention is that a higher quality component signal can be achieved by first pre-processing the audio signal belonging to a virtual source, the preprocessing being independent of the WFS parameter, such that a better interpolation is achieved. The component signal thus has a higher accuracy, wherein the component signal represents the component generated by a virtual source for a loudspeaker signal. Furthermore, the present invention includes improved interpolation of WFS parameters such as delay or delay Scaling values obtained with a low parameter sampling frequency.

Thus, embodiments of the present invention provide an apparatus for determining a component signal for a WFS system having an array of loudspeakers, the WFS system configured to provide an audio signal associated with a virtual source represented as a discrete signal sampled at an audio sampling frequency. and source positions associated with the virtual source to calculate component signals for the loudspeakers due to the virtual source, taking speaker positions into account. The apparatus of the invention comprises means for providing WFS parameters for a component signal using a source position and using the speaker position, the parameters being determined at a parameter sampling frequency that is less than the audio sampling frequency. The apparatus further comprises a WFS parameter interpolator for interpolating the WFS parameters to produce an interpolated WFS parameter having a parameter interpolation frequency greater than a parameter sampling frequency, the interpolated WFS parameters having interpolated fractions that have a higher accuracy than specified by the audio sampling frequency. Finally, the device comprises an audio signal processing device which is designed to apply the interpolated fractional parts to the audio signal in such a way that the component signal is processed with the higher accuracy.

The idea of problem solving is thus based on reducing the complexity of the overall algorithm by exploiting redundancy. In this case, the delay interpolation algorithm is partitioned so that it has a part for calculating intermediate values in a) and b) a efficient algorithm for calculating the final results is divided.

The structure of a WFS playback system is exploited as follows: For each primary source, output signals for all loudspeakers are calculated by means of delay interpolation. This preprocessing per primary source. It must be ensured that this preprocessing is independent of the actual delay. In this case, once preprocessed data can be used for all the speaker signals.

1. (i) Verfahren 1: eine Kombination einer Überabtastung mit einer Delay-Interpolation geringerer Ordnung auszuführen.
   Bei diesem Verfahren werden vor der Speicherung der Eingangssignale in eine Verzögerungsleitung die Eingangssignale durch Überabtastung auf eine höhere Samplerate konvertiert. Dies erfolgt effizient z. B. durch Polyphasen-Verfahren. Die entsprechend größere Zahl "hochgesampelter" Werte wird in der Verzögerungsleitung gespeichert.
   Zur Generierung der Ausgangssignale wird das gewünschte Delay mit dem Überabtast-Verhältnis multipliziert. Dieser Wert wird für den Zugriff auf die Verzögerungsleitung verwendet. Aus den Werten der Verzögerungsleitung wird das endgültige Ergebnis durch einen Interpolations-Algorithmus geringer Ordnung (z. B. Polynom-Interpolation) bestimmt. Der Algorithmus wird mit der geringen, ursprünglichen Taktrate des Systems ausgeführt.
   Die Kombination einer Überabtastung mit einer Polynominterpolation für eine einzelne Delay-Interpolations-Operation ist für die Anwendung in der WFS neu. Durch die mehrfache Verwendung der durch die Überabtastung erzeugten Signale kann damit in der WFS eine deutliche Performancesteigerung realisiert werden.
2. (ii) Verfahren 2: Verwendung einer Farrow-Struktur zur Interpolation.

Exemplary embodiments that implement this principle can be described, for example, by means of two methods.

1. (i) Method 1: perform a combination of oversampling with a lesser order delay interpolation.
   In this method, before storing the input signals into a delay line, the input signals are oversampled to a higher sample rate. This is done efficiently z. B. by polyphase process. The correspondingly larger number of "upsampled" values is stored in the delay line.
   To generate the output signals, the desired delay is multiplied by the oversampling ratio. This value is used to access the delay line. From the values of the delay line the final result is determined by a low order interpolation algorithm (eg polynomial interpolation). The algorithm runs at the system's low, original clock rate.
   The combination of oversampling with polynomial interpolation for a single delay interpolation operation is new to the application in the WFS. By the multiple use of the signals generated by the oversampling Thus, a significant performance increase can be realized in the WFS.
2. (ii) Method 2: Use of a Farrow Structure for Interpolation.

The Farrow structure is a variable digital filter for continuously variable variable delays. It consists of a set of P sub-filters. The input signal is filtered by each of these sub-filter and provides P different outputs c _p output signal is obtained by evaluating a polynomial in d, where d is the fractional portion or fraction of the desired delay the outputs of the subfilters, c _p, the coefficients of the polynomial form.

The proposed algorithm preprocesses the outputs of the sub-filters for each sample of the input signal. These P values are written to the delay line. The output signals are generated by accessing the P values in the delay line and the evaluation of the polynomial. This efficient operation is done for each speaker.

In these embodiments, the audio signal processing device is designed to carry out the methods (i) and / or (ii).

In a further embodiment, the audio signal processing means is adapted to perform an oversampling of the audio signal such that the oversampling is performed up to an oversampling rate which ensures a desired accuracy. This has the advantage that the second interpolation step thereby becomes redundant.

Embodiments of the present invention describe a WFS delay interpolation that is particularly advantageous for audio engineering and sound engineering in the context of wave field synthesis, since a significantly improved suppression of audible artifacts is achieved. The improvement is achieved in particular by an improved delay interpolation, the use of fractional delays and asynchronous sampling rate conversion. It is thus

Fig. 1

eine schematische Darstellung einer Vorrichtung gemäß einem Ausführungsbeispiel der vorliegenden Erfindung;

Fig. 2

einen Frequenzgang für einen Lagrange-Interpolator dritter Ordnung;

Fig. 3

eine kontinuierliche Impulsantwort für einen Lagrange-Interpolator siebenter Ordnung;

Fig. 4

ein Worst-Case-Amplitudengang für Lagrange-Interpolatoren unterschiedlicher Ordnung;

Fig. 5

ein WFS-Renderer mit einer WFS-Signalverarbeitung;

Fig. 6a bis 6c

Darstellungen für Amplituden und Delay-Interpolationen;

Fig. 7

eine Delay-Interpolation mittels Überabtastung und simultanem Auslesen als Lagrange-Interpolation;

Fig. 8

eine Spezifikation des Anti-Imaging-Filters für Überabtastung, Übergangsband nur für Baseband spezifiziert;

Fig. 9

eine Spezifikation des Anti-Imaging-Filters für Überabtastung und eine so genannte "Don't-Care"-Region auch für Images des Übergangsbandes;

Fig. 10

eine Delay-Interpolation mit simultanem Auslesen auf Basis der Farrow-Struktur und

Fig. 11

ein prinzipielles Blockschaltbild eines Wellenfeldsynthesesystems mit Wellenfeldsynthesemodul und Lautsprecherarray in einem Vorführbereich.

Embodiments of the present invention will be explained below with reference to the accompanying drawings. Show it:

Fig. 1

a schematic representation of a device according to an embodiment of the present invention;

Fig. 2

a frequency response for a third order Lagrange interpolator;

Fig. 3

a continuous impulse response for a seventh order Lagrange interpolator;

Fig. 4

a worst-case amplitude response for Lagrangian interpolators of different order;

Fig. 5

a WFS renderer with WFS signal processing;

Fig. 6a to 6c

Representations for amplitudes and delay interpolations;

Fig. 7

a delay interpolation by oversampling and simultaneous readout as Lagrange interpolation;

Fig. 8

a specification of the oversampling anti-imaging filter, transition band specified for baseband only;

Fig. 9

a specification of the anti-imaging filter for oversampling and a so-called "don't care" region also for images of the transition band;

Fig. 10

a delay interpolation with simultaneous reading based on the Farrow structure and

Fig. 11

a schematic block diagram of a wave field synthesis system with wave field synthesis module and speaker array in a demonstration area.

With regard to the following description, it should be noted that in the different embodiments, the same or functionally equivalent functional elements have the same reference numerals and thus the description of these functional elements in the various, in the following illustrated embodiments are interchangeable.

Before going into the present invention in detail, will be described below with reference to Fig. 11 the basic structure of a wave field synthesis system shown. The wave field synthesis system has a speaker array 700 placed with respect to a demonstration area 702. Specifically, this includes in Fig. 11 shown speaker array which is a 360 ° array, four array sides 700a, 700b, 700c and 700d. If the demonstration area 702 z. As a movie theater, it is assumed that the cinema screen is on the same side of the screening area 702, on which the sub-array 700c is arranged with respect to the conventions front / back or right / left. In this case, the observer who is sitting at the so-called optimal point P in the demonstration area 702 would see to the front, ie to the screen. Behind the viewer would then be the sub-array 700a, while to the left of the viewer would be the sub-array 700d, and to the right of the viewer are the sub-array 700b would. Each loudspeaker array consists of a number of different individual loudspeakers 708, each of which is driven by its own loudspeaker signals transmitted by a wave field synthesis module 710 via an in-line loudspeaker signal Fig. 11 only schematically shown data bus 712 are provided. The wave field synthesis module is configured to use the information about e.g. B. type and location of the speaker with respect to the screening area 702, so of speaker information (LS information), and optionally with other data to calculate loudspeaker signals for the individual speakers 708, each of the audio data for virtual sources, which further assigned position information are derived according to the known wave field synthesis algorithms. The wave field synthesis module can also receive further inputs, such as information about the room acoustics of the demonstration area, etc.

Fig. 1 shows a device according to an embodiment of the present invention. The virtual source source position 135 and the loudspeaker positions 145 are input to a device for providing WFS parameters 150. The means for providing WFS parameters 150 may optionally include another input where other data 190 may be read. The other data 190 may include, for example, the room acoustics and other scene data. The means 150 for providing therefrom, with a parameter sampling frequency, determines therefrom the WFS parameters 155 read in the WFS parameter interpolator 160. After interpolation, the interpolated WFS parameters are provided to the audio signal processor 170. The audio signal processor 170 also has an input for an audio signal 125 and an output for component signals 115. Each virtual source provides its own audio signal, which is processed into component signals for the various loudspeakers.

Fig. 2 FIG. 12 shows a WFS system 200 having a WFS signal processing 210 and a WFS parameter calculation 220. The WFS parameter calculation 220 has an input for scene data 225 relating, for example, to N source signals. Assuming that N signal sources (virtual sources) and M loudspeakers are available for the WFS system, the WFS parameter calculation 220 calculates NxM parameter values (scale and delay values). These parameters are output to the WFS signal processor 210. The WFS signal processor 210 includes a WFS delay and scaling device 212, a summing device 214, and a delay line 216. The delay line 216 is generally configured as a means for latching and may be given by, for example, a ring buffer.

The NxM parameters are read in by the WFS delay and scaling device 212. The WFS delay and scaling device 212 also reads the audio signals from the delay line 216. The audio signals in the delay line 216 in this case have an index that corresponds to a certain delay and is accessed by means of a pointer 217, so that the WFS delay and scaling device 212 by accessing an audio signal with a specific index, a Delay for the corresponding audio signal. The index thus simultaneously serves as the address or addressing of the corresponding data in the delay line 216.

The delay line 216 receives audio input data from the N-source signals, which are stored in the delay line 216 according to their timing. By correspondingly accessing an index of the delay line 216, the WFS delay and scaling unit 212 can thus read out audio signals having a desired (calculated) delay value (index). Further The WFS delay and scaling device 212 outputs corresponding component signals 115 to the means 214 for summing 214, and the means 214 for summing sums the component signals 115 of the respective N virtual sources to generate therefrom loudspeaker signals for the M-loudspeakers. The speaker signals are provided at a sound output 240.

Embodiments thus relate to audio signal processing of a WFS rendering system 200. This rendering system contains as input data the audio signals of the WFS sources (virtual sources), the index variable n counting the sources and N representing the number of sources. Typically, these data come from other system components such as audio players, possibly pre-filters, etc. As another input parameter, the block WFS parameter calculation 220 provides amplitude (scaling) and delay values (delay values) for each source / speaker combination (index variable: m , Number: M). This is usually done as a matrix, the corresponding values for the sources n and loudspeaker m are named delay (n, m) and scale (n.m) in the following.

The audio signals are first stored in the delay line 216 to allow later random access (i.e., with variable delay values).

Core component of the embodiments is the block "WFS delay and scaling" 212. This is sometimes referred to as WFS convolution or WFS convolution, but it is not a true convolution in terms of signal processing and therefore the term is usually avoided. Here, an output signal (component signal 115) is generated for each combination (n, m) of source and loudspeaker.

In this case, for the signal y (n, m) a delay (n, m) delayed value from the delay line 216 for source n read. This value is multiplied by the amplitude scale (n, m).

Finally, the signals y (n, m) of all sources n = 1, ..., N are added together in a loudspeaker fashion and thus form the drive signal for each loudspeaker y (m): $$\mathrm{Y}\left(\mathrm{m}\right)=\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">y</figure-callout>}\left(\mathrm{1}.\mathrm{m}\right)+\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="imgf0004.png,imgf0009.png"\; state="\{\{state\}\}">y</figure-callout>}\left(\mathrm{2}.\mathrm{m}\right)+...+\mathrm{y}\left(\mathrm{N}.\mathrm{m}\right)\mathrm{,}$$

This calculation is done for each sample of speaker signals.

For a stationary source, the method according to the invention or the device according to the invention is of little importance in practice. Although the synthesized wave field deviates from a theoretically defined ideal case with a rounding of the delay values, these deviations are very small and are completely covered by other deviations that occur in practice, such as a spatial aliasing. For the practical real-time implementation, however, it makes little sense to distinguish between currently non-moving and moving sources. It should always be consistent with the general case algorithm; H. be calculated for moving sources.

The algorithm is particularly interesting for moving sources, but errors do not only occur when samples are "swallowed" or used twice. Rather, approximation of sampled signals at arbitrary nodes always generates errors. The methods for approximation between nodes are also referred to as fractional-delay interpolation.

These become noticeable among other things in frequency and phase errors of the output signal. If these errors are time-variant (as in the case of moving sources) different (often clearly audible) effects occur, as they do z. B. in the frequency domain as amplitude and frequency modulations and thereby cause quite complex error spectra.

Such errors also occur when using interpolation methods - the decisive factor here is the quality of the method used, which, however, is usually associated with corresponding billing expenditure.

One possibility is to properly omit and insert samples, but this does not necessarily provide the better quality result.

The central point of the present invention is to enable the use of very high-quality delay interpolation methods by means of a corresponding structuring of the WFS signal processing, while at the same time keeping the calculation effort comparatively low.

In embodiments of the present invention, it is not specific to respond to the movement of sources and to attempt to avoid errors by appropriately generated samples in this case. The signal processing does not need information about source positions, but only delay and amplitude values (which are time-variant in the case of a moving source). The errors described arise from the way in which these delay values are applied to the audio signals by the function unit WFS delay and scaling 212 (primarily: which method is used for delay interpolation). At this point, the present invention begins to reduce errors by using high-quality delay interpolation methods.

As described above, it is important for a high quality component signal to use a high quality delay interpolation method. For the evaluation can one informal hearing test, with which the influence of the delay interpolation on the quality of reproduction in a reproduction system can be estimated.

Playback can be done with the current WFS real-time rendering system, using various methods of delay interpolation. The described algorithms for delay interpolation are used.

As scenes, individual moving sources are investigated, which perform geometrically simple, precalculated trajectories. For this purpose, the current authoring and playback application of the playback system is used as a scene player. In addition, a custom renderer is used that generates fixed programmed trajectories without external scene player, so as to evaluate the impact of the scene player and the transmission characteristics of the network on the quality.

The source signals are simple, predominantly tonal signals, as they suggest an increased perceptibility of delay interpolation artifacts. Both signals below and above the system's spatial aliasing frequency are used to evaluate the visibility, both without aliasing influence and the influence of delay interpolation artefacts and aliasing disturbances on each other.

1. 1. Kreisförmige Bewegung einer Punktquelle um das Array herum. Der Radius wird so gewählt, dass die Quelle sich stets in einem ausreichendem Abstand außerhalb des Arrays befindet, um zusätzliche Fehler z. B. durch ein Umschaltung auf den Panning-Algorithmus oder durch einen Wechsel der Amplitudenberechnung zuvermeiden. Das ddd-Flag wird zur Erhöhung der Delay-Änderungsraten aktiviert.
2. 2. Kreisförmige Bewegung einer ebenen Welle um das Array herum. Die Normalenrichtung zeigt stets in Richtung des Array-Mittelpunktes. Die anderen Randbedingungen werden analog zum vorherigen Versuch gewählt.
3. 3. Wiederholte, lineare Bewegung einer Punktquelle auf eine Array-Front zu und wieder zurück. Die Umkehrung der Bewegungsrichtung erfolgt zur Vermeidung impulsartiger Störungen nicht abrupt, sondern durch einen (z. B. linearen) Beschleunigungsvorgang, bis die Quelle mit dem Erreichen der Sollgeschwindigkeit wieder zu einer gleichförmigen Bewegung übergeht. Das dd1-Flag sollte deaktiviert werden, um Beeinflussungen durch Amplitudenänderungen zu verhindern.
4. 4. Lineare Bewegung einer ebenen Welle mit Normalenrichtung zum Array-Zentrum. Die Bewegung des Referenzpunktes der ebenen Welle erfolgt dabei wie im vorhergehenden Versuch. Das ddd-Flag ist aktiviert. Der Zweck dieses Versuches liegt darin, die Wiedergabefehler der Delay-Interpolation weitestgehend von den anderen Artefakten bewegter Quellen zu isolieren: Der Referenzpunkt einer ebenen Quelle dient nur dazu, eine zeitliche Basis für das Quellsignal zu schaffen. Eine Verschiebung erzeugt so eine einheitliche Abtastratenumsetzung für alle Sekundärquellsignale. Die anderen Parameter der Wiedergabe (Skalierungen der Lautsprechergewichte, Dopplerverschiebungen der Sekundärquellen, Ausprägung des Aliasing-Interferenzmusters) bleiben von der Verschiebung unberührt.

The following trajectories are investigated:

1. 1. Circular motion of a point source around the array. The radius is chosen so that the source is always located at a sufficient distance outside the array to avoid additional errors such. B. by switching to the panning algorithm or by changing the amplitude calculation to avoid. The ddd flag is activated to increase the delay change rates.
2. 2. Circular movement of a plane wave around the array. The normal direction always points in the direction of the array center. The other boundary conditions are selected analogously to the previous experiment.
3. 3. Repeated, linear movement of a point source to and from an array front. The reversal of the direction of movement does not occur abruptly in order to avoid impulse-type disturbances but rather through a (for example linear) acceleration process until the source returns to a uniform movement when the setpoint speed is reached. The dd1 flag should be disabled to prevent interference from amplitude changes.
4. 4. Linear movement of a plane wave with normal direction to the array center. The movement of the reference point of the plane wave is carried out as in the previous experiment. The ddd flag is activated. The purpose of this experiment is to isolate the playback errors of the delay interpolation as far as possible from the other artifacts of moving sources: The reference point of a flat source only serves to provide a temporal basis for the source signal. A shift thus produces a uniform sample rate conversion for all secondary source signals. The other parameters of the playback (scaling of the loudspeaker weights, Doppler shifts of the secondary sources, manifestation of the aliasing interference pattern) are unaffected by the shift.

The perceived quality is evaluated informally and subjectively by some test persons.

• Welchen Einfluss haben Delay-Interpolationsalgorithmen auf die wahrgenommene Qualität der WFS-Wiedergabe?
• Welche charakteristischen Störungen können auf die Delay-Interpolation zurückgeführt werden und unter welchen Bedingungen sind diese besonders deutlich?
• Ab welcher Qualität der Delay-Interpolation sind keine Verbesserungen mehr wahrnehmbar?

This should answer the following questions:

• What effect do delay interpolation algorithms have on the perceived quality of WFS playback?
• Which characteristic perturbations can be attributed to the delay interpolation and under which conditions are these particularly clear?
• From which quality of the delay interpolation are no improvements noticeable?

In the following, different measures for the evaluation of the quality of fractional delay algorithms are presented.

These dimensions are to be further developed with regard to their usability and supplemented by new methods. They serve both to assess the quality of algorithms and to specify quality criteria that z. B. be used as targets for design and optimization procedures.

The FD filters designed for a particular fractional delay can be examined using common discrete-system analysis techniques. Assessment measures such as complex frequency response, amplitude response, phase response, phase delay and group delay are used.

The ideal fractional delay element has a constant amplitude response with unity gain, a linear phase, and constant phase or group delay times corresponding to the desired delay. The corresponding measures must be evaluated for different values of d.

Fig. 3 shows by way of example the amplitude response as well as the phase delay of a third-order Lagrange interpolator for different delay values d. Fig. 3a make one Dependence of the amplitude on the normalized frequency and Fig. 3b a dependence of the phase delay of the normalized frequency. In the FIGS. 3a, 3b For example, different graphs are shown for different values of d. Fig. 3a shows by way of example the values for d = 0; 0.1; 0.2; ....; 0.5. Fig. 3b shows by way of example the values for d = 0; 0.1; 0.2; ....; 1.

The evaluation by means of frequency responses is useful only for time-invariant systems and therefore not applicable for time-dependent changes of the fractional delay parameter. To investigate the effects of these changes on the interpolated signal, measures can be used to measure the difference between ideal and real interpolated signal, such as SNR (Signal to Noise Ratio) or THD + N (Total harmonic distortion + noise) measure be used. The THD + N measure is used to evaluate the delay interpolation algorithms. To determine the THD + N, a test signal (usually a sine wave) is interpolated with a defined delay curve and the result is compared with the analytically generated, expected output signal. The delay curve is usually a linear change.

The subjective rating can be done on the single channel as well as in the WFS setup. Similar conditions are used as in the informal hearing test outlined above.

In addition, the use of objective measurement methods to evaluate the perceived signals, especially the PEAQ (Perceptual Evaluation of Audio Quality) method, may be considered. In doing so, quite good correspondences with the subjectively determined quality of perception and with objective quality measures can be ascertained. Nevertheless, the results of further investigations are critical, because z. For example, the PEAQ test for other applications (audio coding) was designed and parameterized.

Fig. 4 shows an example of such a continuous impulse response generated from a discrete, variable FD filter. In detail, a continuous impulse response is shown for a Lagrangian interpolator 7th order, wherein the amplitude of the signal as a function of time with the nodes t = 0, ± 1, ± 2, ± 3, ± 4 are determined. The time is normalized such that a maximum (nodes of the pulse) at t = 0. For smaller and larger t-values, the amplitude quickly tends towards zero.

The continuous impulse response of a continuous variable fractional delay filter can be used to describe the behavior of such a structure. This continuous form of description can be generated by determining the discrete impulse responses for many values of d and combining them into a (quasi-) continuous impulse response. With the help of this form of description, inter alia, the behavior of FD filters when used for asynchronous sample rate conversion, so z. For example, we investigated the suppression of aliasing and imaging components.

From this description, quality measures for variable delay interpolation algorithms can be derived. Based on this, it can be tested whether the quality of such a variable filter can be influenced by the targeted influence on the properties of the continuous impulse response.

In order to be able to provide high-quality component signals, a number of demands have to be placed on the algorithm for delay interpolation.

• Es soll sich eine über den gesamten Audio-Reproduktionsbereich gute Qualität der Interpolation erzielt werden. Es sind sowohl Algorithmen und Parametrisierungen gewählt, die sich am menschlichen Hörvermögen orientieren als auch solche, deren Fehler aufgrund anderer Fehler im WFS-Übertragungssystem nicht mehr wahrnehmbar sind.
• Es sollen beliebige Werte des fraktionalen Delays und beliebige Änderungsraten (im Rahmen der festgelegten maximalen Quellgeschwindigkeiten) möglich sein.
• Stetige Änderungen des fraktionalen Delays dürfen nicht zu Störungen (Transienten) führen.
• Die Verfahren müssen sich modular in der Renderer-Einheit implementieren lassen.
• Die Verfahren müssen so effizient implementierbar sein, dass (zumindest perspektivisch) eine Echtzeitausführung kompletter WFS-Szenen mit ökonomisch vertretbarem Aufwand an Hardware realisierbar ist.

In the following, some requirements for suitable procedures are defined.

• It should be achieved over the entire audio reproduction area good quality of interpolation. Algorithms and parametrizations are chosen that are based on human hearing as well as those whose errors are no longer perceptible due to other errors in the WFS transmission system.
• Any values of the fractional delay and any rate of change (within the specified maximum source speeds) should be possible.
• Constant changes in the fractional delay must not lead to disturbances (transients).
• The methods must be modularly implementable in the renderer unit.
• The methods must be so efficiently implementable that (at least in perspective) a real-time execution of complete WFS scenes can be realized with economically justifiable expenditure on hardware.

As stated above, the change in delay times required in the playback of moving sources results in asynchronous sample rate conversion of the audio signals. The suppression of aliasing and imaging effects is the biggest problem to be solved when implementing a sample rate conversion. For the application in the WFS the large area, in which the conversion factor can move, comes aggravatingly. Therefore, the methods should be examined for their properties to suppress such baseband mirrored frequencies. It is to be analyzed how the fractional-delay algorithms can be examined for their suppression of alias and image components. Based on this, the algorithms to be designed have to be adapted.

Wave field synthesis requires delay interpolation for each combination of virtual source and loudspeaker. Combined with the complexity of delay interpolation necessary for good rendering quality, good quality real-time implementation is not practical.

Lagrange interpolation is one of the most widely used methods for fractional-delay interpolation - it is one of the most attractive algorithms and is recommended for the first-to-be-tested algorithm for most applications. Lagrange interpolation is based on the concept of polynomial interpolation. For an Nth order method, a polynomial of order N is calculated which passes through N + 1 support points surrounding the searched location.

The Lagrange interpolation satisfies the condition of maximum flatness. This means that the error of the approximation and its first N derivatives at a selectable frequency ω (in practice almost exclusively ω = 0 is selected) disappear. Thus, Lagrange interpolators exhibit a very low error at low frequencies. On the other hand, their behavior is less good at higher frequencies.

Fig. 5 shows a so-called worst-case amplitude response for a Lagrange interpolator of different order. In this case, the amplitude as a function of the normalized frequency (ω / ω ₀ with ω ₀ as limit or cutoff frequency) is shown, with Lagrange interpolators being shown for the orders N = 1, 3, 7 and 13. The quality at high frequencies improves even with increasing interpolation order only slowly.

Although these properties do not make the Lagrange interpolation optimal for use in WFS, Thus, this interpolation method can still be used as a basic element of more complex algorithms that do not have these disadvantages mentioned.

The filter coefficients are defined by explicit formulas: $${\mathrm{H}}_{\mathrm{i}}={\displaystyle \underset{\mathrm{k}=\mathrm{1}.\mathrm{k}\ne \mathrm{i}}{\overset{\mathrm{N}}{\Pi }}}\frac{\mathrm{d}-\mathrm{k}}{\mathrm{k}-\mathrm{i}}\mathrm{,}$$

In the direct application of this formula, O (N ² ) operations are required for the calculation of the N + 1 coefficients.

The FIGS. 6a to 6c show representations for an amplitude response and a delay interpolation d.

Fig. 6a shows an example of an amplitude A of an audio signal as a function of time t. A sampling of the audio signal takes place at the times t10, t11, t12, ...., t20, t21, etc. The sample rate is thus given by 1 / (t10-t11) (assuming a constant sample rate).
With a much lower frequency, the delay values are recalculated. In the example as at the Fig. 6a 5, the delay values are calculated at the times t10, t20 and t30, wherein a delay value d1 was calculated at the time t10, a delay value d2 at the time t20 and a delay value of d3 at the time t30 , The times at which delay values are recalculated may vary, for example, a new delay value can be generated every 32 bars, or else more than 1,000 cycles may occur between the calculation of new delay values. Between the delay values, the delay values are interpolated for the individual measures.

Fig. 6b shows an example of how the interpolation of the delay values d can be made. Various interpolation methods are possible. The simplest interpolation consists in a linear interpolation (Lagrangian interpolation 1st order). Better interpolations are based on polynomials of higher order (Lagrangian interpolation of higher order), whereby the corresponding calculation requires more computing time. In Fig. 6b 2, it is shown how the delay value d1 is assumed at the time t10, the delay value d2 is present at the time t20 and the delay value d3 is present at the time t30. An interpolation results, for example, in that there is a delay value d13 at the time t13. The interpolation is chosen such that the interpolation values occur at the times t10, t20, t30, .... as part of the interpolated curve.

Fig. 6c again shows the amplitude A of the audio signal as a function of time t, with the interval between t12 and t14 being shown. The delay value d13 obtained by interpolation at the time t13 now causes the amplitude to be shifted by the delay value d13 to the time ta at the time t13. In the present example, the shift is to smaller values in time, which is only one specific embodiment and may be different in other embodiments. If d13 has a fractional fraction, ta is not at a sampling instant. In other words, the access to A2 need not occur at a clock time, and an approximation (eg, rounding) results in the above-described problems that the present invention solves.

1. (i) Verfahren 1: eine Kombination einer Überabtastung mit einer Delay-Interpolation geringerer Ordnung auszuführen und
2. (ii) Verfahren 2: Verwendung einer Farrow-Struktur zur Interpolation.

As described above, in particular two methods are used according to the invention:

1. (i) Method 1: to perform a combination of oversampling with a lesser order delay interpolation, and
2. (ii) Method 2: Use of a Farrow Structure for Interpolation.

First, the method 1 will be described in more detail.

Methods for changing the sampling rate by a fixed (usually rational) factor are widely used. These methods are also referred to as synchronous sample rate conversion. However, with the aid of such a method, only output signals for fixed output times can be generated. In addition, if the ratio of the input and output rates is almost irrational (i.e., has a very large least common multiple), the methods become very expensive.

For these reasons, the combination of synchronous sample rate conversion with methods for fractional delay interpolation is proposed according to the invention.

The implementation of a fractional delay with the aid of a sampling rate increase and the rounding to the nearest sampling instant is generally regarded as inappropriate, since it requires extremely high oversampling rates for expedient signal-to-noise ratios.

Accordingly, methods have been proposed which consist of two stages: in the first step, a synchronous sampling rate conversion takes place by a fixed, integer factor L or by the oversampling rate L. This is done via an up-sampling (insertion of L-1 zero samples after each input value). and a subsequent low-pass filtering to avoid image spectra. This operation can be performed efficiently by means of polyphase filtering.

In the second step, there is a fractional-delay interpolation between oversampled values. This is done by means of a variable fractional delay filter of low order whose coefficients are calculated directly become. Particularly useful here is the use of Lagrange interpolators (see above).

For this purpose, a linear interpolation between the outputs of a polyphase filter bank can be made. The primary goal is to reduce the storage and computational power requirements needed for near non-rational ("crooked", incommensurate) sample rate ratios.

It is also possible to introduce a "Wideband Fractional Delay Element" which is based on the combination of an up-sampling by a factor of 2, the use of a low-order fractional delay filter and the subsequent down-sampling to the original sampling rate. Implementation as a polyphase structure divides the calculation into two independent branches (even taps and odd taps). This eliminates the need to discretely implement the upsampler and downsampler elements. In addition, the fractional delay element can be implemented at the baseband frequency instead of the oversampled rate. One reason for the improved quality compared to pure fractional filters (such as Lagrange interpolation) is that the variable fractional-delay filter only operates at half the Nyquist frequency due to the increased sampling rate

This is contrary to the Maximally Flat property of Lagrange interpolation filters, as they show very low errors at low frequencies, whereas the errors at higher frequencies can only be reduced by greatly increasing the filter order, with correspondingly increasing cost of coefficient calculation and filtering.

The principle of the wideband fractional delay filter can also be combined with half-band filters as efficient implementations for the anti-imaging filters. The variable fractional delay elements can be based on dedicated structures under which the so-called Farrow structure (see below) is important.

The asynchronous sample rate conversion (DAAU) model consists of a synchronous sample rate converter (oversampling or rational sampling rate conversion) followed by a DA / AD conversion system typically is realized by a variable fractional delay filter.

However, the combination of synchronous oversampling and variable delay interpolation is quite common in audio engineering. This is probably also due to the fact that the methods used in this field have mostly developed from synchronous sample rate converters, which themselves are often multi-level.

A special case is taken by filter design methods where there are explicit, efficient calculation rules for the filter coefficients. These are mostly based on interpolation methods from numerical mathematics. The most widespread are fractional delay algorithms based on Lagrange interpolation. With the help of such methods, variable fractional delays can be implemented relatively efficiently. In addition, there are also filters based on other interpolation methods, eg. B. spline functions. However, these are less suitable for use in signal processing algorithms, especially audio applications.

Compared to fractional-delay interpolation methods based on a direct calculation of the filter coefficients, the large reduction of the filter order of the variable part allows a significant reduction of the calculation effort.

The particular advantage of the proposed method for use in wave-field synthesis is that the oversampling operation must be performed only once for each input signal, while the result of this operation can be used for all loudspeaker signals calculated by this renderer unit. This can be correspondingly higher calculation effort placed on the oversampling, especially to keep the error over the entire audio playback range low. The variable fractional-delay filtering, which must be performed separately for each output signal, can be performed much more efficiently due to the lower filter order required. On the other hand, one of the major drawbacks of FD filters with explicitly calculated coefficients (ie, above all Lagrange FD filters), their poor behavior at high frequencies, is compensated for by the fact that they only have to operate in a much lower frequency range.

• Die in Form diskreter Audiodaten vorliegenden Quellsignale werden mit einem festen, ganzzahligen Faktor L bzw. der Überabtastrate L überabgetastet. Dies erfolgt durch Einfügen von L - 1 Nullsamples zwischen jeweils zwei Eingangssignalen und anschließender Tiefpassfilterung mit einem Anti-Imaging-Filter, um Replikationen des Eingangsspektrums im überabgetasteten Signal zu vermeiden. Diese Operation wird effizient mit Hilfe von Polyphasen-Techniken realisiert.
• Die überabgetasteten Werte werden in eine Verzögerungsleitung 216 (Delay Line) geschrieben, die in der Regel als Ringpuffer implementiert ist. Es ist zu beachten, dass die Kapazität der Verzögerungsleitung 216 gegenüber herkömmlichen Algorithmen um den Faktor L bzw. die Überabtastrate zu vergrößern ist. Hier zeigt sich ein Trade-Off zwischen Speicher- und Berechnungskomplexität, der für den hier entworfenen Algorithmus gewählt werden muss.
• Zum Auslesen der Delay Line ist der gewünschte Wert der Verzögerung mit der Überabtastrate L zu multiplizieren. Durch Abspalten des nichtganzzahligen Anteils wird ein ganzzahliger Index d_int sowie ein fraktionaler Teil d_frac bzw. Bruchteil gewonnen. Falls der optimale Arbeitsbereich des variablen FD-Filters von 0 ≤ d_frac ≤ 1 abweicht, ist diese Operation anzupassen, so dass z.B. für die Lagrange-Interpolation (N-1)/2 ≤ d_frac ≤ (N+1)/2 gilt. Der ganzzahlige Anteil wird als Index zum Zugriff auf die Verzögerungsleitung verwendet, um die Stützstellen der Interpolation zu gewinnen. Aus d_frac werden die Koeffizienten des Lagrange-Interpolationsfilters bestimmt. Die interpolierten Ausgangssignale ergeben sich durch Faltung der Stützstellen mit den berechneten Filter-Koeffizienten. Diese Operation wird für jedes Lautsprechersignal wiederholt.

In a WFS rendering system, the proposed algorithm is implemented according to the invention as follows:

• The source signals present in the form of discrete audio data are oversampled with a fixed, integer factor L or the oversampling rate L, respectively. This is done by inserting L-1 null samples between every two input signals followed by low-pass filtering with an anti-imaging filter to avoid replicating the input spectrum in the oversampled signal. This operation is efficiently realized by means of polyphase techniques.
• The oversampled values are written to a delay line 216 (Delay Line), which is typically implemented as a ring buffer. It should be noted that the capacity of the delay line 216 is increased by a factor of L over conventional algorithms or the oversampling rate is to be increased. Here is a trade-off between memory and computational complexity, which must be chosen for the algorithm designed here.
• To read out the delay line, multiply the desired value of the delay by the oversampling rate L. By splitting off the non-integer part, an integer index d _int and a fractional part d _frac or fraction are obtained. If the optimum operating range of the variable FD filter deviates from 0 ≤ d _frac ≤ 1, this operation should be adapted so that for example for Lagrange interpolation (N-1) / 2 ≤ d _frac ≤ (N + 1) / 2 applies , The integer portion is used as the index to access the delay line to obtain the interpolation nodes. The coefficients of the Lagrange interpolation filter are determined from d _frac . The interpolated output signals result from convolution of the interpolation points with the calculated filter coefficients. This operation is repeated for each speaker signal.

Fig. 7 shows a concrete representation of an oversampling delay interpolation according to a first embodiment of the present invention, wherein a simultaneous readout by means of Lagrange interpolation. The discrete audio signal data x _s (from the audio source 215) is over-sampled in this embodiment by oversampling in the sampler 236 and then stored in the delay line 216 according to the time order. This results in each memory of the delay line 216, a sample of a predetermined time tm (see Fig. 6a ). The corresponding oversampled values in the delay line 216 may then be read out by the WFS delay and scale 212, with the pointer 217 corresponding to the sample of the delay value. This means that a pointer 217 located in the Fig. 7 farther to the left, more recent data, ie with a lesser delay, corresponds to and the pointer 217, which is in the Fig. 7 pointing to the right, corresponding to audio data or samples with an older priority (ie a greater delay). However, according to the index in the delay line 216, only the integer portions of the delay values are detected and the corresponding interpolation to the fractional (rational) fractions occurs in the fractional delay filters 222. The outputs of the fractional delay filters 222 give the component signal 115 off. The component signals 115 (y _i ) are then subsequently summed for various virtual sources x _s and output to the corresponding loudspeakers (loudspeaker signals).

The design of the filters can be done statically outside the runtime of the application. Efficiency requirements for the filter design are thus irrelevant; powerful tools and optimization methods can be used.

dabei entspricht n der Sampling-Frequenz des überabgetasteten Signals.The optimal anti-imaging filter (also prototype filter, as it is the prototype for the sub-filters used for polyphase realization) is an ideal low-pass filter with the discrete cutoff frequency ${\mathrm{f}}_{\mathrm{c}}=\frac{\mathrm{\pi }}{\mathrm{L}}.$

where n corresponds to the sampling frequency of the oversampled signal.

For the design of realizable low-pass filters, it makes sense to specify additional degrees of freedom. This is done primarily by defining transition bands or do not care bands, which do not specify the frequency response specifications.These transition bands are defined by the audio frequency band specified above to achieve a desired Cushioning necessary filter length. The result is a transition region in the range 2f _c ≦ f ≦ 2 (f _s -f _c ). Here, f _{c is} the desired upper limit frequency and f _{s is} the sampling frequency of the non-oversampled signal.

Fig. 8 Figure 11 shows a specification of the frequency response of an anti-imaging filter for oversampling, where transition band 310 is specified for only one base band.

Fig. 9 Figure 11 shows a specification of an anti-imaging filter for oversampling, wherein so-called don't-care regions are also determined for images 310a, 310b, 310c of the transition band 310. The additional don't-care bands may be defined on the reflections (images) of the original transition region 310.

However, since oversampling only serves as the first stage of asynchronous sample rate conversion, and this implementation involves a shift in frequency content, the use of multiple transit bands should be critically examined to avoid shifting imaging components into the audible frequency range ,

The anti-imaging filter is almost exclusively designed as a linear phase filter. Phase errors should definitely be avoided at this point since the purpose of delay interpolation is to target the phase of the input signal. When implemented as a polyphase system, however, the linear phase does not apply to the sub-filters, so that the corresponding complexity savings can not be utilized.

For designing the prototype filter, known methods of filter design can be used. Of particular importance are least-squares methods (in Matlab: firls) and Equiripple methods (also referred to as minimax or Chebyshev optimization, Matlab function: firpm). When using firpm it should be noted that at larger filter lengths (N _pp > 256) often no convergence occurs. However, this is due to the numerics of the tool used (here: Matlab) and could be repealed by an appropriate implementation.

Since the oversampled signal results from the insertion of L - 1 zero samples, there is a gain by the factor or the oversampling rate L, so that the original signal amplitude is maintained. This is possible by multiplying the filter coefficients with this factor without additional calculation effort.

1. (a) Filterlänge des Prototypfilters Npp. Dieser bestimmt die Güte der Antiimaging-Filterung und hat gleichzeitig Einfluss auf die Performance. Da die Filterung jedoch nur einmal für jedes Eingangssignal verwendet wird, ist der Einfluss auf die Performance relativ gering. Die Länge des Prototypfilters bestimmt auch die durch die Delay-Interpolation bedingte Systemlatenz maßgeblich.
2. (b) Überabtastverhältnis bzw. Überabtastrate L. L bestimmt die notwendige Kapazität (Speicherbedarf) der Verzögerungsleitung 216. Über die Cache-Lokalität wirkt sich dies bei modernen Architekturen auch auf die Performance aus. Zusätzlich wird mit steigendem L auch die zum Erzielen einer gewünschten Filtergüte notwendige Filterlänge beeinflusst, da L Polyphasen-Subfilter benötigt werden und die Übergangsbandbreiten mit steigendem L sinken.
3. (c) Wiedergabe-Frequenzbereich. Der Wiedergabe-Frequenzbereich bedingt die Breite des Übergangsbereichs der Filter und hat damit Einfluss auf die zum Erzielen einer gewünschten Filtergüte notwendige Filterlänge.
4. (d) Interpolationsordnung N. Den weitestgehenden Einfluss auf die Performance und Qualität hat die Ordnung des variablen Fractional-Delay-Interpolators, der in der Regel als Lagrange-Interpolator implementiert wird. Dessen Ordnung bestimmt den Berechnungsaufwand zur Gewinnung der Filterkoeffizienten sowie der Faltung selbst. N bestimmt auch die Zahl der zur Faltung benötigten Werte aus der Verzögerungsleitung 216 und gibt damit auch die notwendige Speicher-bandbreite vor. Da die variable Interpolation für jede Kombination aus Eingangssignal und Ausgangssignal benötigt wird, hat die Wahl von N den größten Einfluss auf die Performance.

In contrast to direct methods for delay interpolation such. As the Lagrange interpolation, the combined algorithm on different, interdependent quality and complexity determining parameters. These are above all:

1. (a) Filter length of the prototype filter Npp. This determines the quality of the anti-imaging filtering and also has an impact on the performance. However, since filtering is used only once for each input signal, the impact on performance is relatively low. The length of the prototype filter also determines the system latency caused by the delay interpolation.
2. (b) Oversampling ratio L. L determines the necessary capacity (memory requirement) of the delay line 216. With the cache locality, this also affects performance in modern architectures. In addition, as the L increases, the filter length necessary to achieve a desired filter quality is also affected, since L polyphase sub-filters are needed and the transition bandwidths decrease as the L increases.
3. (c) reproduction frequency range. The playback frequency range determines the width of the transitional region of the filters and thus has an influence on the filter length necessary to achieve a desired filter quality.
4. (d) Interpolation order N. The order of the variable fractional-delay interpolator, which is usually implemented as a Lagrange interpolator, has the greatest influence on performance and quality. Its order determines the calculation effort for obtaining the filter coefficients as well as the convolution itself. N also determines the number of values required for the convolution from the delay line 216 and thus also specifies the necessary memory bandwidth. Since variable interpolation is needed for each combination of input signal and output signal, choosing N has the biggest impact on performance.

From these parameters, an optimum combination of quality and performance aspects for the respective application can be found. For this purpose, the interaction of the various stages of the algorithm must be analyzed and verified by simulations.

• Die Überabtastrate L sollte moderat gewählt werden, ein Verhältnis zwischen 2 und 8 sollte nicht überschritten werden.
• Die variable Interpolation sollte geringe Ordnung (anvisiert: maximal 3) nicht übersteigen. Gleichzeitig sind ungerade Interpolationsordnungen zu verwenden, da gerade Ordnungen, analog zum Verhalten der reinen Lagrange-Interpolation, deutlich höhere Fehler aufweisen.

The following considerations should be considered:

• The oversampling rate L should be chosen moderately, a ratio between 2 and 8 should not be exceeded.
• The variable interpolation should not exceed low order (maximum: 3). At the same time, odd interpolation orders are to be used, since just orders, analogous to the behavior of the pure Lagrangian interpolation, have significantly higher errors.

For analysis of the filter, besides simulations with real input signals, an analysis of the equivalent static filter can also be performed. For a fixed fractional delay, the filter coefficients of the prototype filters involved in the Lagrangian interpolation are determined, multiplied by the corresponding Lagrangian weights and after Application of the necessary index shifts summed. Thus, the algorithm can be analyzed with the criteria described in section 4 (frequency response, phase delay, continuous impulse response), without the peculiarities of the multi-rate processing to be considered.

An algorithm for determining the equivalent static FD filter is therefore to be implemented. The only problem here is the definition of the filter length in order to obtain comparable values for all values of d, since the equivalent filters access different samples of the input signal as a function of d.

The static delay caused by the interpolation filter depends both on the order of the oversampling L or the oversampling rate, the phase delay of the polyphase prototype filter and the interpolation order. If the prototype filter is linear-phase, the following system delay results: $${\mathrm{D}}_{\mathrm{system}}=\frac{{\mathrm{N}}_{\mathrm{pp}}+\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="imgf0004.png,imgf0009.png"\; state="\{\{state\}\}">N</figure-callout>}}{\mathrm{2}\mathrm{L}}\mathrm{,}$$

The algorithm presented is a practical and relatively easy-to-implement approach to improve the delay interpolation. The performance increase compared to a method for delay interpolation with direct calculation of the coefficients is very low. This is opposed to a significant reduction in playback errors, especially at higher frequencies. In contrast to the direct methods such as Lagrange interpolation, it is possible to realize a reproduction of perceptible artifacts over the entire audio reproduction range at a reasonable cost. Critical to the performance of the method is the efficient extraction of integer and fractional delay parameters, the calculation the Lagrangian coefficients and the execution of the filtering.

The design tools used to determine the performance determining parameters are quite simple: L, N _pp and N can be determined by external constraints or by experiment. The filter design of the prototype filter is done using standard methods for low-pass filters, possibly using additional don't-care regions.

Next, the method 2 (using a Farrow structure for interpolation), which represents an alternative procedure according to the invention, will be described in more detail.

The Farrow structure is a variable filter structure for implementing a variable fractional delay. It is a structure based on an FIR filter whose behavior can be controlled by an additional parameter. For the Farrow structure, the fractional part or fraction of the delay is used as a parameter to map a controllable delay. The Farrow structure, though independently developed, is one manifestation of a variable digital filter.

wobei d der steuerbare Parameter ist. Die Transferfunktion des Filters bestimmt sich damit zu: $$\mathrm{H}\left(\mathrm{z},\mathrm{d}\right)={\displaystyle \sum _{\mathrm{n}=\mathrm{0}}^{\mathrm{N}}}{\displaystyle \sum _{\mathrm{m}=\mathrm{0}}^{\mathrm{M}}}{\mathrm{c}}_{\mathrm{nm}}{\mathrm{d}}^{\mathrm{m}}{\mathrm{z}}^{-\mathrm{n}}$$

The variable characteristic is achieved by forming the coefficients of the FIR filter by polynomials. $$\mathrm{H}\left[\mathrm{n}\right]={\displaystyle \underset{\mathrm{m}=\mathrm{0}}{\overset{\mathrm{M}}{\Sigma }}}{\mathrm{c}}_{\mathrm{nm}}{\mathrm{d}}^{\mathrm{m}}.$$

where d is the controllable parameter. The transfer function of the filter is thus determined by: $$\mathrm{H}\left(\mathrm{z},\mathrm{d}\right)={\displaystyle \underset{\mathrm{n}=\mathrm{0}}{\overset{\mathrm{N}}{\Sigma }}}{\displaystyle \underset{\mathrm{m}=\mathrm{0}}{\overset{\mathrm{M}}{\Sigma }}}{\mathrm{c}}_{\mathrm{nm}}{\mathrm{d}}^{\mathrm{m}}{\mathrm{z}}^{-\mathrm{n}}$$

For efficient implementation, this transfer function is often implemented as follows: $$\begin{array}{ll}\mathrm{H}\left(\mathrm{z},\mathrm{d}\right)& ={\displaystyle \underset{\mathrm{m}=\mathrm{0}}{\overset{\mathrm{M}}{\Sigma }}}{\mathrm{d}}^{\mathrm{m}}{\displaystyle \underset{\mathrm{n}=\mathrm{0}}{\overset{\mathrm{N}}{\Sigma }}}{\mathrm{c}}_{\mathrm{nm}}{\mathrm{z}}^{-\mathrm{<figure-callout\; id="6"\; label="n"\; filenames="imgf0009.png,imgf0010.png"\; state="\{\{state\}\}">n</figure-callout>}}\left(6\right)\\ & ={\displaystyle \underset{\mathrm{m}=\mathrm{0}}{\overset{\mathrm{M}}{\Sigma }}}{\mathrm{d}}^{\mathrm{m}}{\mathrm{C}}_{\mathrm{m}}\left(\mathrm{<figure-callout\; id="7"\; label="z"\; filenames="imgf0005.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}\right)\left(7\right)\end{array}$$

The output of the Farrow structure can thus be implemented as a polynomial in d, where the coefficients of the polynomial are the outputs of M fixed sub-filters C _m (z) in FIR structure. The polynomial evaluation can be realized efficiently by using the Horner scheme.

The output signals of the fixed sub-filters C _m (z) are independent of a concrete fractionally rational delay d. Thus, according to the scheme introduced above for using redundant calculations, these values are useful as intermediate results that can be used to evaluate the output signals for all secondary sources.

• Jedes Eingangssignal wird parallel mit M Subfiltern gefaltet.
• Die Ausgangswerte der Subfilter werden (jeweils für einen Abtastzeitpunkt zusammengefasst) in eine Verzögerungsleitung 216 geschrieben.
• Zur Bestimmung der verzögerten Ausgangssignale wird der ganzzahlige Anteil des Delays bestimmt und daraus der Index der gewünschten Daten in der Verzögerungsleitung 216 bestimmt.
• Die Subfilter-Ausgänge an dieser Position werden ausgelesen und als Koeffizienten einer Polynomevaluation in d, dem gebrochen rationalen Delay-Anteil, verwendet.
• Das Ergebnis der Polynomevaluation ist der gewünschte verzögerte Eingangswert. Die letzten drei Schritte werden für jedes Ausgangssignal wiederholt.

The inventive algorithm based thereon is structured as follows:

• Each input signal is folded in parallel with M sub-filters.
• The output values of the sub-filters are written into a delay line 216 (combined for one sampling instant in each case).
• To determine the delayed output signals, the integer part of the delay is determined and from this the index of the desired data in the delay line 216 is determined.
• The subfilter outputs at this position are read out and used as coefficients of a polynomial evaluation in d, the fractionally rational delay component.
• The result of the polynomial evaluation is the desired delayed input value. The last three steps are repeated for each output signal.

Fig. 10 schematically shows this algorithm, which can also be summarized as follows. Simultaneous readout takes place on the basis of a Farrow structure, wherein the data of an audio signal x _s are input to a delay line 216. However, in this embodiment, the audio data itself is not input but instead the coefficients c _{p are} calculated as output values 239 of the Farrow structure (sub-filter 237) and stored in the delay line 216 according to their timing - in contrast to the previously shown embodiment (see FIG. Fig. 7 ). As before, the access to the delay line 216 is made by a pointer 217 whose position is again selected according to the integer part of the delay d. By reading out the corresponding c _i coefficients of the Farrow structure, the corresponding (delayed) loudspeaker signal y _i can be calculated therefrom by means of power series in the delay value or the fractional (non-integer) part of the delay value (in a polynomial evaluation device 250) ,

erfolgen. Dies entspricht einem Least-Squares-Optimierungsproblem.The application of the Farrow structure is not bound to specific design methods for the determination of the coefficients c _nm . For example, a minimization of the error integral $$\mathrm{Q}={\int }_{{\mathrm{<figure-callout\; id="0"\; label="\omega "\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_{\mathrm{0}}}^{{\mathrm{<figure-callout\; id="1"\; label="\omega "\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_{\mathrm{1}}}{\int }_{{\mathrm{<figure-callout\; id="0"\; label="\alpha "\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_{\mathrm{0}}}^{{\mathrm{<figure-callout\; id="1"\; label="\alpha "\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_{\mathrm{1}}}{\left|{\displaystyle \underset{\mathrm{n}}{\Sigma }}{\displaystyle \underset{\mathrm{m}}{\Sigma }}{\mathrm{c}}_{\mathrm{nm}}{\mathrm{e}}^{\mathrm{jn\omega T}}-{\mathrm{<figure-callout\; id="2"\; label="e\; j\omega \alpha T"\; filenames="imgf0004.png,imgf0009.png"\; state="\{\{state\}\}">e\; </figure-callout>}}^{\mathrm{j\omega \alpha T}}\right|}^{\mathrm{2}}\mathrm{d\alpha d\omega }$$

respectively. This corresponds to a least squares optimization problem.

Various methods based on least squares or weighted least squares criteria are possible. These methods aim to minimize the mean square error of the method over the desired frequency range and domain of the control parameter d. The Weighted Least Squares (WLS) method additionally defines a weighting function that allows the error to be weighted in the integration area. On the basis of WLS, iterative methods can be designed with which specific influence on the error in certain regions of the integration surface can be taken, for For example, to minimize the maximum error. Most WLS methods have poor numerical conditioning. This is not due to inappropriate methods but results from the use of don't-care regions in filter design. Therefore, only Farrow structures of comparatively small subfilter length N and polynomial order M can be designed with these methods, since otherwise numerical instabilities limit the accuracy of the parameters or prevent a convergence of the method.

Another class of design methods is aimed at minimizing the maximum error in the working range of the variable fractional delay filter. The work area is defined as the area spanned by the desired frequency range and the permitted range for the control parameter d. This type of optimization is usually referred to as minimax or Chebyshev optimization.

For conventional linear phase FIR filters without control parameters, there are efficient algorithms for Chebyshev approximation, e.g. For example, the remez exchange algorithm or the Parks-McClellan algorithm based thereon. This algorithm can be extended for arbitrary complex frequency responses, and thus also for the phase responses required by fractional delay filters.

Chebyshev or Minimax optimization problems can generally be solved by linear optimization techniques. These methods are orders of magnitude more expensive than those based on the Remez exchange algorithm. However, they allow a direct formulation and solution of the design problem for the Farrow structure subfilters. In addition, these methods allow the formulation of additional constraints in the form of equality or inequality conditions. This is considered a very important feature for the design of asynchronous sample rate converters.

A method for minimax design for Farrow structures is based on algorithms for limited optimization (optimization methods that allow specification of constraints are called constrained optimization). A particular feature of these Farrow structure design techniques is that separate specifications for amplitude and phase errors can be given. For example, the maximum phase error can be minimized while specifying an allowed maximum amplitude error. Together with accurate tolerance specifications for amplitude and phase errors, resulting, for example, from the perception of corresponding errors, this represents a very powerful tool for application-specific optimization of the filter structures.

kann sicherge-stellt werden, dass die Subfilter eines optimalen Farrow-Filters linearphasig sind. Sie weisen, für gerade und ungerade m, alternierend symmetrische und antisymmetrische Koeffizienten auf, so dass sich die Zahl der zu bestimmenden Koeffizienten halbiert. Neben einer dadurch verringerten Komplexität des Filterentwurfs und einer damit einhergehenden verbesserten numerischen Konditionierung des Optimierungsproblems ermöglicht die linearphasige Struktur der C_m(z) auch den Einsatz effizienterer Algorithmen zur Berechnung der Subfilter-Ausgänge.A further development of the Farrow structure represents the proposed modified Farrow structure. By introducing a symmetric domain of definition for the control parameter d, as a rule $-\frac{1}{2}\le \mathrm{d}\le \frac{1}{2}.$

can be ensured that the sub-filters of an optimal Farrow filter are linear-phase. They have, for even and odd m, alternately symmetric and antisymmetric coefficients, so that the number of coefficients to be determined is halved. In addition to a reduced complexity of the filter design and a concomitant improved numerical conditioning of the optimization problem, the linear-phase structure of the C _m (z) also allows the use of more efficient algorithms for calculating the sub-filter outputs.

In addition, various other methods for designing the Farrow structure are possible. A method is based on a singular value decomposition and, based on this, efficient structures for implementation have also been developed. This method provides higher filter design accuracy with reduced filter complexity compared to WLS techniques, but does not provide the ability to specify constraints or selectively affect amplitude or phase error barriers.

Another method is based on Eigenfiltern. Since this approach has not been pursued in the literature so far, no performance statements can be made without its own implementation and evaluation, but it should be similar to the SVD method.

The primary goal of the filter design is to minimize the deviation from the ideal fractional delay. Either the maximum error or the (weighted) average error can be minimized. Depending on the method used, either the complex error or phase and amplitude response can be specified separately.

An important factor in the establishment of the optimization conditions is the choice of the frequency range of interest.

The shape of the associated continuous impulse response (see above) has a major impact on the quality and perceptual quality of asynchronous sample rate conversion. Therefore, the use of constraints directly related to the continuous impulse response should be investigated. For example, continuity requirements can be specified.

One requirement in many applications of delay interpolation is compliance with the interpolation condition. This requires that the interpolation at the discrete interpolation points be exact, i. H. takes the value of the samples. In design procedures that allow the definition of constraints in the form of equality conditions, this requirement can be formulated directly. Farrow implementations of Lagrange interpolators fulfill this requirement due to the definition of Lagrange interpolation. The usefulness of the interpolation condition for asynchronous sampling rate conversion in general and in the context of WFS in particular is considered to be rather low. More important than an exact interpolation at certain interpolation points is a generally small error, a small maximum deviation or the most uniform possible error course.

The Farrow structure provides a very powerful filter structure for delay interpolation. For wavefield synthesis application, efficient partitioning of the algorithm into preprocessing per source signal as well as a low complexity evaluating operation that will be performed for each output signal can be implemented.

For the coefficients of the Farrow structure, there are many different design methods that differ in computational complexity and achievable quality. In addition, in many methods, additional constraints that relate directly or indirectly to the characteristics of the desired filter can be defined. These design freedoms result in greater research effort for the evaluation of various procedures and constraints before optimal parameterizations are found. However, the desired behavior can be adapted very precisely to the specification. This most likely allows a reduction in filter complexity for the same quality requirements.

The Farrow structure-based algorithm for WFS can be efficiently implemented. On the one hand, prefiltering can exploit reductions in the complexity resulting from the linear-phase sub-filter of the modified Farrow structure. On the other hand, the evaluation of the precalculated coefficients as a polynomial evaluation by the Horner scheme is extremely efficient.

A major advantage of this filter structure is also the presence of closed design methods that allow for a targeted design.

Further possibilities for implementations and optimizations can be summarized as follows.

1. (i) Parallelisierbarkeit. Dabei wird vor allem die Parallelisierbarkeit auf Instruktionsebene betrachtet, da die meisten modernen Prozessoren SIMD-Instruktionen anbieten.
2. (ii) Abhängigkeiten von Instruktionen. Starke und lange Abhängigkeitsverhältnisse zwischen Teilergebnissen des Algorithmus erschweren die Kompilation effizienten Codes und setzen die Effizienz moderner Prozessoren herab.
3. (iii) Konditionaler Code. Fallunterscheidungen setzen die Effizienz der Ausführung herab und sind darüber hinaus problematisch zu warten und zu testen.
4. (iv) Code- und Daten-Lokalität. Da die Delay-Interpolation in der innersten Schleife des WFS-Signalverarbeitungsalgorith-mus stattfindet, ist kompakter Code von relativ großer Bedeutung. Des Weiteren beeinflusst auch die Zahl von Cache-Misses für Datenzugriffe die Performance.
5. (v) Speicher-Bandbreite und -Zugriffspattern. Die Zahl der Speicherzugriffe, ihre Verteilung und Ausrichtung (Alignment) können oftmals signifikanten Einfluss auf die Performance haben.

Embodiments are primarily concerned with the development of novel algorithms for delay interpolation for use in wave field synthesis. Although these algorithms are generally independent of a specific implementation and target platform, the implementation aspects can not be ignored here. This is because the algorithms described here are by far the largest contributors to the overall performance of a WFS reproduction system. Therefore, be In addition to the algorithmic complexity (eg the asymptotic complexity or the number of operations), the implementation aspects include the following:

1. (i) parallelism. In particular, parallelism at the instruction level is considered, as most modern processors offer SIMD instructions.
2. (ii) dependencies on instructions. Strong and long dependency relationships between partial results of the algorithm complicate the compilation of efficient codes and lower the efficiency of modern processors.
3. (iii) conditional code. Case distinctions reduce the efficiency of execution and are also problematic to maintain and test.
4. (iv) code and data location. Since the delay interpolation takes place in the innermost loop of the WFS signal processing algorithm, compact code is of relatively great importance. Furthermore, the number of cache misses for data accesses also affects performance.
5. (v) memory bandwidth and access patters. The number of memory accesses, their distribution and alignment can often have a significant impact on performance.

Since the rendering unit of the rendering system will use standard PC components in the near and near future, current PC platforms will be used as the basis for implementation. However, it is believed that the lessons learned are relevant to other system architectures because of the similar underlying concepts.

The prefiltering introduced above is efficiently performed as a polyphase operation. The input data is simultaneously convoluted with L different sub-filters, the outputs of which are multiplexed into the up-sampled output signal. The filtering can be done by linear convolution or by fast convolution based on the FFT. In the case of an implementation by means of FFT, the Fourier transformation of the input data must take place only once and can then be used several times for simultaneous convolution with the subfilters. However, for the relatively short subfilter lengths used, it is important to consider whether Fourier transform convolution provides advantages over a straightforward implementation. So z. For example, a Park-McLellan algorithm designed low-pass filter (Matlab function firpm) of length 192 has a stopband attenuation of over 150 dB. This corresponds to a subfilter length of 48, longer filters can no longer be designed numerically stable. In any case, the results of the sub-filter operations must be nested in the output data stream. One way to efficiently implement such a filter operation is to use library functions for polyphase or multirate filtering, e.g. From the Intel IPP library.

The preprocessing of the algorithm based on the Farrow structure can also be carried out efficiently by means of such a library function for multirate processing. The sub-filters must be combined by nesting (interleaving) into a prototype filter, the output values of the function represent the interleaved output values. However, the linearity of the subfilters designed according to the modified Farrow structure can also be exploited for the number of operations for the filtering to reduce. Here, however, a separate implementation is very likely to be necessary.

It has been proven that the temporal discretization of the delay parameter has a decisive influence on the achievable quality of an FD algorithm for asynchronous delay interpolation. Therefore, all designed algorithms operate on a per-sample calculated value of the delay parameter (hereinafter referred to as sample-accurate). These values are calculated by means of linear interpolation between two interpolation points. It is assumed and supported by informal hearing tests that this interpolation order is sufficiently accurate.

Fractional delay algorithms require the division of the desired delay into an integer and a fractionally rational component. For the modified Farrow structure, the range [0 ... 1) is not mandatory, but the range can be, for example, as [-½ ... ½] or [(N-1) / 2 ... (N + 1) / 2) in the Lagrange interpolation. However, this does not change the basic operation. For sample-accurate parameter interpolation, this operation has to be performed for each elementary delay interpolation and therefore has a significant impact on performance. Therefore, an efficient implementation is very important.

The WFS audio signal processing consists of a delay operation and a scaling of the delayed values for each audio sample and each combination of source signal and speaker. For efficient implementation, these operations are performed together. If these operations are carried out separately, a significant reduction in performance due to the expense of passing parameters, additional control flow and degraded code and data locality is to be expected.

Therefore, it is necessary to generate the scaling factors (this is usually done by linear interpolation between nodes) and the scaling of the interpolated ones Integrate values into the implementation of WFS convolution.

After implementing the procedures, these are to be assessed by means of measurements and subjective assessments.

In addition, it is also to be estimated from which quality no further quality gain can be achieved, since the improvements are obscured by other sources of error of the WFS overall system. The achieved objective and subjective quality must be contrasted with the resources required.

In conclusion, the present concept of signal processing in a wave field synthesis display system may also be described as follows.

It has been found that the delay interpolation, i. H. the delay of the input values by arbitrary delay values has a decisive influence both on the quality of reproduction and on the performance of the overall system.

Due to the very high number of necessary delay interpolation operations and the comparatively high complexity of these operations, the use of known algorithms for fractional-delay interpolation can not be realized with economically justifiable resources.

1. 1. Ein Verfahren auf Basis einer überabgetasteten Verzögerungsleitung 216 und dem vielfachen Zugriff auf diese Werte durch Lagrange-Interpolatoren geringer Ordnung ermöglicht eine gegenüber einer reinen Lagrange-Interpolation geringer Ordnung deutlich erhöhte Wiedergabequalität bei gleichzeitig nur geringfügig erhöhtem Berechnungsaufwand. Dieses Verfahren ist vergleichsweise einfach zu parametrisieren und zu implementieren, bietet jedoch keine Möglichkeiten zur zielgerichteten Beeinflussung der Qualität der Interpolation und besitzt kein geschlossenes Entwurfsverfahren.
2. 2. Ein weiterer Algorithmus basiert auf der Farrow-Struktur und bietet viele Entwurfsfreiheiten, beispielsweise die Anwendung einer Vielzahl von Optimierungsverfahren zum Entwurf der Filterkoeffizienten. Dem höheren Forschungs- und Implementierungsaufwand stehen Möglichkeiten zur gezielten Einflussnahme auf die Eigenschaften der Interpolation sowie Potential für eine effizientere Implementierung entgegen.

Therefore, on the one hand a deep analysis of the algorithms as well as the necessary for a good subjective perception properties of these filters is necessary to ensure a sufficient quality with minimal effort. On the other hand, the overall structure of the WFS algorithm has to be investigated in order to develop procedures that significantly reduce the overall complexity of the process. A processing structure was identified by dividing the delay interpolation algorithm in a preprocessing stage and the multiple access to the preprocessed data allows a significant reduction in the computational effort. Based on this concept two algorithms were designed:

1. 1. A method based on an oversampled delay line 216 and the multiple access to these values by Lagrangian low-order interpolators allows a significantly improved reproduction quality compared to a pure Lagrangian interpolation of low order with at the same time only slightly increased computational effort. This method is comparatively easy to parameterize and implement, but offers no possibilities for the purposeful influencing of the quality of the interpolation and has no closed design method.
2. 2. Another algorithm is based on the Farrow structure and offers many design freedoms, such as the use of a variety of optimization techniques to design the filter coefficients. The increased research and implementation effort is offset by the ability to selectively influence the properties of the interpolation and the potential for more efficient implementation.

In the implementation both methods can be implemented and compared under quality and performance aspects. There are trade-offs between these aspects. The influence of the improved delay interpolation on the overall reproduction quality of the WFS reproduction system can be examined under the influence of the other known reproduction errors. It is necessary to determine up to which interpolation quality an improvement of the overall system can be achieved.

One goal is to design methods that provide a quality of delay interpolation with reasonable effort achieve no perceptible interference even without masking effects from other WFS artifacts. This would also ensure future improvements to the playback system that the delay interpolation has no negative impact on the quality of the WFS playback.

In the following some topics are presented, which are possible as an extension of the present work.

When implementing a WFS rendering system, filter operations for the input and output signals are provided in most cases. In the WFS system, for example, a pre-filter stage (Prefilter) is used. These are static filters applied to each input signal to achieve the 3dB effect resulting from the theory of WFS operators, as well as speaker-independent frequency response matching to the playback room.

It is generally possible to associate such a filtering operation with the oversampling anti-imaging filter. At the same time, the prototype filter is designed once, during the runtime of the system only one filter operation is necessary to realize both functions.

Similarly, a combination of any static and source-independent filtering operation with the Farrow sub-filters is feasible. Both the multiplication of a Farrow filter bank designed with standard methods and the direct adaptation of the filter bank to a given amplitude response are possible.

The combination of the two filters also offers the possibility of reducing the phase delay of the system induced by (especially linear-phase) filters, if this is only necessary in one filter component.

Therefore it is necessary to investigate to what extent a combination of the conventional WFS filters with the filter operations required for the delay operation presented here makes sense. In particular, the necessary workloads for the separate and combined execution of the filtering operations must be contrasted. Furthermore, the changes in the WFS signal processing intended for future further developments (eg, source-position-dependent prefiltering, loudspeaker-specific filtering of the output signals) must be taken into account.

It has been found that sample-accurate interpolation of the delay parameter is indispensable for high-quality delay interpolation. The Scale parameter was interpolated with the same temporal resolution. It has to be investigated which influence on the reproduction impression has a coarser discretization of this parameter. However, it should be noted that a corresponding increase in the step size can be expected only small performance increases of the overall algorithm.

Furthermore, the efficient signal processing for delay interpolation was investigated. The sample rate conversion implemented with it simulates the Doppler effect of a moving virtual source. In many applications, however, the frequency shift through the Doppler spread is undesirable. It is possible that the Doppler effect by the methods implemented here for high-quality delay interpolation more clearly than hitherto appears. Therefore, in future research projects algorithms should be investigated to compensate for the Doppler effect in a playback of moving sources or to control its strength. However, these low-level methods will also be based on the algorithms for delay interpolation presented here.

Thus, embodiments provide an implementation of a high-quality method for delay interpolation. as can be used, for example, in wave field synthesis systems. Embodiments also provide further developments of the algorithms for wave field synthesis reproduction systems. Particular attention is paid to methods for delay interpolation, since these have a great influence on the reproduction quality of moving sources. Due to the quality requirements and the extremely high influence of these algorithms on the performance of the entire reproduction system, novel signal processing algorithms for wave field synthesis are required. As explained in detail above, it is thus possible in particular to consider interpolated fractions with a higher accuracy. The higher accuracy is reflected in a significantly improved listening experience. As described above, because of the increased accuracy, artifacts that occur especially with moving sources are hard to hear.

In particular, embodiments describe two efficient methods that meet these requirements and that have been developed, implemented, and analyzed.

In particular, it should be noted that, depending on the circumstances, the inventive scheme can also be implemented in software. The implementation may be on a digital storage medium, in particular a floppy disk or a CD with electronically readable control signals, which may interact with a programmable computer system such that the corresponding method is executed. In general, the invention thus also consists in a computer program product with program code stored on a machine-readable carrier for carrying out the method according to the invention when the computer program product runs on a computer. In other words, the invention can thus be realized as a computer program with a program code for carrying out the method when the computer program runs on a computer.

Claims (18)

1. Device for determining component signals (115) for loudspeakers of an array of loudspeakers of a wave field synthesis system (200), the device being configured to exploit an audio signal (125) that is associated with a virtual source and exists as a discrete signal sampled at an audio sampling frequency, and a source position (135) associated with the virtual source, so as to calculate the component signals (115) for the loudspeakers on the basis of the virtual source while taking into account loudspeaker positions (145) of the loudspeakers of the array of loudspeakers, the device comprising:

   means for providing wave field synthesis parameters (150) for the component signals (115) for the loudspeakers of the array of loudspeakers while using the source position (135) and while using the loudspeaker positions (145) of the loudspeakers of the array of loudspeakers at a parameter sampling frequency smaller than the audio sampling frequency, the wave field synthesis parameters (155) being delay values;

   a wave field synthesis parameter interpolator (160) for interpolating the wave field synthesis parameters (155) so as to produce interpolated wave field synthesis parameters (165) which are present at a parameter interpolation frequency that is higher than the parameter sampling frequency, the interpolated wave field synthesis parameters (165) having integer portions of delay values and interpolated fractions of delay values, the interpolated fractions representing delays that define fractions of sample intervals of the audio signal (125); and

   audio signal processing means (170) comprising

   means for oversampling (236), the means for oversampling being configured to process the audio signal (125), which is associated with the virtual source and exists as a discrete signal sampled at an audio sampling frequency, independently of the wave field synthesis parameters (150) by means of oversampling so as to obtain a processed audio signal;

   means for buffering (216) the processed audio signal, the means for buffering (216) being configured to store the processed audio signal index by index, so that each index corresponds to a predetermined time value of the processed audio signal (125); and

   means for producing (212) the component signals (115) for the virtual source, the means for producing (212) being configured to produce the component signal (115) for each loudspeaker of the array of loudspeakers from a value, belonging to a specific index, of the same processed audio signal, said specific index being determined from an integer portion of the delay value of the interpolated wave field synthesis parameter for the respective loudspeaker, and to apply, for the loudspeakers of the array of loudspeakers of the wave field synthesis system, the interpolated fractions of delay values of the interpolated wave field synthesis parameters to the processed audio signal (125), wherein the component signals (115) for the loudspeakers of the array of loudspeakers of the wave field synthesis system are calculated, by means of fractional-delay interpolation, with the delays corresponding to the interpolated fractions of delay values.
2. The device as claimed in claim 1, wherein the audio processing means (170) comprises means for summing (214), and the means for summing (214) is configured to sum component signals (115) and to provide them at a sound output (240) for the array of loudspeakers.
3. The device as claimed in any of the previous claims, wherein the means for oversampling (236) is configured to perform oversampling at a predetermined oversampling rate (L).
4. The device as claimed in claim 3, wherein the oversampling rate (L) is between 2 and 8.
5. The device as claimed in any of the previous claims, wherein the means for oversampling comprises a polyphase filter.
6. The device as claimed in any of the previous claims, wherein the means for producing (212) comprises a plurality of delay filters (222), and wherein one delay filter (222), respectively, is configured to read out time values of the processed audio signal from the means for buffering (216) and to perform fractional delay interpolation with a predetermined order,
   the time values of the processed audio signal corresponding to the specific index and its neighboring value, one delay filter (222) producing a component signal (115), respectively.
7. The device as claimed in claim 6, wherein the predetermined order of the fractional delay interpolation is odd, and the predetermined order is ≤ 3 or ≤ 7.
8. The device as claimed in claim 6 or claim 7, wherein the delay filter (222) comprises a Lagrange interpolator.
9. The device as claimed in any of the previous claims, wherein the audio signal processing means (170) further comprises a pre-filtering stage, and the pre-filtering stage is configured to perform a loudspeaker-independent frequency response adaptation to a rendering space, and wherein the pre-filtering stage comprises the means for oversampling (236).
10. Device for determining component signals (115) for loudspeakers of an array of loudspeakers of a wave field synthesis system (200), the device being configured to exploit an audio signal (125) that is associated with a virtual source and exists as a discrete signal sampled at an audio sampling frequency, and a source position (135) associated with the virtual source, so as to calculate the component signals (115) for the loudspeakers on the basis of the virtual source while taking into account loudspeaker positions (145) of the loudspeakers of the array of loudspeakers, the device comprising:

    means for providing wave field synthesis parameters (150) for the component signals (115) for the loudspeakers of the array of loudspeakers while using the source position (135) and while using the loudspeaker positions (145) of the loudspeakers of the array of loudspeakers at a parameter sampling frequency smaller than the audio sampling frequency, the wave field synthesis parameters (155) being delay values;

    a wave field synthesis parameter interpolator (160) for interpolating the wave field synthesis parameters (155) so as to produce interpolated wave field synthesis parameters (165) which are present at a parameter interpolation frequency that is higher than the parameter sampling frequency, the interpolated wave field synthesis parameters (165) having integer portions of delay values and interpolated fractions of delay values, the interpolated fractions representing delays that define fractions of sample intervals of the audio signal (125); and

    audio signal processing means (170) comprising

    a Farrow structure so as to process the audio signal (125), which is associated with the virtual source, independently of the wave field synthesis parameters (150) to obtain a processed audio signal comprising coefficients (c_p);

    means for buffering (216) the processed audio signal, the means for buffering (216) being configured to store the coefficients (c_p) in accordance with their temporal sequence; and

    means for producing (212) the component signals (115) for the virtual source, the means for producing (212) being configured to produce, for the loudspeakers of the array of loudspeakers, the component signals (115) for the virtual source by reading out from positions of the means for buffering (216) which correspond to the integer portions of the delay values which have been produced by the wave field synthesis parameter interpolator, and by applying the interpolated fractions of delay values, which have been produced by the wave field synthesis parameter interpolator, to the read-out values by means of polynomial interpolation, the component signals (115) for the loudspeakers being calculated with the delays represented by the interpolated fractions.
11. The device as claimed in claim 10, wherein subfilters (237) are provided which form the Farrow structure, the subfilters being configured to filter the audio signal (115) and to store output values of the subfilters (237) into the means for buffering (216).
12. The device as claimed in claim 11, wherein the means for producing comprises means for polynomial interpolation (250), the means for polynomial interpolation (250) being configured to determine component signals (115) from the interpolated fractions of delay values and the output values of the subfilters (237).
13. The device as claimed in claim 12, wherein the Farrow structure is determined by coefficients (c_mn), and the coefficients (c_mn) minimize an error integral.
14. The device as claimed in any of claims 11 to 13, wherein the subfilters (237) are configured to perform a source-independent filter operation.
15. Method of determining component signals (115) for loudspeakers of an array of loudspeakers of a wave field synthesis system (200), wherein an audio signal (125) that is associated with a virtual source and exists as a discrete signal sampled at an audio sampling frequency, and a source position (135) associated with the virtual source are exploited so as to calculate the component signals (115) for the loudspeakers on the basis of the virtual source while taking into account loudspeaker positions (145) of the loudspeakers of the array of loudspeakers, the method comprising:

    providing wave field synthesis parameters (155), which comprise delay values, for the component signals (115) for the loudspeakers of the array of loudspeakers while using the source position (135) and while using the loudspeaker positions (145) of the loudspeakers of the array of loudspeakers at a parameter sampling frequency smaller than the audio sampling frequency, the wave field synthesis parameters (155) being delay values;

    interpolating the wave field synthesis parameters (155) so as to produce interpolated wave field synthesis parameters (165) which are present at a parameter interpolation frequency that is higher than the parameter sampling frequency, the interpolated wave field synthesis parameters (165) having integer portions of delay values for the component signals (115) and interpolated fractions of delay values for the component signals (115), the interpolated fractions representing delays that define fractions of sample intervals of the audio signal (125); and

    processing the audio signal so as to apply the interpolated fractions to the audio signal (125) such that the component signals (115) are calculated with the delays represented by the interpolated fractions.

    the step of processing the audio signal comprising:

    oversampling the audio signal (125) at a predetermined oversampling rate (L) so as to produce an oversampled audio signal;

    storing the oversampled audio signal index by index within means for buffering (216), each index corresponding to a predetermined time value of the oversampled audio signal;

    reading out values of the oversampled audio signal from the means for buffering (216) to indices which have been determined by the integer portions of the delay values which have been determined in the interpolation step; and

    interpolating, for each loudspeaker of the array of loudspeakers, the read-out values of the same oversampled and stored audio signal so as to obtain the component signals (115) for the loudspeakers related to the interpolated fractions of the delay values, the read-out values serving as nodes, by means of fractional-delay interpolation.
16. Method of determining component signals (115) for loudspeakers of an array of loudspeakers of a wave field synthesis system (200), wherein an audio signal (125) that is associated with a virtual source and exists as a discrete signal sampled at an audio sampling frequency, and a source position (135) associated with the virtual source are exploited so as to calculate the component signals (115) for the loudspeakers on the basis of the virtual source while taking into account loudspeaker positions (145) of the loudspeakers of the array of loudspeakers, the method comprising:

    providing wave field synthesis parameters (155), which comprise delay values, for the component signals (115) for the loudspeakers of the array of loudspeakers while using the source position (135) and while using the loudspeaker positions (145) of the loudspeakers of the array of loudspeakers at a parameter sampling frequency smaller than the audio sampling frequency, the wave field synthesis parameters (155) being delay values;

    interpolating the wave field synthesis parameters (155) so as to produce interpolated wave field synthesis parameters (165) which are present at a parameter interpolation frequency that is higher than the parameter sampling frequency, the interpolated wave field synthesis parameters (165) having integer portions of delay values for the component signals (115) and interpolated fractions of delay values for the component signals (115), the interpolated fractions representing delays that define fractions of sample intervals of the audio signal (125); and

    processing the audio signal so as to apply the interpolated fractions to the audio signal (125) such that the component signals (115) are calculated with the delays represented by the interpolated fractions.

    the step of processing the audio signal comprising:

    processing the audio signal (125) for a virtual source in subfilters (237), so that each subfilter (237) produces an output signal (239);

    storing the output signals (239) of the subfilters (237) within means for buffering (216) for a virtual source;

    reading out, for the loudspeakers of the array of loudspeakers, the output signals (239) from positions of the means for buffering (216) which correspond to the integer portions of the delay values having been produced in the interpolation step; and

    determining, for each loudspeaker of the array of loudspeakers, an interpolated value by calculating a polynomial in the interpolated fraction from the read-out values so that the component signals (115) are obtained, for the respective loudspeakers, from the interpolated fractions of the respective delay value and from the same read-out values (239) of the subfilters (237) for the virtual source.
17. The method as claimed in claim 16, wherein the subfilters (237) form a Farrow structure.
18. A computer program comprising a program code for performing the method as claimed in claim 15 or claim 16, when the computer program runs on a computer.

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