Efficient filtering with a complex modulated filterbank

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Efficient filtration with a complex modulated filter bank DESCRIPTION

Technical field

The present invention relates to a filter apparatus and a method for filtering a time domain input signal, a filter generator and a method for generating an intermediate filter definition signal, especially for the coding, decoding field, manipulation and filtration of audio signals, for example, in the field of HRTF (head related transfer function).

Background of the invention

It has been demonstrated in [P. Ekstrand, “Bandwidth extension of audio signals by spectral band replication”, Proc. 1st IEEE Benelux Workshop in Model based Processing and Coding of Audio (MpCA-2002), pages 53-58, Leuven, Belgium, 2002], that a complex-exponential modulated filter bank is an excellent tool for spectral wrap wrap adjustment audio signals An application of this feature is audio coding based on Spectral Band Replication (SBR). Other fruitful applications of a complex filter bank include selective frequency focus and spatialization for the parametric stereo, see [E. Schuijers, J. Breebart, H. Purnhagen, J. Engdegárd: "Low complexity parametric stereo coding", Proc. 116th AES convention, 2004, document 6073] and parametric multichannel coding, see [J. Herre et al .: "The reference model architecture for MPEG spatial audio coding", Proc. 118th AES Convention, 2005, document 6447]. In these applications the frequency resolution of the complex filter bank is further improved at low frequencies by means of a sub-sub-band filter. The combined hybrid filter bank thus achieves a frequency resolution that allows the processing of spatial indications at a spectral resolution that closely follows the spectral resolution of the binaural auditory system.

However, in some applications, the resolution of the filter bank is still insufficient, in the sense that simple gain modifications in each sub-band are not sufficient to really model the action of a given filter. For binaural multichannel audio reproduction by means of a HRTF-related filter (head-related transfer function), the intricate phase characteristics of the filters are important for the perceived audio quality. Of course it is possible to apply fast convolution methods based on DFT (Discrete Fourier Transform) as a post-process to multichannel reproduction, but if the playback device already contains the signals in the sub-band domain of the bank of Exponential complex modulated filters, there are significant advantages in terms of computational complexity and algorithmic integration to perform HRTF-derived filtration in the sub-band domain, which will be outlined in more detail later. Since the HRTF's are different for each individual and the derived filters depend on the virtual source and / or positions of the listener that can, for example, be changed by control signals, user interfaces or other description signals, it is also important to be capable of efficiently converting a given HRTF related filter into sub-band domain filters.

EP 0 531 242 A2 discloses a sub-band filtering method that greatly eliminates or restricts the effects of overlap. A source signal is transformed into frequency subbands. Then, each of the subbands is filtered based, at least in part, on a corresponding partial filtering profile associated with each of the respective subbands. The corresponding partial filtering profiles are determined with the definition of the predetermined global filtering profile to ensure that the global filtering profile has horizontal tangents in certain frequency sounds that are transient between the various transformation filters. Different filtered subbands then undergo an inverse transformation.

WO 03/015275 A1 discloses an adaptive signal processing system to improve signal quality. The system includes a bank of analysis filters to transform a primary information signal in time domain into sub-band primary signals oversampled in a frequency domain and a bank of analysis filters to transform a reference signal into a domain of time on oversampled subband reference signals. Sub-band processing circuits process the signals emitted from the filter banks to improve the quality of an output signal. A synthesis filter bank can combine the outputs of the sub-band processing circuits to generate the output signal. Sub-band processing circuits comprise a subtractor to subtract a filtered noise signal from a signal plus noise signal.

It is therefore the objective of the present invention to provide a filter apparatus for filtering a time domain input signal, a method for filtering a time domain input signal, a filter system, which allows for more efficient handling. or more flexible than a time domain input signal with better quality.

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This objective is achieved by a filter apparatus according to claim 1, by a method for filtering a time domain input signal according to claim 26, or a filter system according to claim 25.

Summary of the invention

An embodiment of the present invention relates to a filter apparatus for filtering a time domain input signal to obtain a time domain output signal, which is a representation of the filtered time domain input signal using a filter characteristic that has a non-uniform amplitude / frequency characteristic comprising a complex analysis filter bank to generate a plurality of complex sub-band signals of the time domain input signal, a plurality of intermediate filters, in which an intermediate filter is provided for each complex subband signal, wherein at least one of the intermediate filters of the plurality of intermediate filters has a non-uniform amplitude / frequency characteristic, in which the plurality of intermediate filters has a shorter impulse response compared to an impulse response of a filter having the filter characteristic, and in which the non-uniform amplitude / frequency characteristic of the plurality of intermediate filters together represent the non-uniform filter characteristic, and a complex synthesis filter bank to synthesize the output of the intermediate filters to obtain the time domain output signal.

As a second aspect, a further embodiment of the present invention is a filter generator to provide an intermediate filter definition signal comprising a complex modulated filter bank for filtering a pulse response signal indicative of an amplitude filter characteristic. / frequency in a time domain to obtain a plurality of complex valuated sub-band signals such as the intermediate filter definition signal, wherein each complex valuated sub-band signal of the complex modulated filter bank corresponds to an impulse response for an intermediate filter for a sub-band signal, in which at least one of the complex valuated sub-band signals It comprises at least two different values ​​without dissipation, and in which each complex sub-band valued signal is shorter than the impulse response signal.

The embodiments of the first aspect of the present invention are based on the discovery that more efficient and / or more flexible filtration (or manipulation) of a time domain input signal can be achieved in the sub-band domain, which some Sometimes it is also referred to as a QMF domain (quadrature mirror filter), with a better quality compared to other manipulation schemes. The gain with respect to efficiency, especially computational efficiency, is a consequence of the shorter impulse responses of the intermediate filters compared to the impulse response of a filter having the characteristic of a non-uniform filter in the time domain and the fact that sub-band signals can be processed independently of each other. Due to the shorter impulse responses an embodiment of a filter apparatus can process each of the complex subband signals emitted by the complex analysis filter bank individually. Therefore, filtration can be carried out in parallel, which speeds up the processing of the time domain input signal dramatically compared to the manipulation of the time domain input signal directly due to the responses on impulse shorter.

The embodiments according to the first aspect of the present invention are especially favorable when they balance computational efficiency on the one hand and quality on the other side. Although a direct processing of the time domain input signal in the time domain can be achieved by a convolution with the impulse response of a filter having the characteristic of uneven amplitude / frequency, which usually leads to a very good quality , the convolution requires a high computational effort due to the length of the impulse response of the filter in the time domain.

On the other hand, the transformation of an audio signal in the frequency domain when performing a Fourier Transform represents the tremendous disadvantage that other manipulations, which are necessary in modern acoustic systems, cannot efficiently perform in the Fourier domain with a high quality.

Therefore, by employing a plurality of intermediate filters, each having a shorter impulse response compared to a pulse response of a filter having the filter characteristic of a corresponding filter in the time domain, of which at less one has an impulse response with at least two values ​​without dissipation represents a highly favorable compromise between computational efficiency on the one hand and quality on the other side. As a consequence, the inventive filter apparatus embodiments represent an excellent compromise between a direct processing of the time domain input signal, for example, by convolving the time domain input signal with the response to the longest pulse indicative of the non-uniform filter characteristic, which leads to enormous computational effort, and employs a Fourier transform, which leads to more problems in the additional course of signal processing.

The advantages of the embodiments of the first aspect of the present invention are especially developed in the

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context of FIR filters (response to the final pulse), since each of the intermediate filters of the plurality of intermediate filters has a significantly shorter impulse response compared to the impulse response of the FIR filter in the time domain. Therefore, by processing in parallel the different sub-band signals emitted by the complex analysis filter bank, computational efficiency can be drastically improved. This aspect is especially important in the field of filters that have long impulse responses. An application field, in which filters with very long impulse responses occur frequently, are HRTF-related applications (HRTF = head-related transfer function), such as sub-mixing multiple channel audio signals to feedback to headphones, other head-related speaker systems or stereo sound systems.

In many specific applications computational efficiency is further increased, since audio signals are already present in the sub-band (complex) or QMF domain. Therefore, in many concrete implementations, the complex analysis filter bank and the complex synthesis filter bank to generate the plurality of complex sub-band signals of the time domain input signal and to synthesize the signal from Time domain exit is already present.

With respect to the second aspect, the embodiments of the present invention are based on the discovery that more flexible and more efficient filtration of the time domain input signal with better quality can be achieved by providing an intermediate filter definition signal. , which can, for example, be provided in a filter apparatus according to the first aspect to define its intermediate filters.

A significant advantage of the embodiments according to the second aspect of the present invention is that an intermediate filter definition signal is obtained for a set of intermediate filters by providing an embodiment of the inventive filter generator with a signal defining the filter, such as a pulse response signal indicative of an amplitude / frequency filter characteristic of a time domain filter or other filter definition signals. Therefore, an embodiment of a filter generator provides a filter definition signal for a set of intermediate filters for the same filtration effectively as a filter in the time domain defined by the virtually undefined filter definition signal. alignment effects As a consequence, embodiments of an inventive filter generator allow virtually free performance of aliases of an arbitrary filter in the sub-band domain. By using an embodiment of the inventive filter generator, arbitrary filter characteristics can be transferred from the time domain to the sub-band signal domain, such as virtually alias free equalization, low pass filter characteristics, high pass filter characteristics, characteristics band pass filter, band rejection filter characteristics, resonance filter characteristics, notch filter characteristics or more complex filter characteristics. Among the most complex filter features, it is important to mention a combination of several features, as well as filter features related to HRTf.

Especially in the context of HRTF-related applications in the field of multichannel audio systems and other high-quality applications, it is important to note that the inventive filter generator embodiments allow real modeling of an action of a given filter in the time domain in the sub-band domain. Virtually free alias performance, which is especially important in HRTF-related applications, is made possible since the phase characteristics of a time domain filter are (almost) perfectly transferred to the sub-band domain. The examples illustrating this will be outlined in the additional course of this application.

Among the advantages of the embodiments of the second aspect of the present invention is especially the significant gain with respect to the computational efficiency that can be achieved. The complex modulated filter banks of the inventive filter generator embodiments produce a plurality of complex valuated sub-band signals such as the intermediate filter definition signal, in which each complex valuated sub-band signal is shorter than the impulse response signal indicative of the amplitude / frequency filter characteristic in the time domain. The filter generator, therefore, produces an intermediate filter definition signal that comprises the output of the complex modulated filter bank with its plurality of complex valuated sub-band short signals, which not only allows fast, efficient computing and parallel with respect to the filtration of a time domain input signal to obtain a time domain output signal within the framework of an embodiment of a filter apparatus, It also allows fast, efficient and parallel computing of the intermediate filter definition signal itself. Compared to a direct application of the impulse response signal indicative of the amplitude / frequency filter characteristic in the time domain by convolving the impulse response signal with the time domain input signal, the application of a realization of an inventive filter generator according to the second aspect of the present invention allows simplified, faster and more efficient computing, which leads to an auditory indistinguishable result compared to the more complex convolution method.

In addition, an embodiment of the inventive filter generator also offers the advantage of significantly improved flexibility with respect to the possible filter characteristics applied in the sub domain.

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band. Since arbitrary filter characteristics can be transferred from the time domain to the subband domain by an embodiment of an inventive filter generator, enormous flexibility is introduced to the processing and manipulation of the audio signal. For example, one embodiment of an inventive filter generator is capable of providing an intermediate filter definition signal that corresponds to an individually altered filter characteristic of an HRTF related filter. In the HRTF field, this offers the opportunity to individually modify the HRTF filters according to the needs and hearing abilities of an individual. In addition, the position of the source can be adapted, as well as the position of the listener with respect to each other and with respect to an environment (simulated or calculated) (for example, a concert hall, an open space, or stadium). This offers the great advantage of providing a listener with great flexibility with respect to acoustic conditions. An embodiment of the inventive filter generator, therefore, provides the possibility of virtually switching from a stadium to a concert hall or an open field, without employing the need to transfer the audio signals between the time domain, the domain of sub-band and / or frequency domain. By employing an embodiment of an inventive filter generator all these manipulations of the audio signal can be performed within the sub-band domain with a very high quality, which is perceptually indistinguishable from signal processing in the time domain, but that offers a huge improvement in computational efficiency.

This flexibility is not only limited to changing from one environment to another, for example, changing from a stadium to a concert hall and visa versa. An embodiment of an inventive filter generator offers the possibility of altering the filter characteristics of the plurality of intermediate filters in a quasi-continuous manner. An application in the HRTF field is an application of an embodiment of the filter generator and / or the filter apparatus in a tracking application, in which, for example, the position of the listener with respect to different audio sources varies in a quasi-continuous way. Possible applications include, for example, simulations and computer games with very high quality.

Another advantage of an embodiment of a filter generator is that the application of an embodiment of a filter generator is more efficient with respect to memory use, since a pulse response signal provided to the complex modulated filter bank of the generator Filter is typically a real valued signal, while the intermediate filter definition signal is a complex valued signal of approximately the same total length. As a consequence, storing the impulse response signals compared to the intermediate filter definition signals (or the intermediate filter filter connections) saves memory, more or less, of an order of 2. Due to the possibility of fast and efficient parallel computing, especially in the field of memory-sensitive applications that comprises a larger parameter space with respect to possible impulse response signals, this represents a significant advantage.

In an embodiment of an inventive filter generator the filter generator is provided with a filter definition signal, which may comprise for example the filter connections of a digital filter in the time domain or by a transfer function in the domain. frequency, which can comprise the amplitude / frequency characteristic and / or the phase / frequency characteristic of a filter. In these cases, an embodiment of the filter generator further comprises an impulse response signal generator, which provides the appropriate impulse response signal indicative of the amplitude / frequency filter characteristic resulting in the time domain to the filter bank. complex modulation of the filter generator. Therefore, the inclusion of an impulse response signal generator in some embodiments of an inventive filter generator offers even more flexibility with respect to providing the intermediate filter definition signal, since not only the impulse response signals in the form of discrete time signals can be provided to an embodiment of the filter generator but also the filter connections or the description of the frequency domain of a filter in the time domain can transferred to the sub-band domain by an appropriate embodiment of a filter generator.

Brief description of the drawings

The present invention will now be described by way of illustrative examples, which do not limit the scope or spirit of the invention, with reference to the accompanying drawings, in which:

Figure 1a illustrates the processing of a digital audio signal by means of subband filter in a system comprising a filter generator and a filter apparatus;

Figure 1b illustrates a possible solution for a complex analysis bank;

Figure 1c illustrates a possible solution for a complex synthesis filter bank;

Figure 1d illustrates a possible additional solution for a complex synthesis filter bank;

Figure 1e illustrates an interaction of an embodiment of a filter generator with a plurality of intermediate filters of an embodiment of a filter apparatus;

Figure 2 illustrates the processing of a digital audio signal by means of a direct filter;

Figure 3 illustrates a preferred embodiment of a system with a filter converter;

Figure 4 illustrates a response given to the filter pulse;

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Figure 5 illustrates an impulse response obtained by the complex gain adjustment of the subbands;

Figure 6 illustrates the magnitude response of a given filter;

Figure 7 illustrates the magnitude response of a filter obtained by the complex gain adjustment of the subbands;

Figure 8 compares the performance of the present invention with the complex gain adjustment of the subbands;

Figure 9 illustrates a preferred embodiment of a filter apparatus comprising an optional embodiment of a

filter generator and additional components;

Figure 10 illustrates a filter characteristic along with several frequency bands for different subbands;

Y

Figure 11 illustrates a preferred embodiment of a filter generator.

Description of preferred embodiments

The embodiments described below are merely illustrative for the principles of the present invention of efficient filter with a complex modulated filter bank. It should be understood that the modifications and variations of the facilities and the details described herein will be apparent to other experts in the field. Therefore, it is the attempt to be limited only by the scope of the impending claims of the patent and not by the specific details presented by way of description and explanation of the embodiments therein.

Next, objects with the same or similar functional properties are denoted with the same reference signs. Unless explicitly observed otherwise, the description regarding objects with similar or equal functional properties can be exchanged with each other.

Figure 1a illustrates in the form of a system comprising embodiments of both a filter apparatus and a filter generator the processing of a digital audio signal by means of a subband filter according to the present invention. This signal path, for example, may represent a part of a spatial audio reproduction system in which the input is a received audio channel and the output is a component of a signal to be reproduced in the right ear. The input signal (Digital audio signal or time domain input signal) is analyzed by the complex analysis bank 101 by means of a filter with a set of L analysis filters followed by the subsampling of a factor L, in the that L is a positive integer, preferably larger than 1. Typically the factor L is a power of 2, preferably L = 64. The analysis filters are usually obtained by a complex modulation of a prototype filter p (v), in which v is a positive integer indicating an index in a data set or an index of a value in a signal not sub-sampled by factor L. The output of the filter bank consists of L sub-band signals that are processed by a subband filtration 102. This sub-band filtration consists of a combination of manipulations such as the adjustment of sub-band gain according to control data received and application of finite response filters to the impulse applied separately in each sub-band. The filter connections of the subband filters are obtained from a (inventive) filter converter 104 as an embodiment of a filter generator that takes as input a filter described by direct filter connections, a description of the domain of frequency or a pulse response (signal). The complex synthesis bank 103 reconstructs an output signal by ascending sampling by a factor L, filtration by L synthesis filters, adding all the results, and extracting the real part. The sum of all the results and the extraction of the real part can also be changed with respect to its order, as will be delineated more closely with respect to Figures 1c and 1d.

Figure 1b shows a complex analysis bank 101 in more detail. The complex analysis bank 101 comprises a plurality of L intermediate analysis filters 120 for each sub-band to be emitted by the complex analysis bank 101. To be more precise, each of the L intermediate analysis filters 120 is connected in parallel to a node 130 to which the time domain input signal to be processed is provided. Each of the intermediate analysis filters 120 is adapted to filter the input signal of the complex analysis bank 101 with respect to a central frequency of each sub-band. According to the center frequencies of the different sub-bands, each sub-band is marked by a sub-band index or index n, in which n is a non-negative integer, typically in the range of 0 to L- one. The intermediate analysis filters 120 of the complex analysis bank 101 can be derived from a prototype filter p (v) by a complex modulation according to the subband index n of the subband to which the intermediate analysis filter 120 is applied. Further details that refer to the complex modulation of a prototype filter are explained below.

Either directly by the intermediate analysis filters 120 or by an optional subsampler 140 (denoted by the dotted line in Figure 1b) the sampling frequency of the signal emitted by the bank of intermediate analysis filters 120 is reduced by a factor L . As mentioned above, the subsamplers 140 supplied to each sub-band signal emitted by the corresponding intermediate analysis filters 120 are optional since, depending on the specific implementation, the subsampling can also be carried out in the framework of the filter filters. intermediate analyzes 120. In principle, subsampling of the signal emitted by intermediate analysis filters 120 is not required. However, the presence of explicit or implicit subsamplers 140 is a

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preferred option since the amount of data provided by the complex analysis bank 101 would alternatively be raised by a factor of L, which leads to significant data redundancy.

Figure 1c illustrates a possible solution for a complex synthesis bank 103. The complex synthesis bank 103 comprises L intermediate synthesis filters to which the L subband signals of subband filtration 102 are provided. Depending on the concrete implementation of the complex synthesis bank 103 before filtration within the framework of intermediate synthesis filters 150, sub-band signals are sampled upwards by ascending sampler L 160, which reconstructs the sampled frequency of Subband signals by increasing the sampling frequency by a factor of L. In other words, the optional ascending sampler 160 reconstructs or reshapes the sub-band signals provided to the ascending sampler 160 in such a way that the information contained in each of the sub-band signals is retained while the sampling frequency is increases by a factor of L. However, as explained in the context of Figure 1b, ascending samplers 160 are optional components, since ascending sampling can also be carried out within the framework of intermediate synthesis filters 150. Therefore, the step Upstream sampling of sub-band signals carried out by upstream sampler 160 can be processed simultaneously within the framework of intermediate synthesis filters 150. However, if subsamplers 190 are not implemented explicitly or implicitly, ascending samplers 160 do not have to be implemented explicitly or implicitly.

The intermediate synthesis filters 150 are connected through an output to an additive 170 which adds the filtered subband signals emitted by the L intermediate synthesis filters 150. The addition 170 also connects to a real part extractor 180 , which extracts or forms a real valued signal or instead an output signal from the time domain (actual valued) based on the complex valued signal provided by the additor 170. The real part extractor 180 can perform this task, for example, by extracting the real part of a complex valuated signal provided by the additive 170, by calculating the absolute value of the complex valuated signal provided by the additor 170 or by another method that it forms a real valued output signal based on a complex valued input signal. In the case of the system shown in Figure 1a, the signal emitted by the real part extractor 180 is the output signal of the time domain emitted by the embodiment of the inventive filter apparatus.

The second possible solution for a complex synthesis bank 103 shown in Figure 1d differs from the first possible solution shown in Figure 1c which concerns only the real parts extractor 180 and the additive 170. To be more precise, the outputs of the intermediate synthesis filters 150 are connected separately from each sub-band to a real part extractor 180 that extracts or forms a real valued signal based on the complex valued signal emitted by the filters intermediate synthesis 150. The real part extractor 180 is then connected to the additive 170, which adds the L real valuated signals derived from the L filtered sub-band signals to form the real valuated output signal provided by the adder 170, which in the case of the The system shown in Figure 1a is the output signal of the time domain.

Figure 1e shows sub-band filtration 102 and its interaction with filter converter 104 in more detail. Sub-band filtration 102 comprises a plurality of intermediate filters 190, in which an intermediate filter 190 is provided for each complex valuated sub-band signal provided to sub-band filtration 102. Therefore, the filtration of sub-band 102 comprises L intermediate filters 190.

The filter converter 104 is connected to each of the intermediate filters 190. As a consequence, the filter converter 104 is capable of providing the filter connections for each of the intermediate filters 190 of the sub-band filtration 102. More details concerning the filtration made by intermediate filters 190 will be explained in the additional course of the application. Therefore, the filter connections provided to the different intermediate filters 190 and emitted by the filter converter 104 form the intermediate filter definition signal.

In addition, it should be noted that embodiments, solutions and implementations may comprise additional and / or optional delays to delay any of the signals or a subset of signals, which have been omitted in Figure 1a to 1e for simplicity. Also in Figures 2 to 11 the optional delays have been issued for simplicity. However, delays or delays can be understood in the elements shown (for example, filters) or aggregated as optional elements in all embodiments depending on their specific implementation.

Figure 2 illustrates the processing of a digital audio signal by direct filter 201. If the same filter is given as input to the filter converter 104 of Figure 1 and direct filtration 201, a design objective for the filter converter 104 is that the digital audio output of 103 must be perceptually (or auditory) indistinguishable of the digital audio output of direct filtering 201, if the digital audio inputs to the complex analysis bank 101 and direct filtration 201 are identical and the processing in direct filtration 102 consists of pure fixed subband filter.

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In the embodiment of the system shown in Figures 1a to Figure 1e the filter input to the filter converter 104 is given as a filter definition signal, which, for example, may comprise the filter connections of a time domain filter corresponding, a description of the frequency domain (amplitude / frequency characteristic and / or phase / frequency characteristic) or a pulse response signal of the appropriate filter.

In the case of direct filtration 201 the same filter definition signal, in principle, can be used. Depending on the specific implementation and the filter definition signal, the filtration can be carried out by direct application of the filter connections within the framework of a digital filter, by a discrete Fourier transform together with a transfer function or other description of the frequency domain or by convolution with the impulse response signal.

Figure 3 illustrates a preferred embodiment of a filter converter 104 according to the present invention as an embodiment of a filter generator. It is assumed that the filter is given by its impulse response. Seeing this impulse response as a discrete time signal, it is analyzed by a bank (of filters) of complex analysis of L-band 301. The resulting sub-band signal outputs are then exactly the impulse responses of filters to be applied separately in each sub-band in sub-band filtration 102. In the preferred embodiment shown in Figure 3, the filter definition signal provided to filter converter 104 and its complex analysis bank or complex analysis filter bank 301 is the impulse response signal indicative of the amplitude characteristic / frequency of a filter, which is about to be transferred to the sub-band domain. Therefore, the output of the complex analysis bank (filters) 301 of each of the L subbands represents the impulse response of the intermediate filters comprised in subband filtration 102.

The complex analysis bank 301, in principle, is derived from the analysis bank 101 but has a different prototype filter and a slightly different modulation structure, the details of which will be delineated in the following description. The same rapid algorithms that are used for an implementation of the complex analysis bank 101 can be reused by the complex analysis bank 301, leading to a very fast and very efficient conversion process.

In addition, the length of the prototype filter q (v) can be designed to be only a fraction of the length of the prototype filter p (v). Due to subsampling by a factor L, the length of subband filters is also a factor L smaller than the sum of the lengths of the given time domain filter and the prototype filter q (v). The computational effort is reduced in this way compared to the direct filtration 201 by approximately a factor of L / 4. The compensation factor of 4 is due to the actual filter replacement with complex filtration. Another compensation is the computational cost of complex analysis and synthesis banks 101 and 103. For efficient implementations this cost is comparable to the cost of preferably short FIR filters, and therefore insignificant, as outlined above. In addition, this compensation of the reduction in computational cost does not exist for systems that already use these two filter banks 101 and 103.

Figure 4 illustrates an example of a response given to the impulse of filter 400. It consists of 192 (= 64 3) connections without zero. In other words, the impulse response 400 shown in Figure 4 comprises 192 values ​​without dissipation.

In the present application, a non-dissipating key or value is a key or a value that is ideally not equal to zero. However, due to the limits of implementation within the framework of this application a non-dissipating value or key is a complex or real valued valued key or value with an absolute value that is larger than a predetermined threshold, for example 10-s or 2 -s, in which s is a positive integer depending on the requirements of a specific implementation. In digital systems this threshold is preferably defined in the binary system (base 2), in which the integer s has a predetermined value depending on the specifications of the implementation. Typically, the value s is 4, 5, 6, 7, 8, 10, 12, 14, 16 or 32.

The impulse response 400 of the system of Figure 1 is indistinguishable from this impulse response given in the image resolution, in a case where a bank of filters of band L = 64 is applied with a prototype filter of length 640 (= 64 10) and a prototype filter of length 192 (= 64 3) is used for filter converter 104 of Figure 3. The corresponding intermediate subband filters have only 5 (= 3 + 3-1) connections each one, as will be explained later.

Figure 5 illustrates the impulse response 410 of the system of Figure 1 with a band filter bank 64, in a special case corresponding to a prior art use for wrapping and equalization adjustment. In this case, the sub-band filters or preferably the intermediate filters 190 are all one-key only, so that a constant complex gain is applied to each sub-band. For each sub-band, the corresponding gain is chosen as being equal to the complex frequency response of the filter of Figure 4 evaluated at the center frequency of the particular sub-band. As can be seen from the result, there are severe preeco artifacts and there will be a significant perceptual difference between the application of this filter response compared to the response to the objective pulse 400 of Figure 4.

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Figure 6 illustrates the magnitude 420 response of the filter of Figure 4. The frequency scale of Figure 6 is adjusted to the resolution of a 64-band filter bank (L = 64).

Figure 7 illustrates the magnitude response 430 of the underlying filter to the impulse response 410 shown in Figure 5. As can be seen, the use of only one gain per sub-band resulted in a poor approximation to the desired frequency response. The main reason for this is the rapid variation of the target phase spectrum. In fact, this prior art method is best suited for modeling linear phase responses.

Figure 8 finally compares the performance of an embodiment of the present invention and of the prior art method of complex gain adjustment of the subbands. The dotted curve is a design of the objective magnitude response 420 of Figure 6. The striped curve 440 is the magnitude response of the difference between the complex frequency responses of the target filter and its approximation by the prior art method. The solid curve 450 is the magnitude response of the difference between the complex frequency responses of the target filter and its approximation by the method taught by the present invention with the parameters as discussed during the description of Figure 4. As can be seen, the error of the prior art method is small only in the 64 midpoints of the subbands of the filter bank while the inventive method leads to an approximation quality in the 50 dB range. It should be noted that this is also the level of performance that is measured when comparing the output of the inventive system with the output of the reference system for an arbitrary input signal.

As the comparison of the two curves 440 and 450 in Figure 8 shows, an embodiment of an inventive filter apparatus, an embodiment of a filter generator and a system comprising both embodiments offers a significant advantage that concerns the quality of the manipulation of an input signal. The significant difference concerning the filter quality (or manipulation) of the input signal underlined above is a consequence of the fact that at least one of the intermediate filters 190 has an impulse response with two or more values ​​without dissipation. In other words, at least one of the intermediate filters 190 comprises at least two filter connections without dissipation. Furthermore, it is important to note that the number of subbands L processed by an embodiment of a filter apparatus is larger or at least equal to 2. However, the number of the subbands L is significantly smaller than the number of frequency bands required for comparable quality in the case of a filtration based on the Fourier transform combined with a filter mainly described by an amplitude characteristic / frequency and / or a phase / frequency characteristic such as the filter transfer function.

Due to the fact that the impulse response of intermediate filters 190 is significantly shorter than the impulse response of the underlying filter characteristic in the time domain, computations with respect to each sub-band can be carried out significantly more Quick. Furthermore, since the different sub-band signals can be independently processed, both an embodiment of the filter apparatus, as well as an embodiment of the filter generator 104 can process the respective input signals highly efficiently in a fast and parallel manner. Therefore, the processing of both a digital audio input and an input signal, as well as an impulse response indicative of a filter characteristic can be carried out highly efficiently in a parallel manner. As underlined above, An embodiment of an inventive filter apparatus as well as an embodiment of an inventive filter generator combine the advantages of both direct processing of audio signals in the time domain that leads to a very high quality and the use of a combination of a Fourier transform along with a transfer function in the frequency domain offering high efficiency since each frequency band is only multiplied with a key (actual value or complex) in the signal filter process.

On the other hand, the disadvantages of both, purely processing the input signals in the time domain, which leads to an enormous computing effort, such as that of a Fourier transform, can be significantly reduced and suppressed to a level that the output of An embodiment of a filter apparatus is significantly indistinguishable from the quality of a direct processing in the time domain.

These two advantages offer greater flexibility to filter digital signals with variable filter characteristics. This is especially important in the HRTF field, since HRTF-related filters usually have a very long impulse response. Therefore, an embodiment of an inventive filter apparatus comprising a complex analysis filter bank 101, a plurality of intermediate filters 190 in sub-band filtration 102 and a complex synthesis filter bank 103 offers especially in the Field of applications related to HRTF significant computational advantages due to the possible parallel processing of sub-band signals.

The embodiments of a filter generator and embodiments of systems comprising both a filter apparatus and a filter generator also offer the advantage that filters can be easily adapted to environments,

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Specific parameters or other specific needs of the application at hand. Especially, in terms of HRTF-related applications, an embodiment of such a system can be used in tracking applications, in which various sources of sounds and noises, as well as the position of the listener vary over time. Such an embodiment of a system comprising a filter apparatus and a filter generator therefore offers a highly efficient and flexible way of presenting an audio impression of a three-dimensional installation of sound sources with respect to a variable position and orientation of a hypothetical listener through headphones or other head-related sound systems (stereo sound systems).

As this last example illustrates, an embodiment of an inventive filter apparatus together with an inventive filter generator offers not only a highly efficient system for handling audio with excellent quality, but also a very flexible way of introducing audio prints into alteration in an efficient way.

Complex modulated filter banks

Next, let v = - “be the Fourier transform of the discrete time of a

discrete time signal z (v). As before, v is an integer indicating an index or a time index of a time signal, while w = 2 nf is the circular frequency associated with the frequency f, n is the circular number (n

= 3.1415926 ...) ei = j =

vr

It is the imaginary unit.

The exponential, complex L-band filter bank is defined as a real valuated prototype filter p (v) of finite length. For the computations below it will be assumed by extension with zeros that the prototype filter is defined for all integers v. Given a real valued discrete time signal x (v) the analysis filter bank 101 applies, as explained above, the complex modulated prototype filters followed by subsampling by a factor L to emit the sub-band signals,

C, (A) = J] + kL) p (v) exp - / y (* + |) {V '+ 0)

Vm B *. b J

(1)

for each subband index n = 0.1, ..., L-1, and integer time index k. The time index k differs from the time index v with respect to the fact that k refers to the subsampled signals, while the integer v indicates the signals with the full sample frequency.

Given the complex valuated sub-band signals dn (k), the synthesis filter bank 103 applies filtration followed by ascending sampling by a factor of L and a real value extraction to emit the real valued signals, as already explained, to get the output signal

(2)

In equations (1) and (2) 9 yy represent phase factors (constants) to filter the real valued discrete time signal x (v) to the complex valued sub-band signal and to reconstruct the real valued output samples and (v) of complex valuated sub-band signals dn (k). It is well known that a prototype filter and fixed phase factors 9y and can be chosen to give the perfect reconstruction, y (v) = x (v), in the case where dn (k) = Cn (k), that is when subband signals are not altered. In practice, the perfect reconstruction property will remain until a delay (and / or a signal change), but in the computations that follow, this detail will be ignored by allowing the use of an acausal prototype filter. The present invention is applicable to the pseudo QMF type of the design as taught by PCT / SE02 / 00626 "Aliasing reduction using complex exponential modulated filter banks". Here the prototype filter is symmetric p (-v) = p (v), and its Fourier transform of the discrete time P (m) essentially

dissipates out of range

m \ <n iL

. The perfect reconstruction is also replaced by an almost perfect reconstruction property. For the derivation that follows it will be assumed for simplicity that both reconstruction

ni L <| ^ <n

perfect remains as that P (a) = 0 for. In addition, it is assumed that the phase factors

they satisfy the condition that y- 9 is equal to an integer multiple of 4L.

In a critically sampled filter bank, the alteration of sub-band signals before synthesis usually leads to the introduction of alignment artifacts. This is overcome here due to the fact that oversampling by a factor two is introduced when using complex valuated signals. Although the total sampling rate of the sub-band samples is identical to the sampling rate of the discrete time input signal, the input signal is real valued and the sub-band samples are complex valued. How

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will be delineated below, the absence of alias opens the door for time-efficient invariant signal processing. Sub-band filtration in a complex modulated filter bank

Consider the sub-band filter modification 102 of each sub-band signal obtained when filtering the Cn (k) analysis samples of the complex analysis bank 101 with a pulse response filter gn (k) before synthesis ( 2) performed by the bank (of filters) of complex synthesis 103

■ (3)

The elementary computations show that given the assumptions in the frequency response of the prototype filter, the resulting effect on the reconstructed time signal is that of a discrete time filtration.

Y (m) = G (m) X (m)

(4)

in which

(5)

TO . Gn (m) = Z kgn (k) exp (-ikm) Here, k

sub-band n for n> 0 and

is the Fourier transform of the discrete time of the filter applied in the

:: i 'for n <0. (6)

in which * indicates complex conjugation. Note here that the special case Gn (m) = 1 leads to Gn (m) = 1 in (5) due to the assumed special design of the prototype p (v), which implies

(7)

Another case of interest is Gn (m) = exp (-i®) which leads to Gn (m) = exp (-iLm), so that y (v) = x (vL).

Approximation of a filter response given by sub-band filtration

If H (m) is a given filter (for example, transfer function) with response to the actual valued pulse h (v). This data is considered as input to filter converter 104. In view of (5) and (7), a trivial choice is given for sub-band filters resulting in the desired response G (m) = H (m) by

Gn (&) = H (a / L)

' for

(8)

The disadvantage of this formula is that, although H (m) is a smooth function of m, the segment in periods defined by (8) will show jumps and the impulse response of the sub-band filters will be unnecessarily long. The use of the prior art of the complex pseudo QMF bank for equalization or wrap adjustment consists of applying a single gain gn on each sub-band, resulting in the transfer function

(9)

with the extension gn = -g * -in for n <0 defined according to (6). In view of (7), one achieves

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for

(10)

and the transfer function is interpolated between those frequencies. For objective filter responses H (a>) that vary slowly as a function of the frequency m, a first method of approximation of the filter is therefore obtained by choosing

(11)

An example of the quality resulting from this procedure is given in Figures 5 and 7.

According to an embodiment of the present invention a filter generator or a filter converter 104 is used to teach how to convert the filter (defined by its impulse response) h (v) into intermediate sub-band filters 190 by means of the second bank of analysis filters 301 that uses the real valued prototype filter q (v),

2n (k) = ¿My + * £) í (y) ttÉpl -4 (íJ + f) l

V = -SS \ i

(12)

In terms of Fourier transforms this reads

(13)

The advantage of this procedure is that any given filter h (v) can be efficiently transformed into intermediate subband filter responses. If q (v) has connections Kq ■ L, a time domain filter h (v) of connections Kh ■ L becomes sub-band domain filters (12) with connections Kh + Kq - 1, in which Kh and Kq are positive integers. With respect to the exemplary numbers given in the context of the description of Figure 4, Kh and Kq are equal to 3 and with a prototype filter length and an impulse response corresponding to a length of 3 64 = 192 (L = 64) each. Therefore, each intermediate subband filter 190 has a pulse response length of only 3 + 3 - 1 = 5 connections each.

Prototype filter design for the filter converter

Insertion (13) in (5) produces

(14)

Thus, the condition for G (m) = H (m) to maintain is that

(15)

in which ¿[/] = 1 for l = 0 and or [l] = 0 for l * 0. A simple solution to (15) is given by the brick wall filter

This prototype filter corresponds to the choice (8) and has the disadvantage of having a slowly decaying and infinite response to the impulse q (v). Instead, the present invention teaches to solve (15) approximately (for example, in the sense of least squares) with a finite impulse response filter q (v). The time domain equivalent of (15) is the system of linear equations for n = 0.1, ..., L-1 and for all integers

k,

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^ ~ ^ L) q (n + vQ = r

in which

re

' (17)

is the autocorrelation of p (v). For any given support length, the system of linear equations (16) can be solved in the sense of least squares for a prototype filter q (v). It is desirable to use a support significantly shorter than that of the prototype filter of the original filter bank p (v), and in that case the linear system (16) is overdetermined. A given quality of approach can also be exchanged for other desirable properties through joint optimization. An example of such a property is a low step type of frequency response Q (a>).

Next, the determination of a multi-slot QMF representation (sub-band domain) of the HRTF filters is described. The time domain filter conversion in the complex QMF sub-band domain is performed by a FIR filter in the filter converter 104 of Figure 1a. To be more precise, the following description underlines a method for implementing a given FIR filter h (v) of length Nh in the complex QMF sub-band domain. The principle of the operation is illustrated in Figure 1a in the case of a system that also comprises an embodiment of an inventive filter apparatus.

Subband filtration by itself is carried out by a set of or a plurality of intermediate filters 190 within subband filtration 102. To be more precise, subband filtration consists of the separate application of an intermediate filter FIR rated complex gn (l) for each sub-band QMF with an index n = 0.1, ..., 63. In other words, in the following description special reference will be made to embodiments with L = 64 different sub-band signals. However, this number of specific subband signals is not essential and the appropriate equations will also be given in a more general way.

One of the key components of the system shown in Figure 1a is filter converter 104, which converts the given time domain FIR filter h (v) into complex sub-band domain filters gn (l). The filter converter 104 comprises a complex analysis bank 301 similar to the analysis bank QMF 101. The prototype filter of the complex analysis filter bank 301 of the filter converter 104 q (v) of length 192 (= 3 64) for the specific case of L = 64 sub-band signals is created by resolving in the sense of minimum squares the overdetermined system of equation (16). The filter coefficients q (v) or preferably the ratios they fulfill will be described in more detail in the case of L = 64 sub-band signals later.

To be more exact in terms of mathematical description, an extension with zeros in the time domain FIR filter is defined by

h (o) =

[h (o), v = 0, l, -, Nh -1,

[0, otherwise

(18)

The resulting intermediate subband domain filters are based on equation (12) and can be expressed in the general case as

£, (0 = ¿Hu + Mí- Ü8- fffa) ■ expíi- í and Íh + - y,) 1

■ ■' ' (19)

where lo and vo are delays, l is an integer that indicates an index of the filter connections and Nq (= Nq) is the length of the impulse response of the prototype filter q (v).

It should be noted that, within the framework of the present application under an equation that is based on an equation, an introduction of additional delay factors (cf. lo and vo), additional coefficients and an introduction of a window or other function is understood simple function

In case L = 64, the expression for sub-band domain filters or intermediate filters 190 becomes

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(20)

These subdomain filters have a length Lq = Kh + 2, where

Kh = ¡N „/ 64" | (21)

and Nh is the length of the impulse response h (v) of the filter characteristics to be transferred to the sub-band domain.

In this case, the integer n = 0, 1, 63 again is the index of a sub-band and l = 0, 1, (Kh + 1) is a

integer indicating the connections of the resulting intermediate filters 190.

The extra addition of (-2) in equation (20) compared to equation (12) is there, because equation (12) is developed without considering the filter drop. Actual implementations will always cause delays. Therefore, depending on the specific implementation, additional delays or delays may be implemented in the embodiments shown in Figures 1a to 1e and Figures 2 to 11, which have been omitted for simplicity in the aforementioned Figures.

As noted above, in many cases the system of linear equations (16) is overdetermined. However, it can be solved or approximated in the sense of least squares with respect to the prototype filter coefficients q (v). The resolution of the system of linear equations (16) in the sense of least squares, leads to the filter connections of the prototype filter q (v) to meet the following ratios for whole numbers v from 0 to 191:

-0 "3-oCM <■ OOIACMOCMO

-0,199 <q [1] <; -0,197

-0,194 <q [2] <; -0,192

-0,189 <q [3] <; -0,187

-0.183 <q [4] <; -0,181

-0,178 <q [5] <; -0,176

-0,172 <q [6] <; -0,170

-0,166 <q [7] <; -0,164

-0,160 <q [8] <; -0,158

-0.154 <q [9] <; -0,152

-0,148 <q [10] <-0,146

-0,142 <q [11] <-0,140

-0,135 <q [12] <-0,133

-0,129 <q [13] <-0,127

-0,122 <q [14] <-0,120

-0,116 <q [15] <-0,114

-0.109 <q [16] <-0.107

-0,102 <q [17] <-0,100

-0096 <q [18] <-0,094

-0089 <q [19] <-0.087

-0082 <q [20] <-0,080

-0075 <q [21] <-0.073

-0068 <q [22] <-0.066

-0.061 <q [23] <-0.059

-0054 <q [24] <-0,052

-0046 <q [25] <-0.044

-0039 <q [26] <-0.037

-0032 <q [27] <-0.030

-0024 <q [28] <-0.022

-0.017 <q [29] <-0.015

-0009 <q [30] <-0.007

-0002 <q [31] <0.000

0.006 <q [32] <0.008 0.014 <q [33] <0.016 0.021 <q [34] <0.023