Abstract:
Recordings from microphones that provide 1 st  order Ambisonics signals, so-called B-format signals, offer a limited cognition of sound directivity. Sound sources are perceived broader than they actually are, especially for off-center listening positions, and the sound sources are often located to be coming from the closest speaker positions. In a method and apparatus for enhancing the directivity of 1 st  order Ambisonics signals, additional directivity information is extracted (SFA) from the lower order Ambisonics input signal. The additional directivity information is used to estimate higher order Ambisonics coefficients which are then combined with the coefficients of the input signal. Thus, the directivity of the Ambisonics signal is enhanced, which leads to an increased accuracy of spatial source localization when the Ambisonics signal is decoded to loud speaker signals. The resulting output signal has more energy than the input signal.

Description:
FIELD OF THE INVENTION 
       [0001]    The invention relates to the field of Ambisonics audio signal processing and acoustics. 
       BACKGROUND 
       [0002]    Ambisonics is a technology that describes an audio scene in terms of sound pressure, and addresses the recording, production, transmission and playback of complex audio scenes with superior spatial resolution, both in 2D and 3D. In Ambisonics, a spatial audio scene is described by coefficients A n   m (k) of a Fourier-Bessel series. Microphone arrays that provide 1 st  order Ambisonics signals as so-called B-format signals are known. However, decoding and rendering 1 51  order Ambisonics signals to speaker arrangements for 2D surround or 3D only offers a limited cognition of sound directivity. Sound sources are often perceived to be broader than they actually are. Especially for off-center listening positions, the sound sources are often located as coming from the closest speaker positions, instead of their intended virtual position between speakers. The 1 st  order Ambisonics (B-format) signals are composed out of four coefficients of a Fourier-Bessel series description of the sound pressure, which form a 3D sound field representation. These are the W channel (mono mix, or 0 th  order) and the X,Y,Z channels (1 st  order). Higher order signals use more coefficients, which increases the accuracy of spatial source localization when the coefficients are decoded to speaker signals. However, such higher order signals are not included in B-format signals provided by microphone arrays. 
         [0003]    Directional Audio Coding (DirAC) is a known technique [5,9] for representing or reproducing audio signals. It uses a B-format decoder that separates direct sound from diffuse sound, then uses Vector-Based Amplitude Panning (VBAP) for selective amplification of the direct sound in the frequency domain, and after synthesis filtering finally provides speaker signals at its output. 
         [0004]      FIG. 1  a) shows the structure of DirAC-based B-format decoding. The B-Format signals  10  are time domain signals, and are filtered in an analysis filter bank AFB D  into K frequency bands  11 . A sound field analysis block SFA D  estimates a diffuseness estimate ψ(f k )  13  and directions-of-arrival (DoA)  12 . The DoA are the azimuth φ(f k ) and inclination θ(f k ) of the directions to the source at a particular mid frequency of a band k. A 1 st  order Ambisonics decoder AmbD renders the Ambisonics signals to L speaker signals  14 . A direct-diffuse separation block DDS separates the 1 st  order Ambisonics signals into L direct sound signals  15  and L diffuse sound signals  16 , using a filter that is determined from the diffuseness estimate  13 . The L diffuse sound signals  16  are derived by multiplying the output  14  of the decoder AmbD with √{square root over (ψ(f k ))}, which is obtained from the diffuseness estimate  13 . The directional signals are derived from multiplication with √{square root over (1−ψ(f k ))}. The direct sound signals  15  are further processed using a technique called Vector Base Amplitude Panning (VBAP) [8]. In a VBAP unit VP, a gain value for each speaker signal (in each frequency band) is multiplied to pan the direct sound to the desired directions, according to the DoA  12  and the positions of the speakers. The diffuse signals  16  are de-correlated by de-correlation filtering DF, and the de-correlated diffuse signals  17  are added to the direct sound signals being obtained from the VPAB unit VP. A synthesis filter bank SFB D  combines the frequency bands to a time domain signal  19 , which can be reproduced by L speakers. Smoothing filters (not shown in  FIG. 1 ) for temporal integration are applied to calculate the diffuseness estimate ψ(f)  13  and to smooth the gain values that were derived by VBAP. 
         [0005]      FIG. 1  b) shows details of the sound field analysis block SFA D . The B-format signals represent a sound field in the frequency domain at the origin (observation position, r=0). The sound intensity describes the transport of kinetic and potential energy in a sound field. In the sound field, not all local movement of sound energy corresponds to a net transport. Active intensity I a  (time averaged acoustic intensity, DoA˜I a ) is the rate of directive net energy transport—energy per unit time for the three Cartesian directions. The active intensity  11   a  of the B-format signal  11  is obtained in an active intensity analysis block AIA D , and provided to a diffuseness analysis block DAB D  and a DoA analysis block DOAAB D , which output the DoA  12  and the diffuseness estimate  13 , respectively. More about DirAC is described in [9], the underlying theory in [5]. 
       SUMMARY OF THE INVENTION 
       [0006]    It would be desirable to enhance the directivity of 1 st  order Ambisonics signals, such as B-format microphone recordings. Such directivity enhancement is desired for a more realistic replay, or for mixing real recoded sound with other higher order content, e.g. for dubbing film sound that is intended to be replayed for different speaker setups. One problem to be solved by the invention is to enhance the directivity of 1 st  order Ambisonics signals or B-format signals, even if higher order coefficients for such signals are not available. 
         [0007]    According to the invention, this and other problems can be solved by selectively amplifying direct sound components, while diffuse sound components are not changed. When selectively amplifying direct sound, it is advantageous that an Ambisonics formatted signal with increased order is obtained, because it can easily be mixed with other Ambisonics formatted signals. With the present invention, it is possible to increase the order of a 1 st  order Ambisonics signal, whereby only directional sound components are considered. This results again in an Ambisonics formatted signal, but with higher order (i.e. at least 2 nd  order). In principle, the disclosed method for enhancing directivity of a 1 st  order Ambisonics signal derives higher order coefficients from the 1 st  order coefficient information and adds the derived higher order coefficients to the Ambisonics signal. Thus, the 1 st  order coefficient information (i.e. 0 th  and 1 st  order coefficients) of the 1 st  order Ambisonics signal is advantageously maintained (except for a re-formatting, in one embodiment). 
         [0008]    In other words, additional directivity information is extracted from the lower order 
         [0009]    Ambisonics signal, and the additional directivity information is used to estimate higher order coefficients. In this way, the directivity of the Ambisonics signal is enhanced, which leads to an increased accuracy of spatial source localization when the Ambisonics signal is decoded to loud speaker signals. One effect of the invention is that the resulting output signal has more energy than the input signal. 
         [0010]    The present invention relates to a method for enhancing directivity of an input signal being a 1 st  order Ambisonics signal and having coefficients of 0 th  order and 1 st  order, as defined in claim  1 . 
         [0011]    The present invention relates also to an apparatus for enhancing directivity of a 1 st  order Ambisonics signal having coefficients of 0 th  order and 1 st  order, as defined in claim  9 . 
         [0012]    Further, the present invention relates to a computer readable storage medium having stored thereon computer readable instructions that, when executed on a computer, cause the computer to perform a method for enhancing directivity of a 1 st  order Ambisonics signal having coefficients of 0 th  order and 1 st  order as defined in claim  1 . 
         [0013]    It is noted that Ambisonics signals of any given order generally include coefficients not only of the given order, but also coefficients of all lower orders, even if not explicitly mentioned herein. E.g., a 2 nd  order HOA signal includes coefficients not only of 2 nd  order, but also of 0 th  order and 1 st  order. 
         [0014]    Advantageous embodiments of the invention are disclosed in the dependent claims, the following description and the figures. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]    Exemplary embodiments of the invention are described with reference to the accompanying drawings, which show in 
           [0016]      FIG. 1  a) the structure of a known DirAC-based B-format decoder; 
           [0017]      FIG. 1  b) the general structure of a known Sound Field Analysis block; 
           [0018]      FIG. 2  the structure of an apparatus according to a general embodiment of the invention; 
           [0019]      FIG. 3  the structure of an apparatus according to an embodiment that uses combining in the time domain; 
           [0020]      FIG. 4  the structure of an apparatus according to a first embodiment that uses combining in the frequency domain; 
           [0021]      FIG. 5  the structure of an apparatus according to a second embodiment that uses combining in the frequency domain; 
           [0022]      FIG. 6  a flow-chart of a method according to the invention; and 
           [0023]      FIG. 7  a flow-chart of details of the combining step. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0024]      FIG. 2  shows the structure of an apparatus according to a general embodiment of the invention. A time domain 1 st  order Ambisonics input signal  10  (such as a B-format signal) is filtered in an Analysis Filter Bank AFB, wherein four frequency domain channels  21  are obtained. These are a frequency domain representation of the input signal  10 : one of the frequency domain channels represents 0 th  order coefficients (i.e. the W-channel), and the other three frequency domain channels represent 1 st  order coefficients (the X,Y,Z-channels). 
         [0025]    A Direct Sound Separator unit DSS separates direct sound (i.e. directional sound)  20  in the four frequency domain channels  21  from diffuse sound. In an embodiment, the Direct Sound Separator unit DSS simply selects the W-channel and uses it as direct sound  20 . Further, a Sound Field Analysis unit SFA performs a sound field analysis of the four frequency domain channels, obtaining source directions OP  22  and a diffuseness estimate ψ  23  for every frequency band of the frequency channels. In an embodiment, the Sound Field Analysis unit SFA includes a Direction of Arrival (DoA) analysis unit for obtaining the direction information  22 . 
         [0026]    The direct sound  20  obtained by the direct sound separator DSS is then filtered in a filter F, whereby diffuse components are damped and thus the directional sound is selectively (relatively) amplified. The filter F uses the diffuseness estimate ψ  23  for the selective amplification; in principle, it multiples the direct sound  20  with √{square root over (2(1ψ(f)))} ( 1  W(f)) to obtain selectively amplified direct sound  24 . The selectively amplified direct sound  24  is then Ambisonics encoded in a HOA encoder HOAe, wherein a HOA signal  25  of a pre-defined order N 0  (N 0 &gt;1, i.e. at least 2 nd  order) is obtained. The HOA encoder HOAe uses the source directions θΦ 22  for the encoding. It may use an Ambisonics format that has 0 th  order and 1 st  order coefficients according to the B-format. It may also use a different Ambisonics format instead. Different Ambisonics formats usually have a defined sequential order of coefficients that is different from the sequential order of the B-format, or a coefficient scaling that is different from the coefficient scaling of the B-format, or both. 
         [0027]    A selector SEL selects defined portions of the HOA signal  25 , and the selected portions  25   a  are then combined in a Combiner and Synthesis unit CS with the original B-format signal. The selected portions  25   a  are higher order portions of the HOA signal  25 , i.e. portions (coefficients, in an embodiment) of at least 2 nd  order. The Combiner and Synthesis unit CS provides on its output time domain signals  29  (in HOA format), which can be used to render speaker signals. The Combiner and Synthesis unit CS includes a synthesis filter SF for filtering Ambisonics formatted signals and obtaining the time domain signals. 
         [0028]      FIG. 2  shows also an optional additional mixer unit MX, in which the obtained HOA output signal  29  can be mixed with another HOA input signal  30  of higher order. The other HOA input signal  30  can also have a different Ambisonics format than the input signal  10 , due to a HOA format adapter HFA described below. The mixer MX generates a HOA signal  31  that includes a mixture of the obtained HOA output signal  29  (i.e.enhanced B-format input signal) and the HOA input signal  30 . 
         [0029]    Two basic types of embodiments of the Combiner and Synthesis unit CS are described in the following: In one type of embodiments, the Combiner and Synthesis unit CS combines the selected portions  25   a  with the original B-format signal  10  in the time domain. Therefore, it performs a synthesis of only the selected portions  25   a  into the time domain. 
         [0030]    In the other type of embodiments, the Combiner and Synthesis unit CS combines the selected portions  25   a  with the original B-format signal  10  in the frequency domain, and performs a synthesis into the time domain afterwards. 
         [0031]      FIG. 3  shows an embodiment of the first type. In this embodiment, the Combiner and Synthesis unit CS synthesizes only the selected higher order coefficients  25   a  of the HOA signal  25  in a Synthesis Filter Bank SFB to obtain a synthesized time domain signal  26 . A time domain Combiner unit CB t  combines the synthesized time domain signal  26  with the input signal in the time domain, to obtain the time domain output signal  29 . In one embodiment, a time domain HOA Format Adapter unit HFA t  adapts the format of the time domain input signal according to the format that the HOA encoder HOAe uses. This simplifies the combining of the obtained time domain HOA signal  28  with the synthesized time domain signal  26  in the time domain Combiner unit CB t . In some embodiments, e.g. where the HOA encoder HOAe uses a format that is compatible with the HOA input signal, a HOA Format Adapter unit HFA t  may not be required. The HOA Format Adapter unit HFA t  may re-arrange and/or re-scale the coefficients of the HOA signal. 
         [0032]    The Analysis Filter Bank AFB obtains different frequency bands, e.g. by performing an FFT (Fast Fourier Transform). This generates a time delay. In one embodiment, a Delay Compensation unit DC of the time domain input signal compensates filter bank delays, e.g. of the Analysis Filter Bank AFB, the selective amplification filter F etc. While in the depicted embodiment the delay compensation is made before HOA format adaptation HFA, it can in another embodiment be made after the HOA format adaptation. In yet another embodiment, the delay compensation is made in two steps, with one delay compensation unit before the format adaptation and another one thereafter. 
         [0033]      FIGS. 4 and 5  show embodiments that use the second type of the Combiner and Synthesis unit CS. In this embodiment, the Combiner and Synthesis unit CS receives frequency domain 0 th  order and 1 st  order Ambisonics coefficients of the input signal, as obtained from an Analysis Filter Bank. This may be a separate Analysis Filter Bank AFB′, as in an embodiment shown in  FIG. 4 , or it may be the previously mentioned Analysis Filter Bank AFB, as in an embodiment shown in  FIG. 5 . In the latter case, the four frequency domain channels  21  provided by the Analysis Filter Bank AFB are directly input to the Combiner and Synthesis unit CS. A frequency domain Combiner unit CB f  combines the selected higher order coefficients  25   a  of the HOA signal  25  with the 0 th  order and 1 st  order Ambisonics coefficients of the input signal in the frequency domain. A Synthesis Filter Bank SFB&#39; synthesizes the combined Ambisonics coefficients, wherein the time domain output signal  29  is obtained. In one embodiment, an optional frequency domain HOA format adaptation HFA f  is performed on the 0 th  order and 1 St  order Ambisonics coefficients of the input signal, before combining them with the selected higher order coefficients of the HOA signal  25 . The HOA Format Adapter unit HFA f  may re-arrange and/or re-scale the coefficients of a HOA signal. As mentioned above, the HOA Format Adapter unit HFA f  may be not required in some embodiments. Further, as also mentioned above, Delay Compensation (not shown) may be used in one embodiment for any delay possible inserted in the processing chain (e.g. selective amplification filter F, HOA encoder HOAe). However, it will usually not be required, since the delay inserted by the Analysis Filter Bank AFB,AFB′ needs not be compensated. 
         [0034]    A time domain combiner CB t  is a combiner that operates in the time domain, while a frequency domain combiner CB f  is a combiner that operates in the frequency domain. Both types of combiner add the obtained coefficients of the selected portions  25   a  to the (possibly re-formatted) coefficients of the input signal  10 . 
         [0035]    Generally, an apparatus for enhancing directivity of a 1 st  order Ambisonics time domain signal having coefficients of 0 th  order and 1 st  order includes an Analysis Filter Bank AFB for filtering the 1 st  order Ambisonics signal, wherein four frequency domain channels  21  are obtained that are a frequency domain representation of the 1 st  order Ambisonics signal, and wherein one frequency domain channel  20  of the frequency domain channels represents 0 th  order coefficients and three of the frequency domain channels represent 1 st  order coefficients, a Sound Field Analysis unit SFA for performing a sound field analysis of the four frequency domain channels, whereby source directions OP  22  and a diffuseness estimate W  23  are obtained, a selective amplification Filter F for filtering the frequency domain channel  20  that has 0 th  order coefficients, wherein the diffuseness estimate W  23  is used and wherein a direct sound component  24  is obtained, a Higher Order Ambisonics encoder HOAe for encoding the direct sound component  24  in Ambisonics format with a pre-defined order of at least two, wherein said source directions Θ,Φ 22  are used and wherein encoded direct sound  25  in Ambisonics format of the pre-defined order is obtained, the encoded direct sound in Ambisonics format having Ambisonics coefficients of at least 0 th , 1 st  and 2 nd  order, a Selector SEL for selecting, from the obtained encoded direct sound  25  in Ambisonics format of the pre-defined order, Ambisonics coefficients  25   a  of at least 2 nd  order, and a Combining and Synthesis unit CS for combining the selected Ambisonics coefficients of at least 2 nd  order of the encoded direct sound  25   a  with the Ambisonics coefficients of the 1 st  order Ambisonics input signal  10 , wherein a time domain representation of an Ambisonics signal of at least 2 nd  order  29  is obtained. It is noted that the selected Ambisonics coefficients  25   a  of at least 2 nd  order do not include coefficients of 0 th  order or 1 st  order. That is, the Selector SEL omits the lower order coefficients. 
         [0036]    In one embodiment, the present invention relates to a method for enhancing directivity of a 1 st  order Ambisonics signal  10  (i.e. an Ambisonics signal with only 0 th  and 1 st  order coefficients). Generally, the method includes steps of generating, in a Sound Field Analysis unit SFA, a diffuseness estimate W  23  and direction information Θ,Φ  22  from the 1 st  order Ambisonics signal, separating and selectively amplifying direct sound  24  from the 1 st  order Ambisonics signal, wherein a filter F for the selective amplifying uses the diffuseness estimate W  23 , encoding the selectively amplified direct sound  24  in a HOA encoder HOAe, wherein the direction information Θ,Φ  22  is used and a HOA signal  25  of at least 2 nd  order is obtained, selecting a higher order portion of the HOA signal  25 , wherein the selected higher order portion includes only coefficients of higher order than 1 st  order (i.e. does not include 0 th  order coefficients, and does not include 1 st  order coefficients), and combining the selected higher order coefficients of the HOA signal  25  with the input 1 st  order Ambisonics signal in a Combiner and Synthesis unit CS, wherein a time domain representation  29  of a Higher Order Ambisonics signal (i.e. an Ambisonics signal of at least 2 nd  order) is obtained. 
         [0037]    In one embodiment, the step of combining the selected higher order coefficients of the HOA signal  25  with the input 1 st  order Ambisonics signal  10  includes receiving frequency domain 0 th  order and 1 st  order Ambisonics coefficients of the input signal from an Analysis Filter Bank AFB, combining the selected higher order (i.e. 2 nd  order or higher) coefficients  25   a  of the HOA signal  25  with the 0 th  order and 1 st  order Ambisonics coefficients of the input signal in the frequency domain, and synthesizing the combined Ambisonics coefficients in a Synthesis Filter Bank SFB to obtain the time domain output signal  29 . 
         [0038]    In an embodiment, the method further includes a step of performing a frequency domain HOA format adaptation HFA f  on the 0 th  order and 1 st  order Ambisonics coefficients of the input signal before combining them with the selected higher order coefficients of the HOA signal  25 . 
         [0039]    In another embodiment, the step of combining the selected higher order coefficients  25   a  of the HOA signal  25  with the input 1 st  order Ambisonics signal  10  includes steps of synthesizing only the selected higher order coefficients  25   a  of the HOA signal  25  in a Synthesis Filter Bank SFB to obtain a synthesized time domain signal  26 , and combining the obtained synthesized time domain signal with the input signal in the time domain to obtain the time domain output signal  29 . In an embodiment, a time domain HOA format adaptation HFA t  of the time domain input signal is performed before the combining. In a further embodiment, a Delay Compensation DC of the time domain input signal for compensating a filter bank delay is performed before the step of combining. 
         [0040]    The higher order coefficients are obtained by filtering the 1 st  order Ambisonics input signal  10  in an Analysis Filter Bank AFB, performing a Direction of Arrival (DoA) analysis of the filtered signal, whereby a diffuseness estimate ψ  23  and directions Θ,Φ  22  are obtained, filtering the W-channel (0 th  order coefficients) using the diffuseness estimate ψ  23 , whereby the direct sound S(f)  20  is separated, and encoding the direct sound S(f)  20  in Ambisonics format in a Higher Order Ambisonics encoder HOAe. From the resulting HOA signal  25 , only the higher order coefficients are used, combined with the lower order coefficients of the input signal, and from the result an Ambisonics output signal  29  is synthesized. 
         [0041]    Generally, the step of combining the selected higher order coefficients  25   a  of the HOA signal  25  with the input 1 st  order Ambisonics signal  10  includes adding their respective coefficients, i.e. the output signal  29  includes all coefficients of the input signal  10  and additional coefficients, namely higher order coefficients of the selected portion  25   a.    
         [0042]      FIG. 6  shows a flow-chart of a method according to one embodiment of the invention. The method  60  for enhancing directivity of an input signal  10  (a 1 st  order Ambisonics signal having coefficients of 0 th  order and 1 st  order) includes steps of 
         [0043]    filtering s 1  the input signal  10 , wherein four frequency domain channels  21  are obtained, one of them being the Ambisonics W-channel  20 , 
         [0044]    performing s 2  a Sound Field Analysis SFA of the four frequency domain channels  21 , 
         [0045]    whereby source directions  22  and a diffuseness estimate  23  are obtained, 
         [0046]    selecting and filtering s 3  the frequency domain Ambisonics W-channel  20 , wherein the diffuseness estimate  23  is used and wherein a direct sound component  24  of the input signal  10  is obtained, 
         [0047]    encoding s 4  in a Higher Order Ambisonics encoder HOAe the direct sound component  24  in Ambisonics format with a pre-defined order N., wherein said source directions  22  are used and wherein encoded direct sound  25  in Ambisonics format of the pre-defined order N o  is obtained, 
         [0048]    selecting s 5 , from the obtained encoded direct sound in Ambisonics format  25 , defined portions  25   a  including Ambisonics coefficients of at least 2 nd  order (i.e. 2 nd  order or higher order, omitting lower orders), and 
         [0049]    combining s 6  a signal representing the Ambisonics coefficients of at least 2 nd  order of the selected portions of the encoded direct sound  25   a  with a signal representing the input signal  10 , wherein an Ambisonics signal of at least 2 nd  order  29  is obtained. 
         [0050]    The four frequency domain channels  21  obtained in the filtering step s 1  are a frequency domain representation of the 1 st  order Ambisonics signal, wherein one first frequency domain channel (W-channel)  20  of the frequency domain channels  21  represents O th  order coefficients, while the three remaining frequency domain channels  21  (X,Y,Z-channels) represent 1 st  order coefficients. 
         [0051]    In the encoding step s 4 , a Higher Order Ambisonics encoder HOAe encodes the direct sound component  24  in Ambisonics format with a pre-defined order N o , using said source directions Θ,Φ  22 , wherein the pre-defined order N o  is at least two and the encoded direct sound in Ambisonics format of the pre-defined order have Ambisonics coefficients of at least 2 nd  order. 
         [0052]      FIG. 7  a) shows an embodiment where the step of combining s 6  uses the four frequency domain channels  21  as representation of the input signal  10  (corresponding to the apparatus shown in FIGS.  4 , 5 ). It includes steps of combining s 61  in a frequency domain Combiner unit CB f  the Ambisonics coefficients of the 1 st  order Ambisonics signal  10 , represented by coefficients of the four frequency domain channels  21 , 21 ′, 28 , with the selected frequency coefficients  25   a  of the enhancement Higher Order Ambisonics signal  25  of at least 2 nd  order, wherein a signal  37  is obtained that is a frequency domain representation of an Ambisonics signal of at least 2 nd  order and that has enhanced directivity as compared to the 1 st  order Ambisonics input signal  10 , and filtering s 64  in a Synthesis Filter Bank SFB′ the obtained signal  37 , wherein a time domain representation of an enhancement Higher Order Ambisonics signal is obtained that has coefficients of at least 2 nd  order. 
         [0053]      FIG. 7  b) shows an embodiment where the step of combining s 6  uses the time domain coefficients of the input signal  10  (corresponding to the apparatus shown in  FIG. 3 ). It includes steps of filtering s 62  in a Synthesis Filter Bank SFB the selected Ambisonics coefficients of at least 2 nd  order  25   a  from the encoded direct sound  25 , wherein a time domain representation of an enhancement Higher Order Ambisonics signal  26  is obtained that has coefficients of at least 2 nd  order, and 
         [0054]    combining s 65  in a time domain combiner CB t  the Ambisonics coefficients of the 1 st  order Ambisonics signal  10  (or rather coefficients representing the Ambisonics coefficients of the 1 st  order Ambisonics signal  10 , since the actual HOA format may be adapted) with the time domain representation of said enhancement Higher Order Ambisonics signal of at least 2 nd  order  26 , wherein the time domain representation of an Ambisonics signal of at least 2 nd  order  29  is obtained that has enhanced directivity as compared to the 1 st  order Ambisonics signal  10 . 
         [0055]    The following description provides more details concerning Ambisonics. In the Ambisonics theory, a spatial audio scene is described by coefficients A n   m (k) of a Fourier-Bessel series. For a source-free volume, the sound pressure at an observation position (r, θ, φ) can be described as a function of its spherical coordinates (radius r, inclination Θ, azimuth Φ(1) and spatial frequency 
         [0000]    
       
         
           
             k 
             = 
             
               
                 ω 
                 c 
               
               = 
               
                 
                   2 
                    
                   π 
                    
                   
                       
                   
                    
                   f 
                 
                 c 
               
             
           
         
       
     
         [0000]    by 
         [0000]    
       
         
           
             
               
                 
                   
                     p 
                      
                     
                       ( 
                       
                         r 
                         , 
                         θ 
                         , 
                         φ 
                         , 
                         k 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         n 
                         = 
                         0 
                       
                       N 
                     
                      
                     
                       
                         ∑ 
                         
                           m 
                           = 
                           
                             - 
                             n 
                           
                         
                         n 
                       
                        
                       
                         
                           
                             A 
                             n 
                             m 
                           
                            
                           
                             ( 
                             k 
                             ) 
                           
                         
                          
                         
                           
                             j 
                             n 
                           
                            
                           
                             ( 
                             kr 
                             ) 
                           
                         
                          
                         
                           
                             Y 
                             n 
                             m 
                           
                            
                           
                             ( 
                             
                               θ 
                               , 
                               φ 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where A n   m (k) are the Ambisonic coefficients; j n (kr) are the Spherical-Bessel functions of first kind which describe the radial dependency; K n   m (Θ,φ) are the Spherical Harmonics (SH), which have real values in practice. They are responsible for the angular dependencies. n is the Ambisonics order index, and m the degree. Due to the nature of the Bessel function, which has only significant values for small kr, the summation series can be truncated at some order n=N with sufficient accuracy; for theoretical perfect reconstruction N→∞. More information and details may be reviewed in [11], [6], [7], [3], [13]. The Ambisonics coefficients A n   m  form the Ambisonics signal; they have the physical unit of the sound pressure (1 Pa) and are time varying. The signal A 0   0  can be seen as a mono version of the Ambisonic recording. The actual values of the Ambisonics coefficients are determined by the definition of the SH, more accurate its normalization scheme. The number of coefficients A n   m  in eq. (1) is given for 2D representations by O=2N+1, and for 3D representations by O=(N+1) 2 . 
         [0056]    In practice, Ambisonics uses real valued Spherical Harmonics (SH). A definition is provided below, since there are different formulations and kinds of normalization schemes for SH that affect encoding and decoding operations, i.e. the values of the Ambisonics coefficients. The formulation of real valued SH using unsigned expressions will be followed herein: 
         [0000]        Y   n   m (θ,φ)=Ñ n,m   P   n,|m| (cos(θ)) φ m (φ)   (2)
 
         [0000]    with Ñ n,m  the normalization factor (see Tab.1), which corresponds to the orthogonal relationship between Y n   m  and Y n′   m′ *. That is, 
         [0000]    
       
         
           
             
               
                 ∫ 
                 
                   Ω 
                   ∈ 
                   
                     S 
                     2 
                   
                 
               
                
               
                 
                   
                     Y 
                     n 
                     m 
                   
                    
                   
                     ( 
                     Ω 
                     ) 
                   
                 
                  
                 
                   
                     
                       Y 
                       
                         n 
                         ′ 
                       
                       
                         m 
                         ′ 
                       
                     
                      
                     
                       ( 
                       Ω 
                       ) 
                     
                   
                   * 
                 
                  
                 
                     
                 
                  
                 
                    
                   Ω 
                 
               
             
             = 
             
               
                 
                   
                     N 
                     ~ 
                   
                   
                     n 
                     , 
                     m 
                   
                 
                 
                   
                     
                       
                         ( 
                         
                           2 
                           - 
                           
                             δ 
                             
                               0 
                               , 
                               m 
                             
                           
                         
                         ) 
                       
                        
                       
                         ( 
                         
                           
                             2 
                              
                             n 
                           
                           + 
                           1 
                         
                         ) 
                       
                        
                       
                         
                           ( 
                           
                             n 
                             - 
                             
                                
                               m 
                                
                             
                           
                           ) 
                         
                         ! 
                       
                     
                     
                       4 
                        
                       
                         
                           π 
                            
                           
                             ( 
                             
                               n 
                               + 
                               
                                  
                                 m 
                                  
                               
                             
                             ) 
                           
                         
                         ! 
                       
                     
                   
                 
               
                
               
                 
                   
                     N 
                     ~ 
                   
                   
                     
                       n 
                       ′ 
                     
                     , 
                     
                       m 
                       ′ 
                     
                   
                 
                 
                   
                     
                       
                         ( 
                         
                           2 
                           - 
                           
                             δ 
                             
                               0 
                               , 
                               m 
                             
                           
                         
                         ) 
                       
                        
                       
                         ( 
                         
                           
                             2 
                              
                             
                               n 
                               ′ 
                             
                           
                           + 
                           1 
                         
                         ) 
                       
                        
                       
                         
                           ( 
                           
                             
                               n 
                               ′ 
                             
                             - 
                             
                                
                               
                                 m 
                                 ′ 
                               
                                
                             
                           
                           ) 
                         
                         ! 
                       
                     
                     
                       4 
                        
                       
                         
                           π 
                            
                           
                             ( 
                             
                               
                                 n 
                                 ′ 
                               
                               + 
                               
                                  
                                 
                                   m 
                                   ′ 
                                 
                                  
                               
                             
                             ) 
                           
                         
                         ! 
                       
                     
                   
                 
               
                
               
                 δ 
                 
                   nn 
                   ′ 
                 
               
                
               
                 δ 
                 
                   mm 
                   ′ 
                 
               
             
           
         
       
     
         [0000]    with Kronecker delta δ αα′  equals 1 for α=α′, 0 else. In the following, use is made of the ortho-normalization scheme. 
         [0057]    P n,|m|  are the associated Legendre functions, which describe the dependency of the inclination cos(θ). P n,|m| :[−1,1]→         , n≧|m|≧0. P n,|m|  can be expressed using the Rodrigues formula by eq. (3) (i.e., all definitions presented here do without the use of the Condon-Shortley phase, whose compensation for real valued variables can produce ambiguities), but more efficient methods for calculation for implementation exist. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       P 
                       
                         n 
                         , 
                         
                            
                           m 
                            
                         
                       
                     
                      
                     
                       ( 
                       x 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       
                         
                           2 
                           n 
                         
                          
                         
                           n 
                           ! 
                         
                       
                     
                      
                     
                       
                         ( 
                         
                           1 
                           - 
                           
                             x 
                             2 
                           
                         
                         ) 
                       
                       
                         
                            
                           m 
                            
                         
                         2 
                       
                     
                      
                     
                       
                          
                         
                           n 
                           + 
                           
                              
                             m 
                              
                           
                         
                       
                       
                          
                         
                           x 
                           
                             n 
                             + 
                             
                                
                               m 
                                
                             
                           
                         
                       
                     
                      
                     
                       
                         ( 
                         
                           
                             x 
                             2 
                           
                           - 
                           1 
                         
                         ) 
                       
                       n 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0058]    The dependency on the azimuth part φ is given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       φ 
                       m 
                     
                      
                     
                       ( 
                       φ 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               cos 
                                
                               
                                 ( 
                                 
                                   m 
                                    
                                   
                                       
                                   
                                    
                                   φ 
                                 
                                 ) 
                               
                             
                             , 
                           
                         
                         
                           
                             m 
                             &gt; 
                             0 
                           
                         
                       
                       
                         
                           1 
                         
                         
                           
                             m 
                             = 
                             0 
                           
                         
                       
                       
                         
                           
                             sin 
                              
                             
                               ( 
                               
                                 
                                    
                                   m 
                                    
                                 
                                  
                                 φ 
                               
                               ) 
                             
                           
                         
                         
                           
                             m 
                             &lt; 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0059]    Tab.1 shows common normalization schemes used within Ambisonics. δ 0,m , takes a value of 1 for m=0 and 0 else. Naming convention SN3D, N3D is taken from [3]. 
         [0000]    
       
         
               
             
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Common normalization schemes used within Ambisonics 
               
               
                 {tilde over ( N )} n,m  Normalization schemes for real SH 
               
             
          
           
               
                   
                 Schmidt 
                 4 π  Normalized, 
                   
               
               
                 Not 
                 Semi Normalized, 
                 N3D, 
                   
               
               
                 Normalized 
                 SN3D 
                 Geodesy 4 π   
                 Ortho-Normalized 
               
               
                   
               
               
                 {square root over (2 −  δ   0,m )} 
                 
                   
                     
                       
                         
                           
                             ( 
                             
                               2 
                               - 
                               
                                 δ 
                                 
                                   0 
                                   , 
                                   m 
                                 
                               
                             
                             ) 
                           
                            
                           
                             
                               
                                 ( 
                                 
                                   n 
                                   - 
                                   
                                      
                                     m 
                                      
                                   
                                 
                                 ) 
                               
                               ! 
                             
                             
                               
                                 ( 
                                 
                                   n 
                                   + 
                                   
                                      
                                     m 
                                      
                                   
                                 
                                 ) 
                               
                               ! 
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             ( 
                             
                               2 
                               - 
                               
                                 δ 
                                 
                                   0 
                                   , 
                                   m 
                                 
                               
                             
                             ) 
                           
                            
                           
                             
                               
                                 ( 
                                 
                                   
                                     2 
                                      
                                     n 
                                   
                                   + 
                                   1 
                                 
                                 ) 
                               
                                
                               
                                 
                                   ( 
                                   
                                     n 
                                     - 
                                     
                                        
                                       m 
                                        
                                     
                                   
                                   ) 
                                 
                                 ! 
                               
                             
                             
                               
                                 ( 
                                 
                                   n 
                                   + 
                                   
                                      
                                     m 
                                      
                                   
                                 
                                 ) 
                               
                               ! 
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             ( 
                             
                               2 
                               - 
                               
                                 δ 
                                 
                                   0 
                                   , 
                                   m 
                                 
                               
                             
                             ) 
                           
                            
                           
                             
                               
                                 ( 
                                 
                                   
                                     2 
                                      
                                     n 
                                   
                                   + 
                                   1 
                                 
                                 ) 
                               
                                
                               
                                 
                                   ( 
                                   
                                     n 
                                     - 
                                     
                                        
                                       m 
                                        
                                     
                                   
                                   ) 
                                 
                                 ! 
                               
                             
                             
                               4 
                                
                               
                                 
                                   π 
                                    
                                   
                                     ( 
                                     
                                       n 
                                       + 
                                       
                                          
                                         m 
                                          
                                       
                                     
                                     ) 
                                   
                                 
                                 ! 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                   
               
             
          
         
       
     
         [0060]    Signals recorded by SoundField™ like microphones are represented using the B-Format. The technology is described in [2]. There are four B-Format signals: The W signal carries a signal proportional to the sound pressure recorded by an omni-directional microphone, but is scaled by a factor of 1/√{square root over (2)}. The X,Y,Z signals carry signals proportional to the pressure gradients in the three Cartesian directions. The four B-Format coefficients VV,X,Y,Z are related to first order HOA coefficients using N3D normalization schemes [3], [4] by W=A 0 N3D   0 /√{square root over (2)}, X=A 1 N3D   1 /√{square root over (3)}, Y=A 1 N3D   −1 /√{square root over (3)}, Z=A 1 N3D   0 /√{square root over (3)} and to HOA coefficients using SN3D normalization by W=A 0 N3D   0 /√{square root over (2)}, X=A 1 SN3D   1 , Y=A 1 SN3D   −1 , Z=A 1 SN3D   0 . Further, the B-Format assumes a plane wave encoding model where the factor i n  is omitted within coefficient representation. 
         [0061]    HOA signals can also be represented by plane waves. The sound pressure of a plane wave is given by [11]: 
         [0000]    
       
         
           
             
               
                 
                   
                     p 
                      
                     
                       ( 
                       
                         r 
                         , 
                         θ 
                         , 
                         φ 
                         , 
                         k 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         n 
                         = 
                         0 
                       
                       N 
                     
                      
                     
                       
                         ∑ 
                         
                           m 
                           = 
                           
                             - 
                             n 
                           
                         
                         n 
                       
                        
                       
                         
                           i 
                           n 
                         
                          
                         
                           P 
                           
                             S 
                             0 
                           
                         
                          
                         
                           
                             
                               Y 
                               n 
                               m 
                             
                              
                             
                               ( 
                               
                                 
                                   Θ 
                                   s 
                                 
                                 , 
                                 
                                   φ 
                                   s 
                                 
                               
                               ) 
                             
                           
                           * 
                         
                          
                         
                           
                             j 
                             n 
                           
                            
                           
                             ( 
                             kr 
                             ) 
                           
                         
                          
                         
                           
                             Y 
                             n 
                             m 
                           
                            
                           
                             ( 
                             
                               θ 
                               , 
                               φ 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0000]    using the N3D normalization scheme for spherical harmonics, and strictly A n   m  would become: 
         [0000]        A   n   m ( f )=4πi n   P   S     0   ( f )  Y   n   m (θ( f ) S , φ( f ) s )*   (6)
 
         [0000]    where P S     0   (f) is the sound pressure at the coordinate system&#39;s origin at frequency f. θ(f) s , φ(f) s  are the directions (inclination, azimuth) to the source (DoA), and * indicates a conjugate complex. Many Ambisonics formats and systems, including the B-Format and the SoundField™ microphone system, assume a plane wave encoding and decoding model and the factor in is omitted. Then A n   m  becomes: 
         [0000]        A   n   m ( f )=4 πP   S     0   ( f )  Y   n   m (θ s ( f ), φ s ( f ))*   (7)
 
         [0062]    As mentioned above,  FIG. 1   b ) depicts building blocks of a sound field analysis block SFA D . It is in principle like the Sound Field Analysis block SFA of the present invention, except that a generalized time-frequency consideration is used here, which allows using an arbitrary time window. I.e. the Sound Field Analysis is simplified to different temporal normalizations. This generalization allows using an arbitrary complex filter bank. Another generalization taken here is that the active sound field is assembled from a superposition of plane waves. All sound field parameters are functions of frequency, and they can be calculated for each center frequency of filter bank band k. The dependency of f k  from k is omitted in the following detail description. 
         [0063]    Active Intensity is described next. 
         [0064]    The active Intensity I a (f) is defined according to (see [5]): 
         [0000]        I   α =Re{ P ( f )* U ( f )}  (8)
 
         [0065]    The unit of the active Intensity is W/m 2 =N/(ms). P(f)* is the conjugate complex sound pressure (in Pascal=1 N/m 2 ) and U(f) is particle velocity in m/s a vector in three Cartesian dimensions. Re{.} denotes the real part. Other formulations of the active intensity use an additional factor of ½, as in [11], which would then lead to an additional factor for eq.(13). B-Format signal W is proportional to the sound pressure signal P(f), and the signals X(f)=[X(f),Y(f),Z(f)] T  are proportional to the sound velocity U. 
         [0000]    
       
         
           
             
               
                 
                   
                     U 
                      
                     
                       ( 
                       f 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       
                         Z 
                         0 
                       
                     
                      
                     
                       ( 
                       
                         
                           
                             X 
                              
                             
                               ( 
                               f 
                               ) 
                             
                           
                            
                           
                             e 
                             x 
                           
                         
                         + 
                         
                           
                             Y 
                              
                             
                               ( 
                               f 
                               ) 
                             
                           
                            
                           
                             e 
                             y 
                           
                         
                         + 
                         
                           
                             Z 
                              
                             
                               ( 
                               f 
                               ) 
                             
                           
                            
                           
                             e 
                             z 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where e, are the unit vectors of the Cartesian coordinate axes and e u  of the unit vector direction of the propagating plane wave. Z 0  is the characteristic impedance (the product of speed of sound and the density of air Z 0 =ρ 0 c). Then the active Intensity I a  can be expressed using B-Format signals as (see [5]): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       I 
                       a 
                     
                      
                     
                       ( 
                       f 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         2 
                       
                       
                         Z 
                         0 
                       
                     
                      
                     Re 
                      
                     
                       { 
                       
                         
                           W 
                            
                           
                             ( 
                             f 
                             ) 
                           
                         
                         * 
                         
                           X 
                            
                           
                             ( 
                             f 
                             ) 
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where the factor √{square root over (2)} respects the scaling of the W coefficient within the B Format; denotes conjugate complex. I a (f), X(f) are a vector functions of frequency in Cartesian coordinates. 
         [0066]    Direction of Arrival is described next. 
         [0067]    The unit vector of the active Intensity e l (f)=[e lx (f),e ly (f) e lz (f)] T  is given by: e l (f)=I a (f)/∥I a (f)∥ The azimuth angle of DoA is given in rad by: 
         [0000]    
       
         
           
             
               
                 
                   
                     φ 
                      
                     
                       ( 
                       f 
                       ) 
                     
                   
                   = 
                   
                     atan 
                      
                     
                         
                     
                      
                     2 
                      
                     
                       ( 
                       
                         
                           
                             e 
                             Iy 
                           
                            
                           
                             ( 
                             f 
                             ) 
                           
                         
                         
                           
                             e 
                             Ix 
                           
                            
                           
                             ( 
                             f 
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where I a i (f) are the Cartesian components of I a (f) and a tan2 is the four-quadrant inverse tangent. The elevation angle θ(f) can be calculated by: 
         [0000]    
       
         
           
             
               
                 
                   
                     θ 
                      
                     
                       ( 
                       f 
                       ) 
                     
                   
                   = 
                   
                     atan 
                      
                     
                         
                     
                      
                     2 
                      
                     
                       ( 
                       
                         
                           
                             
                               
                                 
                                   e 
                                   Ix 
                                 
                                  
                                 
                                   ( 
                                   f 
                                   ) 
                                 
                               
                               2 
                             
                             + 
                             
                               
                                 
                                   e 
                                   Iy 
                                 
                                  
                                 
                                   ( 
                                   f 
                                   ) 
                                 
                               
                               2 
                             
                           
                         
                         
                           
                             e 
                             Iz 
                           
                            
                           
                             ( 
                             f 
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0068]    Diffuseness is described next. 
         [0069]    The energy density, i.e. the sound energy per unit volume (in physical units N/m 2 =kg m/s 2 1/m 2 ), of the sound field is described by [5]: 
         [0000]    
       
         
           
             
               
                 
                   
                     E 
                      
                     
                       ( 
                       f 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         ρ 
                         0 
                       
                       2 
                     
                      
                     
                       ( 
                       
                         
                           
                             Z 
                             0 
                             
                               - 
                               2 
                             
                           
                            
                           
                             
                                
                               
                                 P 
                                  
                                 
                                   ( 
                                   f 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                         
                         + 
                         
                           
                              
                             
                               U 
                                
                               
                                 ( 
                                 f 
                                 ) 
                               
                             
                              
                           
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where ||U|| describes the matrix norm 2, the Euclidean length of vectors. 
         [0070]    For Ambisonics signals, 1 st  order/B-Format becomes: 
         [0000]    
       
         
           
             
               
                 
                   
                     E 
                      
                     
                       ( 
                       f 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         ρ 
                         0 
                       
                       
                         Z 
                         0 
                       
                     
                      
                     
                       ( 
                       
                         
                           
                              
                             
                               W 
                                
                               
                                 ( 
                                 f 
                                 ) 
                               
                             
                              
                           
                           2 
                         
                         + 
                         
                           
                             
                                
                               
                                 X 
                                  
                                 
                                   ( 
                                   f 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
         [0071]    In the following, dependency of frequency in the notation is dropped for better readability. The Diffuseness estimation ψ is defined as [5]: 
         [0000]    
       
         
           
             
               
                 
                   Ψ 
                   = 
                   
                     
                       
                         
                            
                            
                           
                             ( 
                             E 
                             ) 
                           
                         
                         - 
                         
                           
                              
                             
                                
                                
                               
                                 ( 
                                 
                                   I 
                                   a 
                                 
                                 ) 
                               
                             
                              
                           
                           / 
                           c 
                         
                       
                       
                          
                          
                         
                           ( 
                           E 
                           ) 
                         
                       
                     
                     = 
                     
                       1 
                       - 
                       
                         
                            
                           
                              
                              
                             
                               ( 
                               
                                 I 
                                 a 
                               
                               ) 
                             
                           
                            
                         
                         
                           c 
                            
                           
                               
                           
                            
                           
                              
                              
                             
                               ( 
                               E 
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
         [0000]               is the expected value operator which can be implemented using temporal averaging realized by a windowed average or a first order by an IIR filter. ψ expresses the contribution of the non-active energy parts of the sound field. A value of 1 describes a completely diffuse sound field (no kinetic energy contribution), and a value of 0 a fully active sound field. Using B-format signals, the Diffuseness can be expressed as: 
         [0000]    
       
         
           
             
               
                 
                   Ψ 
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           2 
                         
                          
                         
                            
                           
                              
                             ( 
                             
                               Re 
                                
                               
                                 { 
                                 
                                   W 
                                   * 
                                   X 
                                 
                                 ) 
                               
                             
                             } 
                           
                            
                         
                       
                       
                          
                         ( 
                         
                           
                             
                                
                               W 
                                
                             
                             2 
                           
                           + 
                           
                             
                               
                                  
                                 X 
                                  
                               
                               2 
                             
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
         [0072]    An alternative realization of the Diffuseness estimate [1] is given by 
         [0000]    
       
         
           
             
               
                 
                   Ψ 
                   = 
                   
                     
                       1 
                       - 
                       
                         
                            
                           
                              
                              
                             
                               ( 
                               
                                 I 
                                 a 
                               
                               ) 
                             
                           
                            
                         
                         
                            
                            
                           
                             ( 
                             
                                
                               
                                 I 
                                 a 
                               
                                
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
         [0073]    Average filtering is described next. 
         [0074]    The Diffuseness estimate and the DoA directions require temporal averaging. To approximate the expectation y≅         (x), a smoothing filter output is defined by [12]: 
         [0000]        y ( n, k )=(1 −g ) x ( n, k )+ g y ( n− 1,  k )   (18)
 
         [0000]    where x(n, k) is the input and y(n−1, k) the sample (transform block) delayed output in filter band k. The filter parameter g is given by: 
         [0000]    
       
         
           
              
             = 
             
               exp 
                
               
                 ( 
                 
                   - 
                   
                     1 
                     
                       
                         f 
                         c 
                       
                        
                       τ 
                     
                   
                 
                 ) 
               
             
           
         
       
     
         [0000]    where f c  is the sample rate of the sub-sampling filter bank. For block-based filter banks with 50% overlapping windows, f c  becomes 
         [0000]    
       
         
           
             
               
                 f 
                 c 
               
               = 
               
                 
                   f 
                   s 
                 
                 
                   N 
                   hop 
                 
               
             
             , 
           
         
       
     
         [0000]    witn hop size s hop  pang half the window size for this 50% overlap case. The time constant ti determines the characteristic of the averager. A small value is suitable when fast variations of the input signals need to be followed, a large value is suited for a long-term average. 
         [0075]    Alternative realizations exist, for example (see [10]): 
         [0000]        y ( k, n )=α x ( k, n )+(1−α) y ( k, n− 1)   (19)
 
         [0000]    with 
         [0000]    
       
         
           
             a 
             = 
             
               
                 
                   
                     N 
                     hop 
                   
                   
                     τ 
                      
                     
                         
                     
                      
                     
                       f 
                       s 
                     
                   
                 
                  
                 
                     
                 
                  
                 and 
                  
                 
                     
                 
                  
                 τ 
               
               ≥ 
               
                 
                   
                     N 
                     hop 
                   
                   
                     f 
                     s 
                   
                 
                 . 
               
             
           
         
       
     
         [0000]    Here τ is seen in absolute relation to f s . 
         [0076]    Adaptive filter with block dependent switch parameter cc and two time constants τ max , τ min  can be used for the time constant: 
         [0000]    
       
         
           
             
               
                 
                   τ 
                   = 
                   
                     
                       τ 
                       min 
                     
                     + 
                     
                       
                         
                           
                             cc 
                             max 
                           
                           - 
                           cc 
                         
                         
                           cc 
                           max 
                         
                       
                        
                       
                           
                       
                        
                       
                         ( 
                         
                           
                             τ 
                             max 
                           
                           - 
                           
                             τ 
                             min 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
         [0077]    In most cases, any 1 st  order Ambisonics recording will be a B-Format signal. A method according to the present invention derives higher order Ambisonics coefficients for an existing 1 st  order Ambisonics recording, while maintaining first order coefficient information. A Direction of Arrival (DoA) analysis is performed to derive the strongest directions over frequency. The W-channel represents a mono mix of all of these signals. The W-channel is filtered such that the diffuse parts are removed over frequency. Thus, the filtered W-channel becomes an estimate of the direct sounds over frequency. The DoA directions are used for Ambisonics encoding of the filtered W-channel signal to form a new HOA signal of a pre-assigned Ambisonics order N_order&gt;1, with O=(N order +1) 2  for 3D and O=(2N order +1) coefficients for 2D realizations. The four coefficients of the B-Format recording (i.e. 1 st  order signals) are format converted into the same format as the new Ambisonics signals, if necessary, and combined with the new coefficients to form the output signal. The resulting output HOA signal coefficients C n   m  are compiled out of the converted B-Format coefficients of zero and first order components and from the new HOA coefficients of higher order components. 
         [0078]    Processing or parts of the processing are applied in a filter bank frequency domain of the analysis filter bank. 
         [0079]    One embodiment uses a FFT based analysis filter bank. A 50% overlapping sine window is applied to 960 samples, or alternatively to e.g. 640 or 512 samples. Zero padding to left and right is used to obtain a 1024 sample FFT length. The inverse filter bank (synthesis filter bank) uses windowing and overlay add to restore a block of 480 (320, 256) samples. An alternatively usable filter bank, which uses filter bandwidths that better match human perception, is described in ISO/IEC 23003 /2007/2010 (MPEG Surround, SAOC). When using a FFT filter bank, two or more filter bands can be combined to better adapt to human perception especially for high frequencies. In one embodiment, a bandwidth of approximately a quarter of a bark is used with a granularity of one FFT-filter band, and mean values of active Intensity and energy over the combined bands are used. In various embodiments, the sound field parameters “active Intensity” and/or “energy density” are used to derive DoA angles and the Diffuseness estimate. 
         [0080]    In one embodiment, special smoothing filters according to eq.(1 8) for DoA directions and Diffuseness estimates are used; then, smoothing of the Diffuseness estimate is realized as follows (the frequency band dependency is omitted for clarity): 
         [0081]    The Diffuseness estimate according to eq.(15) is given by 
         [0000]    
       
         
           
             Ψ 
             = 
             
               1 
               - 
               
                 
                   
                      
                     
                        
                        
                       
                         ( 
                         
                           I 
                           a 
                         
                         ) 
                       
                     
                      
                   
                   
                     c 
                      
                     
                         
                     
                      
                     
                        
                        
                       
                         ( 
                         E 
                         ) 
                       
                     
                   
                 
                 . 
               
             
           
         
       
     
         [0000]    The smoothing filters of the enumerator Ĩ α ≅         ( I   α )=[         ( I   αx ),          ( I   αy ),          (I αz )] T  are realized by first order IIR filters using the same time constants for the three components. Further, the filters have double coefficients characterized by a small T min  and a large time constant τ max . Switching between time constants is performed depending on the change of ∥I α ∥ and an additional state counter cc, where I α (n) is the filter input and Ĩ α (n−1) is the filter output of previous operation. 
         [0082]    If cc==0 and ∥I α (n)∥≦∥Ĩ α (n−1)+ε 1 ∥ the coefficient with the large time constant τ max  is used. 
         [0083]    If ∥I α (n)∥&gt;∥Ĩ α (n−1)+ε 1 ∥, the coefficient characterized by the small time constant τ min  is used and cc is set to cc max  larger 1 (e.g. cc max =10). 
         [0084]    If cc&gt;0 and ∥I α (n)∥≦∥Ĩ α (n−1)+ε 1 ∥, then a time constant 
         [0000]    
       
         
           
             τ 
             = 
             
               
                 τ 
                 min 
               
               + 
               
                 
                   
                     
                       cc 
                       max 
                     
                     - 
                     cc 
                   
                   
                     cc 
                     max 
                   
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     
                       τ 
                       max 
                     
                     - 
                     
                       τ 
                       min 
                     
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    is used and cc is decremented afterwards (block processing) as long as it is unequal zero. 
         [0085]    ε 1  is a positive constant. Smoothing of energy E is performed in an analogous way, using a separate filter but the same adaptive filter structure. It is characterized by τ max , τ min  and an own cc state counter, where changes of |E(n)| are used to switch between large, small and interpolated time constants. 
         [0086]    φ(f), θ(f) are derived from the unit vector of the active Intensity e 1 (f)=I α (f)/∥I α (f)∥ by creating two complex signals: 
         [0000]      α 1   =e   lx   +ie   ly    (21)
 
         [0000]      and 
         [0000]      α 2 =√{square root over ( e   lx   2   e   ly   2 )}+i e lz    (22)
 
         [0000]    where i=√{square root over (−1)} and e lx , e ly , e lz  are the Cartesian components of the unit vector of the active Intensity. The signals α 1 , α 2  are filtered using an adaptive IIR first order filter per sub-band according to eq.(18): 
         [0000]        b   1 ( n )=(1 −g (ψ))α 1 ( n )+ g (ψ) b   1 ( n− 1)   (23)
 
         [0000]    and analogous for b 2 (n) using input α 2  (n) and the same filter parameters g(ψ) which depends on the Diffuseness ψ. The dependency may be linear: g(ψ)=(g max −g max )ψ+g min  with g min  close to zero and g max ≦1. The directional signals φ, θ can be calculated from the filter outputs as follows: 
         [0000]    
       
         
           
             
               
                 
                   φ 
                   = 
                   
                     atan 
                      
                     
                         
                     
                      
                     2 
                      
                     
                       ( 
                       
                         
                           Im 
                            
                           
                             { 
                             
                               b 
                               1 
                             
                             } 
                           
                         
                         
                           Re 
                            
                           
                             { 
                             
                               b 
                               1 
                             
                             } 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
             
               
                 
                   θ 
                   = 
                   
                     atan 
                      
                     
                         
                     
                      
                     2 
                      
                     
                       ( 
                       
                         
                           Re 
                            
                           
                             { 
                             
                               b 
                               2 
                             
                             } 
                           
                         
                         
                           Im 
                            
                           
                             { 
                             
                               b 
                               2 
                             
                             } 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
           
         
       
     
         [0087]    The embodiments described above with reference to  FIGS. 2-5  use four analysis filters for the first order coefficients denoted by W,X,Y,Z in the B-format case. A DoA and Diffuseness estimation analysis is performed using the above described adaptive smoothing filters in K frequency bands with center frequency f k . The W coefficient signal is multiplied with √{square root over (2(1−ψ(f k )))} in the case of B-Format, and in case of other normalized first order signals with √{square root over ((1−ψ(f k )))} in each frequency band to realize signal S. The DoA directions are used to Ambisonics encode signal S in frequency bands to form a new HOA signal of a pre-assigned Ambisonics order N_order&gt;1 with 0=(N order +1) 2  for 3D and 0=(2N order+1) coefficients for 2D realizations. The 0 new Ambisonics signals are denoted by B n   m . In one embodiment, the HOA encoder uses N3d or ortho-normalized spherical harmonics omitting the factor i n . A plane wave encoding scheme is used: 
         [0000]        B ( f   k )=Ξ( f   k ) S ( f   k )   (26)
 
         [0000]    where B(f k ) is a vector for each frequency band k with mid center f k  holding the 0 Ambisonics coefficients B(f k )=[B 0   0 (f k ), B 1   −1  (f k ), B 0   1 (f k ), B 1   1 (f k ), B 2   −2 (f k ), . . . ] T  and Ξ is the Mode Vector of size 0×1 holding the directional spherical harmonics: 
         [0000]      Ξ( f   i )=[ Y   0   0 (θ s ( f   k ), φ s ( f   k ))*,  Y   1   −1 (θ s ( f   k ), φ s ( f   k ))*,  Y   1   0 (θ s ( f   k ), φ s ( f   k ))*, . . . ] T .
 
         [0000]    The four coefficients of the B-Format input signal, e.g. a recording, are format converted into the same format as the new Ambisonics signals generated by the HOA encoder HOAe. This can imply adaptation to different normalization of spherical harmonics as well as optional consideration of the factor f 41 , which is sometimes included within Ambisonics coefficients, and a 3D-to-2D conversion for adapting to 2D spherical harmonics or vice versa. The converted and resorted B-Format coefficients are denoted AS, /4 - 1, A, Al with relationship: [W,Y,Z,X]→[A 0   0 , A 1   −1 , A 1   0 , A 1   1 ] and for 2D: [W,Y,X]→[A 0   0 , A 1   −1 , A 1   1 ]. 
         [0088]    The resulting HOA signal C n   m    29  is compiled out of the converted B-format signals and the new HOA coefficients B n   m , with the zero and first order components omitted: C n   m : [A 0   0 , A 1   −1 , A 1   0 , A 1   1 , B 2   −2 , B 2   −1 , B 2   0 , B 2   1 , B 2   2 , . . . ′]. The resulting HOA signal C n   m    29  has O=(N order +1) 2  components for 3D realizations, or O=(2N order +1) components for 2D realizations with C n   m : [A 0   0 , A 1   −1 , A 1   1 , B 2   −2 , B 2   2 , . . . ]. This procedure can be regarded as an order upmix for Ambisonics signals. 
         [0089]    The embodiment described above with respect to  FIG. 3  combines original coefficients with new coefficients in the time domain and uses O- 4  synthesis filters (note that the letter “O” is meant, not zero) and an additional delay to compensate for the filter bank delay. The embodiments shown in  FIG. 4-5  combine in the filter bank domain and make use of O (not zero) synthesis filters. 
         [0090]    After an order upmix according to the present invention, the new signals C n   m  can be used for several purposes, e.g. mixing with other Ambisonics content of N_order to form signal D n   m , decoding of C n   m  or D n   m  for replay using L speakers using a N_order Ambisonics decoder, transmitting and/or storing of C n   m  or D n   m  in a database, etc. In some cases, e.g. transmitting and/or storing, metadata can be used for indicating the origin and performed processing of the Ambisonics signal. 
         [0091]    While the invention is suitable for enhancing the directivity of any lower order Ambisonics signal to a respective higher order Ambisonics signal, exemplary embodiments described herein use only 1 st  order (B-format) signals for being enhanced e.g. to 2 nd  order signals. However, the same principle can be applied to enhance an Ambisonics signal of given order to any higher order, e.g. a 2 nd  order signal to a 3 rd  order signal, a 1 st  order signal to a 4 th  order signal etc. Generally, it makes no sense to generate coefficients of higher order than 4 th  order. 
         [0092]    One advantage of the invention is that it allows mixing B-format signals (such as e.g. 1 st  order microphone recordings) with higher order content to enhance the spatial reproduction accuracy when decoding the mixture. 
         [0093]    While various omissions, substitutions and changes in the apparatus and method described, in the form and details of the devices disclosed, and in their operation, may be made by those skilled in the art, it is expressly intended that all combinations of those elements that perform substantially the same function in substantially the same way to achieve the same results are within the scope of the invention. It will be understood that the present invention has been described by way of example, and each feature disclosed in the description and (where appropriate) the claims and drawings may be provided independently or in any appropriate combination. Features may, where appropriate be implemented in hardware, software, or a combination of the two. Reference numerals appearing in the claims are by way of illustration only and shall have no limiting effect on the scope of the claims. 
       CITED REFERENCES 
       [0000]    
       
         
           
             [1] Jukka Ahonen and Ville Pulkki. Diffuseness estimation using temporal variation of intensity vectors. 2009  IEEE Workshop on Applications of Signal Processing to Audio and Acoustics,  October 18-21,2009, New Peitz, N.Y. 
             [2] Peter G. Craven and Michael A. Gerzon. Coincident microphone simulation covering three dimensional space and yielding various directional outputs, 1975. 
             [3] Jérôme Daniel. Représentation de champs acoustiques, application à la transmission et a la reproduction de scènes sonores complexes dans un contexte multimédia. PhD thesis, Universite Paris 6,2001. 
             [4] Dave Malham.  Space in Music—Music in Space.  PhD thesis, University of York, April 2003. 
             [5] Juha Merimaa.  Analysis, Synthesis, and Perception of Spatial Sound—Binaural Localization Modeling and Multichannel Loudspeaker Reproduction.  PhD thesis, Helsinki University of Technology, 2006. 
             [6] M. A. Poletti. Three-dimensional surround sound systems based on spherical harmonics.  J. Audio Eng. Soc.,  53(11):1004-1025, November 2005. 
             [7] Mark Poletti. Unified description of ambisonics using real and complex spherical harmonics. In  Proceedings of the Ambisonics Symposium  2009, Graz. Austria, June 2009. 
             [8] Ville Pulkki. Virtual sound source positioning using vector base amplitude panning.  J. Audio Eng. Soc.,  45(6):456-466, June 1997. 
             [9] Ville Pulkki. Spatial Sound Reproduction with Directional Audio Coding.  J. Audio Eng. Soc.,  55(6):503-516, June 2007. 
             [10] Oliver Thiergart, Giovanni Del Galdo, Magdalena Prus, and Fabian Kuech. Three-dimensional sound field analysis with directional audio coding based on signal adaptive parameter estimators. In AES 40 TH INTERNATIONAL CONFERENCE, Tokyo, Japan, October 85â∈″10, 2010. 
             [11] Earl G. Williams.  Fourier Acoustics.  Academic Press, 1999. 
             [12] Udo Zölzer, editor.  DAFX—Digital Audio Effects.  John Wiley &amp; Sons, 2002. 
             [13] Franz Zotter.  Analysis and Synthesis of Sound Radiation with Spherical Arrays.  PhD thesis, Institute of Electronic Music and Acoustics (IEM), 2009.