Classifications

• • 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
  • 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
  • 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
  • H04R1/40—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
  • 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 a correction 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 equalisation of the transfer function of the microphone array is a big problem for HOA recordings. If the Ambisonics representation of the array response is known, the impact can be removed by the multiplication of the Ambisonics rep- resentation with the inverse array response. However, using the reciprocal of the transfer function can cause high gains for small values and zeros in the transfer function. There ⁇ fore, the microphone array should be designed in view of a robust inverse transfer function. For example, a B-format microphone uses cardioid capsules to overcome the zeros in the transfer function of omni-directional capsules.
• the invention is related to spherical microphone arrays on a rigid sphere.
• the shading effect of the rigid sphere enables a good directivity for frequencies with a small wavelength with respect to the diameter of the array.
• the filter responses of these microphone arrays have very small values for low frequencies and high Ambisonics orders (i.e. greater than one) .
• the Ambisonics representa ⁇ tion of the captured pressure has therefore small higher or- der coefficients, which represent the small pressure differ ⁇ ence at the capsules for wave lengths that are long when compared to the size of the array.
• the pressure differences, and therefore also the higher order coefficients are af ⁇ fected by the transducer noise.
• the inverse filter response amplifies mainly the noise in ⁇ stead of the higher order Ambisonics coefficients.
• a known technique for overcoming this problem is to fade out (or high pass filter) the high orders for low frequencies (i.e. to limit there the filter gain), which on one hand de- creases the spatial resolution for low frequencies but on the other hand removes (highly distorted) HOA coefficients, thereby corrupting the complete Ambisonics representation.
• a corresponding compensation filter design that tries to solve this problem using Tikhonov regularisation filters is de- scribed in Sebastien Moreau, Jerome Daniel, Stephanie
• a Tikhonov regularisation filter minimises the squared error resulting from the limitation of the Ambisonics order.
• the Tikhonov filter requires a regularisation parameter that has to be adapted manually to the characteristics of the recorded signal by 'trial and error', and there is no analytic expression defining this parameter.
• the invention shows how to obtain automatically the regularisation parameter from the signal statistics of the microphone signals.
• a problem to be solved by the invention is to minimise noise, in particular low frequency noise, in an Ambisonics representation of the signals of a spherical microphone ar ⁇ ray arranged on a rigid sphere.
• 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 is used for computing the regularisation Tikhonov parameter in dependence of the signal-to- noise ratio of the average sound field power and the noise power of the microphone capsules, i.e. that optimisation pa- rameter is computed from the signal-to-noise ratio of the recorded microphone array signals.
• the computation of the optimisation or regularisation parameter includes the following steps:
• the filter design requires an estimation of the average power of the sound field in order to obtain the SNR of the recording.
• the estimation is derived from the simulation of the average signal power at the capsules of the array in the spherical harmonics representation.
• This estimation includes the computation of the spatial coherence of the capsule sig ⁇ nal in the spherical harmonics representation. It is known to compute the spatial coherence from the continuous repre ⁇ sentation of a plane wave, but according to the invention the spatial coherence is computed for a spherical array on a rigid sphere, because the sound field of a plane wave on the rigid sphere cannot be computed in the continuous represen- tation. I.e, according to the invention the SNR is estimated from the capsule signals.
• the order of the Ambisonics representation is optimally adapted to the SNR of the recording for each frequency sub-band. This reduces the audible noise at the reproduc ⁇ tion of the Ambisonics representation.
• the estimation of the SNR is required for the filter de ⁇ sign. It can be implemented with a low computational com- plexity by using look-up tables. This facilitates a time- variant adaptive filter design with manageable computa ⁇ tional effort.
• the directional information is partly restored for low frequencies.
• 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: means being adapted for converting said microphone cap ⁇ sule signals representing the pressure on the surface
• 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. 2 noise reduction filter for
• FIG. 3 block diagram for a block-based adaptive Ambisonics processing
• Fig. 4 average power of weight components following the op- timisation filter of Fig. 2.
• Ambisonics decoding is defined by assuming loudspeakers that are radiating the sound field of a plane wave, cf. M.A.
• the arrangement of L loudspeakers reconstructs the three- dimensional sound field stored in the Ambisonics coeffi ⁇ cients .
• the processing is carried out separately for
• dex n runs from 0 to the finite order N, whereas index m runs from —n to n for each index n.
• the total number of co ⁇ efficients is therefore
• the loudspeaker position is defined by the direction vector in spherical
• Equation (1) defines the conversion of the Ambisonics coef ⁇ ficients to the loudspeaker weights .
• weights are the driving functions of the loudspeakers. The superposition of all speaker weights reconstructs the sound field .
• decoding coefficients are describing the general
• complex spherical harmonics denote the directional coefficients of a plane wave.
• the definition of the spheri ⁇ cal harmonics 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.
• C being the total number of capsules.
• the conjugated complex spherical harmonics can be replaced by the columns of the pseudo-inverse matrix
• 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 aliasing is caused by
• the radius r is equal to the radius of the sphere R.
• the transfer function is derived from the physical principle of scattering the pressure on a rigid sphere, which means that the radial velocity vanishes on the surface of a rigid sphere. In other words, the superposition of the radial derivation of the incoming and the scattered sound field is zero, cf. section 6.10.3 of the "Fourier Acoustics" book.
• the pressure on the surface of the sphere at the posi ⁇ tion for a plane wave impinging from is given in sec
• the isotropic noise signal 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
• the total pressure recorded at the capsule c is defined by:
• the Ambisonics coefficients can be separated into the reference coefficients the aliasing coefficients
• the optimisation uses the resulting loudspeaker weight
• Equation (15) provides from equations (1) and (14b), where L is the
• Equation (15b) shows that can also be separated into the three weights .
• the reference coefficients are the weights that a synthetically generated plane wave of order n would create.
• equation (16a) the reference pres ⁇ sure from equation (13b) is substituted in equation
• Equation (16a) can be simplified to the sum of the weights of a plane wave in the Ambisonics representation from equation (3) .
• equation (16a) can be simplified to the sum of the weights of a plane wave in the Ambisonics representation from equation (3) .
• Fig. 1 shows the power of the weight components a) b) w noise (/c) and c) w alias (/c) from the resulting loudspeaker weight for a plain wave from direction for a microphone array with 32 capsules on a rigid sphere (the Eigenmike from the above-mentioned Agmon/Rafaely article has been used for the simulation) .
• Ambisonics 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 for 25 uniformly distributed loudspeaker positions ac ⁇
• the reference power w ref (/c) is constant over the entire fre ⁇ quency range.
• the resulting noise weight noise (/c) shows high power at low frequencies and decreases at higher frequen ⁇ cies.
• 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 de- pends on the plane wave direction. However, the average ten ⁇ dency is consistent for all directions.
• the two error signals w noise (/c) and w alias (/c) distort the reference weight in different frequency ranges. Furthermore, the error signals are independent of each other. Therefore it is proposed to minimise the noise signal without taking into account the alias signal.
• the mean square error between the reference weight and the distorted reference weight is minimised for all incoming plane wave directions.
• the weight from the aliasing signal w aiias(O is ignored because w alias (/c) cannot be corrected after being spatially band-limited by the order of the Ambisonics representation. This is equivalent to the time domain alias ⁇ ing where the aliasing cannot be removed from the sampled and band-limited time signal.
• the noise reduction minimises the mean squared error intro ⁇ cuted by the noise signal.
• the Wiener filter processing is used in the frequency domain for computing the frequency re- sponse of the compensation filter for each order n.
• the error signal is obtained from the reference weight and
• phase transfer function is derived by minimising the
• the power of the reference weight is obtained from
• equation (16) according to section Appendix, equation (34) of the above-mentioned Rafaely "Analysis and design " ar ⁇ ticle :
• Equation (24c) shows that the power is equal to the sum of the squared absolute HOA coefficients added up over
• the power of can be separated into the sum of the power of each order n. If this is also true for the expectation value of , the error signal can be mini-
• the capsule positions have to be nearly equally distributed on the surface of the sphere, so that the condi ⁇ tion from equation (9) is satisfied. Furthermore, the power of the noise pressure has to be constant for all capsules. Then the noise power is independent of and can be ex ⁇
• equation (25b) reduces to
• the restriction for the capsule positions is commonly ful ⁇ filled for spherical microphone arrays as the array should sample the pressure on the sphere uniformly.
• a constant noise power can always be assumed for the noise that is pro- prised by the analog processing (e.g. sensor noise or ampli ⁇ fication) and the analog-to-digital conversion for each microphone signal.
• the restrictions are valid for common spherical microphone arrays.
• the expectation value from equation (21b) is a linear super- position of the reference power and the noise power.
• the power of each weight can be separated to the sum of the power of each order n.
• the expectation value from equation (21b) can also be separated into a superposition for each order n. This means that the global minimum can be de- rived from the minimum of each order n so that one optimisa ⁇ tion transfer function can be defined for each order n:
• the transfer function is obtained from the transfer
• the transfer function depends on the number of capsules and the signal to noise ration for the wavenumber k:
• the transfer function is independent of the Ambisonics decoder, which means that it is valid for three-dimensional Ambisonics decoding and directional beam forming.
• the transfer function can also be derived from the mean squared error of the Ambisonics coefficients without taking the sum over the decoding coefficients into account. Because the power changes over time an
• adaptive transfer function can be designed from the current of the recorded signal. That transfer function design
• equation (32) in the above-mentioned Mo- reau/Daniel/Bertet article shows that the regularisation pa- rameter can be derived from equation (29c) .
• the optimised weight is computed from
• the processing of the coefficients can be regarded as a
• the FFT can be used for transforming the coefficients to
• 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 by transforming it to the time do ⁇
• nals are converted in step or stage 31 to the Ambisonics representation using equation (14a), whereby the divi-
• Step/stage 32 is instead carried out in step/stage 32.
• Step/stage 32 per ⁇ forms then the described linear filtering operation in the time domain or frequency domain in order to obtain the coefficients .
• the second processing path is used for an
• the step/stage 33 performs the estimation of the signal-to-noise ratio for a considered time period
• the value is specified by the two power signals .
• the power of the noise signal is constant for a given array and represents the noise pro ⁇ cuted by the capsules.
• the power of the plane wave has to be estimated from the pressure signals .
• the filter design comprises the design of the Wiener filter given in equation (29c) and the inverse array response or inverse transfer function .
• step/stage 32 is then adapted to the corresponding linear filter processing in the time or frequency domain of step/stage 32.
• the value is to be estimated from the recorded cap ⁇ sules signals: it depends on the average power of the plane wave and the noise power of the ⁇
• the noise power is obtained from equation (26) in a silent environment without any sound sources so that can be assumed.
• the noise power should be measured for several amplifier gains. The noise power can then be adapted to the used amplifier gain for several recordings .
• the average source power is estimated from the pres-
• the noise power has to be subtracted from the meas ⁇
• the expectation value can also be estimated for the
• equation (36b) the orthonormal condition from equation (4) can be applied to the expansion of the absolute magni ⁇ tude to derive equation (36c) . Thereby the average signal power is estimated from the cross-correlation of the spherical harmonics .
• equation (36c) the orthonormal condition from equation (4) can be applied to the expansion of the absolute magni ⁇ tude to derive equation (36c) .
• the average signal power is estimated from the cross-correlation of the spherical harmonics .
• Equation (37) The denominator from equation (37) is constant for each wave number k for a given microphone array. It can therefore be computed once for the Ambisonics order N max to be stored in a look-up table or store for each wave number k .
• the estimation of the average source power from the given capsule signals is also known from the linear microphone ar- ray processing.
• the cross-correlation of the capsule signal is called the spatial coherence of the sound field.
• the spatial coherence is determined from the continuous representation of the plane wave.
• the description of the scattered sound field on a rigid sphere is known only in the Ambisonics representation. Therefore, the presented estimation of the SNR(k) is based on a new processing that determines the spatial coherence on the sur ⁇ face of a rigid sphere.
• the average power components of w'(/c) obtained from the optimisation filter of Fig. 2 are shown in Fig. 4 for a mode matching Ambisonics decoder.
• the total power is raised by lOdB above 10kHz, which is caused by the aliasing power. Above 10kHz the HOA order of the microphone array does not sufficiently describe the pressure distribution on the surface for a sphere with a radius equal to R.
• the average power caused by the ob ⁇ tained Ambisonics coefficients is greater than the reference power .

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• 2011
  • 2011-11-11 EP EP11306471.1A patent/EP2592845A1/en not_active Withdrawn
• 2012
  • 2012-10-31 WO PCT/EP2012/071535 patent/WO2013068283A1/en not_active Ceased
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