Classifications

• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04R—LOUDSPEAKERS, MICROPHONES, GRAMOPHONE PICK-UPS OR LIKE ACOUSTIC ELECTROMECHANICAL TRANSDUCERS; ELECTRIC HEARING AIDS; PUBLIC ADDRESS SYSTEMS
  • H04R3/00—Circuits for transducers
  • H04R3/005—Circuits for transducers for combining the signals of two or more microphones
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04R—LOUDSPEAKERS, MICROPHONES, GRAMOPHONE PICK-UPS OR LIKE ACOUSTIC ELECTROMECHANICAL TRANSDUCERS; ELECTRIC HEARING AIDS; PUBLIC ADDRESS SYSTEMS
  • H04R1/00—Details of transducers, loudspeakers or microphones
  • H04R1/20—Arrangements for obtaining desired frequency or directional characteristics
  • H04R1/32—Arrangements for obtaining desired frequency or directional characteristics for obtaining desired directional characteristic only
  • H04R1/326—Arrangements for obtaining desired frequency or directional characteristics for obtaining desired directional characteristic only for microphones
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04R—LOUDSPEAKERS, MICROPHONES, GRAMOPHONE PICK-UPS OR LIKE ACOUSTIC ELECTROMECHANICAL TRANSDUCERS; ELECTRIC HEARING AIDS; PUBLIC ADDRESS SYSTEMS
  • H04R1/00—Details of transducers, loudspeakers or microphones
  • H04R1/20—Arrangements for obtaining desired frequency or directional characteristics
  • H04R1/32—Arrangements for obtaining desired frequency or directional characteristics for obtaining desired directional characteristic only
  • H04R1/40—Arrangements for obtaining desired frequency or directional characteristics for obtaining desired directional characteristic only by combining a number of identical transducers
  • H04R1/406—Arrangements for obtaining desired frequency or directional characteristics for obtaining desired directional characteristic only by combining a number of identical transducers microphones
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04R—LOUDSPEAKERS, MICROPHONES, GRAMOPHONE PICK-UPS OR LIKE ACOUSTIC ELECTROMECHANICAL TRANSDUCERS; ELECTRIC HEARING AIDS; PUBLIC ADDRESS SYSTEMS
  • H04R2201/00—Details of transducers, loudspeakers or microphones covered by H04R1/00 but not provided for in any of its subgroups
  • H04R2201/40—Details of arrangements for obtaining desired directional characteristic by combining a number of identical transducers covered by H04R1/40 but not provided for in any of its subgroups
  • H04R2201/401—2D or 3D arrays of transducers
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04R—LOUDSPEAKERS, MICROPHONES, GRAMOPHONE PICK-UPS OR LIKE ACOUSTIC ELECTROMECHANICAL TRANSDUCERS; ELECTRIC HEARING AIDS; PUBLIC ADDRESS SYSTEMS
  • H04R29/00—Monitoring arrangements; Testing arrangements
  • H04R29/004—Monitoring arrangements; Testing arrangements for microphones
  • H04R29/005—Microphone arrays
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04R—LOUDSPEAKERS, MICROPHONES, GRAMOPHONE PICK-UPS OR LIKE ACOUSTIC ELECTROMECHANICAL TRANSDUCERS; ELECTRIC HEARING AIDS; PUBLIC ADDRESS SYSTEMS
  • H04R5/00—Stereophonic arrangements
  • H04R5/027—Spatial or constructional arrangements of microphones, e.g. in dummy heads
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04S—STEREOPHONIC SYSTEMS 
  • H04S2400/00—Details of stereophonic systems covered by H04S but not provided for in its groups
  • H04S2400/15—Aspects of sound capture and related signal processing for recording or reproduction

Definitions

• the invention relates to a method and to an apparatus for processing signals of a spherical microphone array on a rigid sphere used for generating an Ambisonics representa ⁇ tion of the sound field, wherein an equalisation filter is applied to the inverse microphone array response.
• Spherical microphone arrays offer the ability to capture a three-dimensional sound field.
• One way to store and process the sound field is the Ambisonics representation.
• Ambisonics uses orthonormal spherical functions for describing the sound field in the area around the point of origin, also known as the sweet spot. The accuracy of that description is determined by the Ambisonics order N, where a finite number of Ambisonics coefficients describes the sound field.
• Ambisonics representation is that the reproduction of the sound field can be adapted individually to any given loudspeaker arrangement. Furthermore, this rep ⁇ resentation enables the simulation of different microphone characteristics using beam forming techniques at the post production .
• the B-format is one known example of Ambisonics.
• a B-format microphone requires four capsules on a tetrahedron to cap ⁇ ture the sound field with an Ambisonics order of one.
• Ambisonics of an order greater than one is called Higher Order Ambisonics (HOA)
• HOA microphones are typically spherical microphone arrays on a rigid sphere, for example the Eigenmike of mhAcoustics.
• HOA Higher Order Ambisonics
• For the Ambisonics processing the pressure distribution on the surface of the sphere is sampled by the capsules of the array. The sampled pressure is then converted to the Ambisonics representation.
• Am ⁇ bisonics representation describes the sound field, but in ⁇ cluding the impact of the microphone array.
• the impact of the microphones on the captured sound field is removed using the inverse microphone array response, which transforms the sound field of a plane wave to the pressure measured at the microphone capsules. It simulates the directivity of the capsules and the interference of the microphone array with the sound field.
• the distorted spectral power of a reconstructed Ambisonics signal captured by a spherical microphone array should be equalised.
• that distortion is caused by the spatial aliasing signal power.
• due to the noise reduction for spherical microphone arrays on a rigid sphere higher order coefficients are missing in the spheri ⁇ cal harmonics representation, and these missing coefficients unbalance the spectral power spectrum of the reconstructed signal, especially for beam forming applications.
• a problem to be solved by the invention is to reduce the distortion of the spectral power of a reconstructed Ambison ⁇ ics signal captured by a spherical microphone array, and to equalise the spectral power. This problem is solved by the method disclosed in claim 1. An apparatus that utilises this method is disclosed in claim 2.
• the inventive processing serves for determining a filter that balances the frequency spectrum of the reconstructed Ambisonics signal.
• the signal power of the filtered and re ⁇ constructed Ambisonics signal is analysed, whereby the im ⁇ pact of the average spatial aliasing power and the missing higher order Ambisonics coefficients is described for Ambi ⁇ sonics decoding and beam forming applications. From these results an easy-to-use equalisation filter is derived that balances the average frequency spectrum of the reconstructed Ambisonics signal: dependent on the used decoding coeffi ⁇ cients and the signal-to-noise ratio SNR of the recording, the average power at the point of origin is estimated.
• the equalisation filter is obtained from:
• the frequency response of the equalisation filter is formed from the square root of the fraction of a given reference power and the computed average spatial signal power at the point of origin.
• the resulting filter is applied to the spherical harmonics representation of the recorded sound field, or to the recon ⁇ structed signals.
• the design of such filter is highly compu ⁇ tational complex.
• the computational complex processing can be reduced by using the computation of con- stant filter design parameters. These parameters are con ⁇ stant for a given microphone array and can be stored in a look-up table. This facilitates a time-variant adaptive fil ⁇ ter design with a manageable computational complexity.
• the filter removes the raised average signal power at high frequencies. Furthermore, the filter balances the frequency response of a beam forming decoder in the spherical harmonics representation at low frequencies. With ⁇ out usage of the inventive filter the reconstructed sound from a spherical microphone array recording sounds unbal- anced because the power of the recorded sound field is not reconstructed correctly in all frequency sub-bands.
• the inventive method is suited for processing microphone capsule signals of a spherical microphone array on a rigid sphere, said method including the steps:
• the inventive apparatus is suited for process ⁇ ing microphone capsule signals of a spherical microphone ar ⁇ ray on a rigid sphere, said apparatus including:
• said means being adapted for converting said microphone cap- sule signals representing the pressure on the surface of said microphone array to a spherical harmonics or Ambisonics representation ATM(t);
• means being adapted for computing per wave number k an estimation of the time-variant signal-to-noise ratio SNR(k) of said microphone capsule signals, using the average source power ⁇ P 0 (k) ⁇ 2 of the piane wave recorded from said microphone array and the corresponding noise power
• - means being adapted for computing per wave number k the average spatial signal power at the point of origin for a diffuse sound field, using reference, aliasing and noise signal power components, and for forming the frequency response of an equalisation filter from the square root of the fraction of a given ref ⁇ erence power and said average spatial signal power at the point of origin,
• means being adapted for applying said adapted transfer function to said spherical harmonics representation ATM(t) using a linear filter processing, resulting in adapted directional coefficients d (t).
• Fig. 1 power of reference, aliasing and noise components from the resulting loudspeaker weight for a microphone array with 32 capsules on a rigid sphere;
• Fig. 3 average power of weight components following the op- timisation filter of Fig. 2, using a conventional
• Fig. 4 average power of the weight components after the
• Fig. 5 optimised array response for a conventional Ambison ⁇ ics decoder and an SNR(k) of 20dB;
• Fig. 6 optimised array response for a beam forming decoder and an SNR(k) of 20dB;
• Fig. 7 block diagram for the adaptive Ambisonics processing according to the invention.
• Fig. 8 average power of the resulting weight after the
• noise optimisation filter n (/c) and the filter E Q(/C) have been applied, using conventional Ambisonics de ⁇ coding, whereby the power of the optimised weight, the reference weight and the noise weight are com ⁇ pared;
• Ambisonics decoding is defined by assuming loudspeakers that are radiating the sound field of a plane wave, cf. M.A.
• f the frequency and c sound is the speed of sound.
• ⁇ dex n runs from 0 to the finite order N, whereas index m runs from —n to n for each index n.
• Equation (1) defines the conversion of the Ambisonics coef- ficients dTM(k) to the loudspeaker weights w(/2j,/c). These weights are the driving functions of the loudspeakers. The superposition of all speaker weights reconstructs the sound field .
• the decoding coefficients DTM(J2i) are describing the general Ambisonics decoding processing. This includes the conjugated complex coefficients of a beam pattern as shown in section 3 ⁇ ⁇ ⁇ ) i n Morag Agmon, Boaz Rafaely, "Beamforming for a
• the Ambisonics coefficients dTM(k) can always be decomposed into a superposition of plane waves, as described in section 3 in Boaz Rafaely, "Plane-wave decomposition of the sound field on a sphere by spherical convolution", J. Acoustical Society of America, vol.116, no.4, pages 2149-2157, 2004. Therefore the analysis can be limited to the coefficients of a plane wave impinging from a direction s :
• the coefficients of a plane wave dTM ⁇ ane (k) are defined for the assumption of loudspeakers that are radiating the sound field of a plane wave.
• the pressure at the point of origin is defined by P (k) for the wave number k .
• the conjugated complex spherical harmonics YTM( s y denote the directional coefficients of a plane wave.
• the definition of the spheri ⁇ cal harmonics YTM( S ) given in the above-mentioned M.A. Po- letti article is used.
• the spherical harmonics are the orthonormal base functions of the Ambisonics representations and satisfy
• N (N + l) 2 of Ambisonics coefficients.
• the conjugated complex spherical harmonics can be replaced by the columns of the pseudo-inverse matrix , which is obtained from the L X 0 spherical harmonics matrix Y_, where the 0 coefficients of the spherical harmonics
• YTM( ⁇ Q C ) are the row-elements of Y_, cf. section 3.2.2 in the above-mentioned Moreau/Daniel/Bertet article:
• a complete HOA processing chain for spherical microphone ar- rays on a rigid (stiff, fixed) sphere includes the estima ⁇ tion of the pressure at the capsules, the computation of the HOA coefficients and the decoding to the loudspeaker
• the description of the microphone array in the spherical harmonics representation enables the estimation of the average spectral power at the point of origin for a given decoder.
• the power for the mode matching Ambisonics decoder and a simple beam forming decoder is evaluated.
• the estimated average power at the sweet spot is used to design an equalisation filter.
• the following section describes the decomposition of w(/c) into the reference weight w ref (/c), the spatial aliasing weight w alias (/c) and a noise weight w noise (/c).
• the aliasing is caused by the sampling of the continuous sound field for a finite or ⁇ der N and the noise simulates the spatially uncorrelated signal parts introduced for each capsule.
• the spatial alias ⁇ ing cannot be removed for a given microphone array.
• the isotropic noise signal P no i se (Jl c >k) is added to simulate transducer noise, where 'isotropic' means that the noise signals of the capsules are spatially uncorrelated, which does not include the correlation in the temporal domain.
• the pressure can be separated into the pressure P Ye f(J2 c , kR) computed for the maximal order N of the microphone array and the pressure from the remaining orders, cf. section 7, equa- tion (24) in the above-mentioned Rafaely "Analysis and de ⁇ sign " article.
• the pressure from the remaining orders Paiias (Ji c , kR) is called the spatial aliasing pressure because the order of the microphone array is not sufficient to re ⁇ construct these signal components.
• the total pressure recorded at the capsule c is defined by:
• the Ambisonics coefficients dTM(k are obtained from the pres ⁇ sure at the capsules by the inversion of equation (11) given in equation (13a), cf. section 3.2.2, equation (26) of the above-mentioned Moreau/Daniel/Bertet article.
• the Ambisonics coefficients dTM(k can be separated into the reference coefficients dTM re ⁇ (k) , the aliasing coefficients d alias (/c) and the noise coefficients dTM noise (k) using equations (13a) and (12a) as shown in equations (13b) and (13c) .
• Equation (14) provides w(/c) from equations (1) and (13b), where L is the number of loudspeakers:
• Equation (14b) shows that w(/c) can also be separated into the three weights w ref (/c), w alias (/c) and noise (/c). For simplicity, the positioning error given in section 7, equation (24) of the above-mentioned Rafaely "Analysis and design " arti ⁇ cle is not considered here.
• the reference coefficients are the weights that a synthetically generated plane wave of order n would create.
• the reference pres ⁇ sure P Ye f(J2 c ,kR) from equation (12b) is substituted in equation (14a), whereby the pressure signals ⁇ are ignored (i.e. set to zero) :
• Equation (15a) can be simplified to the sum of the weights of a plane wave in the Ambisonics representation from equation (3) .
• equation (15a) can be simplified to the sum of the weights of a plane wave in the Ambisonics representation from equation (3) .
• the maximal Ambi- sonics order N supported by this array is four.
• the mode matching processing as described in the above-mentioned M.A.
• Poletti article is used to obtain the decoding coefficients DTM(J2i) for 25 uniformly distributed loudspeaker positions according to Jorg Fliege, Ulrike Maier, "A Two-Stage Approach for Computing Cubature Formulae for the Sphere", Technical report, 1996, labor Schlauer, Universitat Dortmund, Germany.
• the node numbers are shown at http: //www. mathematik . uni-dortmund . de/lsx/research/projects/fliege/nodes /nodes, html .
• the power of the reference weight w ref (/c) is constant over the entire frequency range.
• the resulting noise weight noise (/c) shows high power at low frequencies and decreases at higher frequencies.
• the noise signal or power is simulated by a normally distributed unbiased pseudo-random noise with a variance of 20dB (i.e. 20dB lower than the power of the plane wave) .
• the aliasing noise a j ias (/c) can be ignored at low frequencies but increases with rising frequency, and above 10kHz exceeds the reference power.
• the slope of the aliasing power curve depends on the plane wave direction. However, the average tendency is consistent for all directions.
• the noise signal is compensated using the method de ⁇ scribed in the European application with internal reference PD110039, filed on the same day by the same applicant and having the same inventors.
• the overall signal power is equalised under consideration of the alias ⁇ ing signal and the first processing step.
• the mean square error between the refer ⁇ ence weight and the distorted reference weight is minimised for all incoming plane wave directions.
• the weight from the aliasing signal w alias (/c) is ignored because w alias (/c) cannot be corrected after having been spatially band-limited by the order of the Ambisonics representation. This is equivalent to the time domain aliasing where the aliasing cannot be re ⁇ moved from the sampled and band-limited time signal.
• the average power of the reconstructed weight is estimated for all plane wave directions.
• a filter is described below that balances the power of the recon ⁇ structed weight to the power of the reference weight. That filter equalises the power only at the sweet spot. However, the aliasing error still disrupts the sound field represen ⁇ tation for high frequencies.
• the spatial frequency limit of a microphone array is called spatial aliasing frequency.
• fa alniaass £ 2TMR0.73 i (20) is computed from the distance of the capsules (cf. WO 03/ 061336 Al), which is approximately 5594Hz for the Eigenmike with a radius R equal to 4.2cm .
• the parameters of transfer function F n (k) depend on the number of microphone capsules and on the signal-to-noise ratio for the wave number k .
• the filter is independent of the Am- bisonics decoder, which means that it is valid for three- dimensional Ambisonics decoding and directional beam form ⁇ ing.
• the SNR(k) can be obtained from the above-mentioned European application with internal reference PD110039.
• the filter is a high-pass filter that limits the order of the Ambisonics representation for low frequencies.
• the cut-off frequency of the filter decreases for a higher SNR(k).
• the transfer functions F n (k) of the filter for an SNR(k) of 20dB are shown in Fig.
• the average power of the optimised weight w'(/c) is obtained from its squared magnitude expectation value.
• the noise weight ' noise (/c) is spatially uncorrelated to the weights w 'ref(k) and ' alias (/c) so that the noise power can be computed independently as shown in equation (23a) .
• the power of the reference and aliasing weight are derived from equation (23b).
• the combination of the equations (22), (15a) and (17) results in equation (23c) , where ' noise (/c) is ignored in equa ⁇ tion (22) .
• the expansion of the squared magnitude simplifies equations (23c) and (23d) using equation (4).
• the resulting power depends on the used decoding processing. However, for conventional three-dimensional Ambisonics de- coding it is assumed that all directions are covered by the loudspeaker arrangement. In this case the coefficients with an order greater than zero are eliminated by the sum of the decoding coefficients DTM(J2i) given in equation (23) . This means that the pressure at the point of origin is equivalent to the zero order signal so that the missing higher order coefficients at low frequencies do not reduce the power at the sweet spot.
• the power is equivalent to the sum of the squared magnitudes of DTM(J2i), so that for one loudspeaker I the power increases with the order N.
• Fig. 3 The average power components of w'(/c), obtained from the noise optimisation filter, are shown in Fig. 3 for conventional Ambisonics decoding.
• Fig. 3b shows the reference + alias power
• Fig. 3c shows the noise power
• Fig. 3a the sum of both.
• the noise power is reduced to -35dB up to a frequency of 1kHz. Above 1kHz the noise power increases linearly to -lOdB.
• the total power is raised by lOdB above 10kHz, which is caused by the alias ⁇ ing power.
• Fig. 4b shows the reference + alias power
• Fig. 4c shows the noise power
• Fig. 4a the sum of both.
• the first increase is caused by the extenuation of the higher order coeffi- cients because 3kHz is approximately the cut-off frequency of F n (k) for the fourth order coefficients shown in Fig. 2e.
• the second increase is caused by the spatial aliasing power as discussed for the Ambisonics decoding.
• Equation (26a) The real-valued equalisation filter E Q(/C) is given in equation (26a) . It compensates the average power of w'(/c) to the reference power of w ref (/c) .
• equations (23e) and (27) are used to show in equation (26b) that E Q(/C) is also a function of the SNR(k). +w' alias (/c))
• Equation (28d) it is shown that the highly complex compu- tation of E ⁇ w' rei (k) + ' alias (/c)
• Each element of these sums is a multiplication of the filter F n (/c), its conjugated complex value, the infinite sums over n' and ⁇ ' of the product of ATM,' n , and its conjugated complex value.
• the results of these sums give the constant filter design coefficients for each combination of n and n" . These coefficients are computed once for a given array and can be stored in a look-up table for a time- variant signal-to-noise ratio adaptive filter design.
• the reciprocal of the transfer function b n (kR) converts ATM(t) to the directional co ⁇ efficients d (t) , where it is assumed that the sampled sound field is created by a superposition of plane waves that were scattered on the surface of the sphere.
• the coefficients dTM(t) are representing the plane wave decomposition of the sound field described in section 3, equation (14) of the above-mentioned Rafaely "Plane-wave decomposition " arti- cle, and this representation is basically used for the transmission of Ambisonics signals.
• the optimisation transfer function F n (k) reduces the contribution of the higher order coefficients in order to remove the HOA coefficients that are covered by noise.
• the power of the reconstructed signal is equalised by the filter EQ (/C) for a known or assumed decoder processing.
• the second processing step results in a convolution of ATM(t) with the designed time domain filter.
• the resulting optimised array responses for the conventional Ambisonics decod ⁇ ing are shown in Fig. 5, and the resulting optimised array responses for the beam forming decoder example are shown in Fig. 6.
• the processing of the coefficients ATM(t) can be regarded as a linear filtering operation, where the transfer function of the filter is determined by F niarray (/c) . This can be performed in the frequency domain as well as in the time domain.
• the FFT can be used for transforming the coefficients ATM(t) to the frequency domain for the successive multiplication by the transfer function f ⁇ array CO ⁇
• the inverse FFT of the prod ⁇ uct results in the time domain coefficients d (t).
• This transfer function processing is also known as the fast convolution using the overlap-add or overlap-save method.
• the linear filter can be approximated by an FIR filter, whose coefficients can be computed from the transfer function ⁇ arra C ⁇ ) by transforming it to the time do- main with an inverse FFT, performing a circular shift and applying a tapering window to the resulting filter impulse response to smooth the corresponding transfer function.
• the linear filtering process is then performed in the time do ⁇ main by a convolution of the time domain coefficients of the transfer function ⁇ arra C ⁇ ) an d the coefficients ATM(t) for each combination of n and m.
• Fig. 7 The inventive adaptive block based Ambisonics processing is depicted in Fig. 7.
• the time do- main pressure signals P(Jl c ,t) of the microphone capsule sig ⁇ nals are converted in step or stage 71 to the Ambisonics representation ATM(t) using equation (13a), whereby the division by the microphone transfer function b n (kR) is not car- ried out (thereby ATM(t is calculated instead of dTM(k)) , and is instead carried out in step/stage 72.
• Step/stage 72 per ⁇ forms then the described linear filtering operation in the time domain or frequency domain in order to obtain the coef- ficients d (t), whereby the microphone array response is re ⁇ moved from ATM(t).
• the second processing path is used for an automatic adaptive filter design of the transfer function F narray (_k) .
• the step/stage 73 performs the estimation of the signal-to-noise ratio SNR(k) for a considered time period (i.e. block of samples) .
• the estimation is performed in the frequency domain for a finite number of discrete wave num ⁇ bers k .
• the regarded pressure signals ⁇ ( ⁇ ⁇ , t) have to be transformed to the frequency domain using for example an FFT .
• the SNR(k) value is specified by the two power signals lP n oise(k)l 2 ancl ⁇ P 0 (k) ⁇ 2 .
• P no i S e(k)l 2 of the noise signal is constant for a given array and represents the noise pro ⁇ cuted by the capsules.
• the power ⁇ Po(k) ⁇ 2 of the plane wave is estimated from the pressure signals ⁇ ( ⁇ ⁇ , t). The estimation is further described in section SNR estimation in the above- mentioned European application with internal reference
• the transfer function F narray (k) with n ⁇ N is designed in step/stage 74 in the fre ⁇ quency domain using equations (30), (26c), (21) and (10).
• the filter design can use a Wiener filter and the inverse array response or inverse transfer function l/b n (kR) .
• the filter implementation is then adapted to the corresponding linear filter processing in the time or frequency domain of step/stage 72. The results of the inventive processing are discussed in the following. Therefore, the equalisation filter EQ (/C) from equation (26c) is applied to the expectation value E ⁇ w'(k) ⁇ 2 ⁇ .
• 2 ⁇ , the reference power £ ⁇ l w ref(Ol 2 ⁇ an d the resulting noise power for the examples of the conventional Ambisonics decoding from Fig. 3 and the beam forming from Fig. 4 are discussed.
• the resulting power spectra for a conventional Ambisonics decoder are depicted in Fig. 8, and for the beam forming decoder in Fig. 9, wherein curves a) to c) show
• the power of the reference and the optimised weight are identical so that the resulting weight has a balanced fre- quency spectrum.
• the resulting signal-to- noise ratio at the sweet spot has increased for the conven ⁇ tional Ambisonics decoding and decreased for the beam form ⁇ ing decoding, compared to the given SNR(k) of 20db.
• the signal-to-noise ratio is equal to the given SNR(k) for both decoders.
• the SNR at high frequencies is greater with respect to that at low frequencies, while for the Ambisonics decoder the SNR at high frequencies is smaller with respect to that at low frequencies.
• Example beam pattern is a nar- row beam pattern that has strong high order coefficients.
• Decoding coefficients that produce beam pattern with wider beams can increase the SNR. These beams have strong coeffi ⁇ cients in the low orders. Better results can be achieved by using different decoding coefficients for several frequency bands in order to adapt to the limited order at low frequen ⁇ cies .
• optimised beam forming Other methods for optimised beam forming exist that minimise the resulting SNR, wherein the decoding coefficients DTM(J2i) are obtained by a numerical optimisation for a specific steering direction.
• the optimal modal beam forming presented in Y. Shefeng, S. Haohai, U.P. Svensson, M. Xiaochuan, J.M. Hovem, "Optimal Modal Beamforming for Spherical Microphone Arrays", IEEE Transactions on Audio, Speech, and language processing, vol.19, no.2, pages 361-371, February 2011, and the maximum directivity beam forming discussed in M. Agmon, B. Rafaely, J. Tabrikian, "Maximum Directivity Beamformer for Spherical-Aperture Microphones", 2009 IEEE Workshop on Applcations of Signal Processing to Audio and Acoustics
• the example Ambisonics decoder uses mode matching process ⁇ ing, where each loudspeaker weight is computed from the de ⁇ coding coefficients used in the beam forming example.
• the loudspeaker sig ⁇ nals have the same SNR as for the beam forming decoder example. However, on one hand the superposition of the loud ⁇ speaker signals at the point of origin results in an excel ⁇ lent SNR. On the other hand, the SNR becomes lower if the listening position moves out of the sweet spot.
• the described optimisation is produc ⁇ ing a balanced frequency spectrum with an increased SNR at the point of origin for a conventional Ambisonics decoder, i.e. the inventive time-variant adaptive filter design is advantageous for Ambisonics recordings.
• the inventive procesing can also be used for designing a time-invariant filter if the SNR of the recording can be assumed constant over the time.
• the inventive procesing can balance the resulting frequency spectrum, with the drawback of a low SNR at low frequencies.
• the SNR can be increased by selecting appropriate decoding coefficients that produce wider beams, or by adapting the beam width on the Ambisonics order of different frequency sub-bands.
• the invention is applicable to all spherical microphone re ⁇ cordings in the spherical harmonics representation, where the reproduced spectral power at the point of origin is un- balanced due to aliasing or missing spherical harmonic coef ⁇ ficients .

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