(12) United States Patent
`Elko et al.
`
`(10) Patent No.:
`(45) Date of Patent:
`
`US 8,942,387 B2
`Jan. 27, 2015
`
`USOO8942387B2
`
`(54) NOISE-REDUCING DIRECTIONAL
`MCROPHONE ARRAY
`
`(75) Inventors: Gary W. Elko, Summit, NJ (US); Jens
`M. Meyer, Fairfax, VT (US); Tomas
`Fritz Gaensler, Warren, NJ (US)
`
`(73) Assignee. MH Acoustics LLC, Summit, NJ (US)
`(*) Notice:
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`U.S.C. 154(b) by 1194 days.
`
`(21) Appl. No.:
`
`12/281,447
`
`(22) PCT Filed:
`
`Mar. 9, 2007
`
`(86). PCT No.:
`S371 (c)(1)
`C
`.
`(2), (4) Date:
`
`PCT/US2007/006093
`
`Sep. 2, 2008
`
`(87) PCT Pub. No.: WO2007/106399
`PCT Pub. Date: Sep. 20, 2007
`
`(65)
`
`Prior Publication Data
`
`US 2009/O175466A1
`
`Jul. 9, 2009
`
`Related U.S. Application Data
`(63) YUSEF, fil f EP",6
`s f e i. Nov.19,
`f , and a
`continuation-in-part of application No. 10/193,825,
`filed on Jul. 12, 2002, now Pat. No. 7,171,008.
`(Continued)
`
`(51) Int. Cl.
`H04B I5/00
`H04R 3/00
`
`(2006.01)
`(2006.015
`(Continued)
`
`(52) U.S. Cl.
`CPC .............. H04R 3/005 (2013.01); H04R 25/407
`(2013.01); G 10L 2021/02166 (2013.01); H04R
`
`2410/07 (2013.01); H04R 2430/20 (2013.01);
`H04R 2430/21 (2013.01); H04R 2430/23
`(2013.01)
`USPC ............................ 381/94.2: 381/94.1: 381/92
`(58) Field of Classification Search
`USPC ........................... 381/94.1, 94.2, 92.3,92, 56
`See application file for complete search history.
`References Cited
`U.S. PATENT DOCUMENTS
`
`(56)
`
`3,626,365 A 12/1971 Press
`4,281,551 A * 8/1981 Gaudriot et al. ................ 73/647
`(Continued)
`
`FOREIGN PATENT DOCUMENTS
`
`EP
`JP
`
`9, 2005
`1581 O26 A1
`9, 1994
`HO6-269084. A
`(Continued)
`OTHER PUBLICATIONS
`
`Olson, HF (1946), Gradient Microphones. Journal of the Acoustic
`Society of America, vol. 17. No. 3, pp. 192-198.*
`(Continued)
`Primary Examiner — Duc Nguyen
`Assistant Examiner — Kile Blair
`(74) Attorney, Agent, or Firm — Mendelsohn, Drucker &
`Dunleavy, P.C.; Steve Mendelsohn
`57
`ABSTRACT
`f e embodiment, a directional microphone array having
`(at least) two microphones generates forward and backward
`cardioid signals from two (e.g., omnidirectional) microphone
`signals. An adaptation factor is applied to the backward car
`dioid signal, and the resulting adjusted backward cardioid
`signal is subtracted from the forward cardioid signal to gen
`erate a (first-order) output audio signal corresponding to a
`beampattern having no nulls for negative values of the adap
`tation factor. After low-pass filtering, spatial noise Suppres
`sion can be applied to the output audio signal. Microphone
`arrays having one (or more) additional microphones can be
`designed to generate second- (or higher-) order output audio
`signals.
`
`55 Claims, 15 Drawing Sheets
`
`1502(1)
`O
`IC 1
`
`1502(2)
`
`IC 2
`1503(2)
`
`
`
`
`
`1510
`
`1508(1)
`1506(1)
`1505(1) S 1507(1)
`
`1518
`
`1509(2)
`1507(2)
`1505(2)
`1506(2)
`1508(2)
`1520(1)
`
`1513
`
`
`
`1514
`
`1516
`
`1520(2)
`
`Page 1 of 38
`
`GOOGLE EXHIBIT 1006
`
`

`

`US 8,942,387 B2
`Page 2
`
`Related U.S. Application Data
`(60) Provisional application No. 60/781,250, filed on Mar.
`10, 2006, provisional application No. 60/737,577,
`filed on Nov. 17, 2005, provisional application No.
`60/354,650, filed on Feb. 5, 2002.
`
`(51) Int. Cl.
`H04R 25/00
`G 10L 2 1/0216
`
`(2006.01)
`(2013.01)
`
`(56)
`
`References Cited
`
`U.S. PATENT DOCUMENTS
`
`:
`
`: :
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`5,325,872
`5,473,701
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`5,524,056
`5,602,962
`5,610,991
`5,687.241
`5,878,146
`5,982,906
`6,041,127
`6,272,229
`6,292,571
`6,339,647
`6,584,203
`6,668,062
`6,983,055
`7,242,781
`7,577,262
`7,817,808
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`2003, OO31328
`2003.0053646
`2003/014.7538
`2003/0206640
`2004/0022397
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`Killion et al.
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`Janse
`Ludvigsen
`Andersen
`Ono ............................. 381 (94.2
`Elko ............................... 381/92
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`Sjursen
`Andersen et al.
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`Luo et al.
`Luo
`Hou
`Kanamori et al.
`Konchitsky et al.
`Fischer et al.
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`... 381.93
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`381 (94.3
`Aubauer et al.
`Feng et al. ....................
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`381 (94.2
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`381 (94.3
`Solbach et all
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`
`
`
`FOREIGN PATENT DOCUMENTS
`
`10, 1994
`06-303.689
`JP
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`JP
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`JP
`2001-124621
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`JP
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`WO95/16259 A1
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`WO WO2006042540 A1
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`OTHER PUBLICATIONS
`
`F. Luo, J. Yang, C. Pavlovic, and A. Nehorai, "Adaptive null-forming
`scheme in digital hearing aids'. IEEE Trans. Signal Process., vol. 50,
`pp. 1583-1590, 2002.*
`Gary W. Elko et al., “A simple adaptive first-Order differential micro
`phone.” IEEE ASSP Workshop on New Paltz, NY, Oct. 15-18, 1995,
`XP010 154658, 4 pages.
`Markus Buck, "Aspects of First-Order Differential Microphone
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`13, No. 2, Mar. 2002, XP001 123749, pp. 115-122.
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`XP0040 16546, pp. 215-227.
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`for corresponding EP Application No. 07 752 770.3.
`
`* cited by examiner
`
`Page 2 of 38
`
`

`

`U.S. Patent
`
`Jan. 27, 2015
`
`Sheet 1 of 15
`
`US 8,942,387 B2
`
`FIG. 2
`
`
`
`4N2n (N 77-xxY
`^XX
`yx\x>-1)
`X3 M
`
`
`
`Page 3 of 38
`
`

`

`U.S. Patent
`U.S. Patent
`
`Jan. 27, 2015
`Jan. 27, 2015
`
`Sheet 2 of 15
`Sheet 2 of 15
`
`US 8,942,387 B2
`US 8,942,387 B2
`
`FIG. 3
`FIG. 3
`
`
`
`
`180
`
`
`
`Page 4 of 38
`
`Page 4 of 38
`
`

`

`U.S. Patent
`
`Jan. 27, 2015
`
`Sheet 3 of 15
`
`US 8,942,387 B2
`
`FIG. 6
`
`YPF CARDIOID-DERVED OVN AND DIPOLE
`
`- DIPOLE
`
`
`
`.
`
`61 8
`
`Page 5 of 38
`
`

`

`U.S. Patent
`
`Jan. 27, 2015
`
`Sheet 4 of 15
`
`US 8,942,387 B2
`
`FIC. 7
`700
`
`FIG. 8
`
`opt
`
`
`
`0.95
`0.9
`0.85
`0.8
`0.75
`0.7
`0.65
`0,6
`0.55
`0.5
`
`FIG. 9
`
`Page 6 of 38
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`

`

`U.S. Patent
`
`Jan. 27, 2015
`
`Sheet 5 Of 15
`
`US 8,942,387 B2
`
`FIG. 10
`
`5
`
`O
`
`-15
`
`-20
`
`10.
`
`
`
`-TURBULENT
`LACOUSTIC
`
`0.
`
`10
`FREQUENCY (Hz)
`
`FIG. 1 1
`
`(sa, Rmax)
`4.
`
`POWER RATIO SR
`
`Page 7 of 38
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`

`

`U.S. Patent
`
`Jan. 27, 2015
`
`Sheet 6 of 15
`
`US 8,942,387 B2
`
`MULTICHANNEL
`ANALYSIS
`FILTERBANK
`
`
`
`
`
`
`
`
`
`1212
`
`1214
`WIND DETECTION
`
`1216
`NEARFIELD
`DETECTION
`
`Page 8 of 38
`
`

`

`U.S. Patent
`
`Jan. 27, 2015
`
`Sheet 7 Of 15
`
`US 8,942,387 B2
`
`
`
`
`
`1202-2
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`S ARE
`SCALE
`ES
`ONSPACING 1312
`
`1314
`
`MULTICHANNEL
`ANALYSIS
`FILTERBANK
`
`1310
`
`1312
`
`NORMALIZATION BY SUMMED
`MAGNITUDE OF ALL CHANNELS
`
`1316
`
`WFOR
`eWIND
`W
`f
`
`w
`
`W
`WFOR
`BEAMFORMER
`
`
`
`1318
`THRESHOLD
`DETECTOR
`
`FRONT-END
`CALIBRATION
`
`1212
`
`WIND DETECTION
`
`NEARFIELD DETECTION
`
`Page 9 of 38
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`

`

`U.S. Patent
`
`Jan. 27, 2015
`
`Sheet 8 of 15
`
`US 8,942,387 B2
`
`FIG. 14
`1400
`
`S ARE
`SCALE
`FACTORS
`DEPENDENT
`ONSPACING 1412
`
`1414
`
`1410
`
`1412
`
`1418
`THRESHOLD
`DETECTOR
`
`BEAMFORMER
`
`WIND DETECTION
`
`NEARFIELD DETECTION
`
`MULTICHANNEL
`ANALYSIS
`FILTERBANK
`
`FRONT-END
`CALIBRATION
`
`
`
`
`
`
`
`
`
`Page 10 of 38
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`

`

`U.S. Patent
`
`Sheet 9 Of 15
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`US 8,942,387 B2
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`
`
`(Z)
`
`M MOTS
`
`M MOTS
`M ISWE
`
`
`
`
`
`
`
`
`
`
`
`
`
`Page 11 of 38
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`

`

`2015 Jan. 27
`
`Jan. 27, 2015
`
`Sheet 10 of 15
`Sheet 10 of 15
`
`US 8,942,387 B2
`US 8,942,387 B2
`
`JIVaanvo
`
`8191
`
`dal
`
`U.S. Patent
`U.S. Patent
`
`
`
`GI
`9 /
`OA
`
`0091
`
`Page 12 of 38
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`Page 12 of 38
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`U.S. Patent
`
`Jan. 27, 2015
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`Sheet 11 of 15
`
`US 8,942,387 B2
`
`Z
`/
`
`M MOTS
`
`M ISW] M MOTS
`
`| 01W C
`
`Z OIW
`
`Page 13 of 38
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`

`

`U.S. Patent
`
`Jan. 27, 2015
`
`Sheet 12 of 15
`
`US 8,942,387 B2
`
`
`
`??R? 8 / "f)IJI
`
`M MOTS
`
`M MOTS
`M ISWE
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`Z OIW
`
`Page 14 of 38
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`

`

`U.S. Patent
`
`Jan. 27, 2015
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`Sheet 13 of 15
`
`US 8,942,387 B2
`
`FIG. 19
`
`
`
`FIG. 20
`
`Page 15 of 38
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`

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`U.S. Patent
`U.S. Patent
`
`Page 16 of 38
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`Jan. 27, 2015
`Jan. 27, 2015
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`Sheet 14 of 15
`Sheet 14 of 15
`
`FIG.27
`
`US 8,942,387 B2
`US 8,942,387 B2
`
`cBB
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`s
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`
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`ce
`m
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`
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`
`C
`
`Page 16 of 38
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`

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`U.S. Patent
`
`Jan. 27, 2015
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`Sheet 15 Of 15
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`US 8,942,387 B2
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`
`
`puZ
`
`M MOTS
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`Page 17 of 38
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`

`

`1.
`NOISE-REDUCING DIRECTIONAL
`MICROPHONE ARRAY
`
`US 8,942,387 B2
`
`CROSS-REFERENCE TO RELATED
`APPLICATIONS
`
`This application is a continuation-in-part of PCT patent
`application no. PCT/US06/44427, filed on Nov. 15, 2006,
`which (i) claimed the benefit of the filing date of U.S. provi
`sional application No. 60/737,577, filed on Nov. 17, 2005,
`and (ii) was itself a continuation-in-part of U.S. patent appli
`cation Ser. No. 10/193,825, filed on Jul. 12, 2002 and issued
`on Jan. 30, 2007 as U.S. Pat. No. 7,171,008, which claimed
`the benefit of the filing date of U.S. provisional application
`No. 60/354,650, filed on Feb. 5, 2002, the teachings of all of
`which are incorporated herein by reference. This application
`also claims the benefit of the filing date of U.S. provisional
`application No. 60/781,250, filed on Mar. 10, 2006 the teach
`ings of which are incorporated herein by reference.
`
`10
`
`15
`
`BACKGROUND OF THE INVENTION
`
`1. Field of the Invention
`The present invention relates to acoustics, and, in particu
`lar, to techniques for reducing wind-induced noise in micro
`phone systems, such as those in hearing aids and mobile
`communication devices, such as laptop computers and cell
`phones.
`2. Description of the Related Art
`Wind-induced noise in the microphone signal input to
`mobile communication devices is now recognized as a seri
`ous problem that can significantly limit communication qual
`ity. This problem has been well known in the hearing aid
`industry, especially since the introduction of directionality in
`hearing aids.
`Wind-noise sensitivity of microphones has been a major
`problem for outdoor recordings. Wind noise is also now
`becoming a major issue for users of directional hearing aids as
`well as cell phones and hands-free headsets. A related prob
`lem is the Susceptibility of microphones to the speechjet, or
`flow of air from the talker's mouth. Recording studios typi
`cally rely on special windscreen socks that either cover the
`microphone or are placed between the talker and the micro
`phone. For outdoor recording situations where wind noise is
`an issue, microphones are typically shielded by windscreens
`45
`made of a large foam or thick fuzzy material. The purpose of
`the windscreen is to eliminate the airflow over the micro
`phone's active element, but allow the desired acoustic signal
`to pass without any modification.
`
`25
`
`30
`
`35
`
`40
`
`50
`
`SUMMARY OF THE INVENTION
`
`Certain embodiments of the present invention relate to a
`technique that combines a constrained microphone adaptive
`beam former and a multichannel parametric noise Suppression
`scheme to allow for a gradual transition from (i) a desired
`directional operation when noise and wind conditions are
`benign to (ii) non-directional operation with increasing
`amount of wind-noise Suppression as the environment tends
`to higher wind-noise conditions.
`In one possible implementation, the technique combines
`the operation of a constrained adaptive two-element differen
`tial microphone array with a multi-microphone wind-noise
`Suppression algorithm. The main result is the combination of
`these two technological Solutions. First, a two-element adap
`tive differential microphone is formed that is allowed to
`adjust its directional response by automatically adjusting its
`
`55
`
`60
`
`65
`
`2
`beampattern to minimize wind noise. Second, the adaptive
`beam former output is fed into a multichannel wind-noise
`Suppression algorithm. The wind-noise Suppression algo
`rithm is based on exploiting the knowledge that wind-noise
`signals are caused by convective airflow whose speed of
`propagation is much less than that of desired propagating
`acoustic signals. It is this unique combination of both a con
`strained two-element adaptive differential beam former with
`multichannel wind-noise suppression that offers an effective
`Solution for mobile communication devices in varying acous
`tic environments.
`In one embodiment, the present invention is a method for
`processing audio signals. First and second cardioid signals
`are generated from first and second microphone signals. A
`first adaptation factor is generated and applied to the second
`(e.g., backward) cardioid signal to generate an adapted sec
`ond cardioid signal. The first (e.g., forward) cardioid signal
`and the adapted second cardioid signal are combined to gen
`erate a first output audio signal corresponding to a first beam
`pattern having no nulls for at least one value of the first
`adaptation factor.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`Other aspects, features, and advantages of the present
`invention will become more fully apparent from the following
`detailed description, the appended claims, and the accompa
`nying drawings in which like reference numerals identify
`similar or identical elements.
`FIG. 1 illustrates a first-order differential microphone:
`FIG. 2(a) shows a directivity plot for a first-order array
`having no nulls, while FIG. 2(b) shows a directivity plot for a
`first-order array having one null;
`FIG.3 shows a combination of two omnidirectional micro
`phone signals to obtain back-to-back cardioid signals;
`FIG. 4 shows directivity patterns for the back-to-back car
`dioids of FIG. 3;
`FIG. 5 shows the frequency responses for signals incident
`along a microphone pair axis for a dipole microphone, a
`cardioid-derived dipole microphone, and a cardioid-derived
`omnidirectional microphone;
`FIG. 6 shows a block diagram of an adaptive differential
`microphone;
`FIG. 7 shows a block diagram of the back end of a fre
`quency-selective adaptive first-order differential micro
`phone;
`FIG. 8 shows a linear combination of microphone signals
`to minimize the output power when wind noise is detected;
`FIG. 9 shows a plot of Equation (41) for values of OsCs1
`for no noise;
`FIG. 10 shows acoustic and turbulent difference-to-sum
`power ratios for a pair of omnidirectional microphones
`spaced at 2 cm in a convective fluid flow propagating at 5 m/s;
`FIG. 11 shows a three-segment, piecewise-linear Suppres
`sion function;
`FIG. 12 shows a block diagram of a microphone amplitude
`calibration system for a set of microphones;
`FIG. 13 shows a block diagram of a wind-noise detector;
`FIG. 14 shows a block diagram of an alternative wind
`noise detector;
`FIG.15 shows a block diagram of an audio system, accord
`ing to one embodiment of the present invention
`FIG.16 shows a block diagram of an audio system, accord
`ing to another embodiment of the present invention;
`FIG.17 shows a block diagram of an audio system, accord
`ing to yet another embodiment of the present invention;
`
`Page 18 of 38
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`

`

`US 8,942,387 B2
`
`3
`FIG. 18 shows a block diagram of an audio system 1800,
`according to still another embodiment of the present inven
`tion;
`FIG. 19 shows a block diagram of a three-element array:
`FIG. 20 shows a block diagram of an adaptive second-order
`array differential microphone utilizing fixed delays and three
`omnidirectional microphone elements;
`FIG. 21 graphically illustrates the associated directivity
`patterns of signals C(t), C(t), and C(t) as described in
`Equation (62), and
`10
`FIG. 22 shows a block diagram of an audio system com
`bining a second-order adaptive microphone with a multichan
`nel spatial noise Suppression (SNS) algorithm.
`
`4
`difference between two closely spaced microphones. This
`specific case results in a dipole directivity pattern cos(0) as
`can easily be seen in Equation (2). However, any first-order
`differential microphone pattern can be written as the sum of a
`Zero-order (omnidirectional) term and a first-order dipole
`term (cos(0)). A first-order differential microphone implies
`that wis-W. Thus, a first-order differential microphone has
`a normalized directional pattern Ethat can be written accord
`ing to Equation (3) as follows:
`
`(3)
`E(0)=Cit(1-C)cos(0)
`where typically OsCs1, such that the response is normalized
`to have a maximum value of 1 at 0–0, and for generality, the
`it indicates that the pattern can be defined as having a maxi
`mum either at 0=0 or 0–1. One implicit property of Equation
`(3) is that, for OsCs1, there is a maximum at 0–0 and a
`minimum at an angle between JL/2 and L. For values of
`0.5<Cs1, the response has a minimum at It, although there is
`no Zero in the response. A microphone with this type of
`directivity is typically called a “sub-cardioid microphone.
`FIG. 2(a) shows an example of the response for this case. In
`particular, FIG. 2(a) shows a directivity plot for a first-order
`array, where C=0.55.
`When C. 0.5, the parametric algebraic equation has a spe
`cific form called a cardioid. The cardioid pattern has a zero
`response at 0=180°. For values of 0s.O.s0.5, there is a null at:
`
`full = cos
`
`--.
`a - 1
`
`(4)
`
`FIG. 2(b) shows a directional response corresponding to
`C=0.5 which is the cardioid pattern. The concentric rings in
`the polar plots of FIGS. 2(a) and 20h) are 10 dB apart.
`A computationally simple and elegant way to form a gen
`eral first-order differential microphone is to form a scalar
`combination of forward-facing and backward-facing cardioid
`signals. These signals can be obtained by using both solutions
`in Equation (3) and setting C-0.5. The sum of these two
`cardioid signals is omnidirectional (since the cos(0) terms
`subtract out), and the difference is a dipole pattern (since the
`constant term C. Subtracts out).
`FIG.3 shows a combination of two omnidirectional micro
`phones 302 to obtain back-to-back cardioid microphones.
`The back-to-back cardioid signals can be obtained by a
`simple modification of the differential combination of the
`omnidirectional microphones. See U.S. Pat. No. 5,473,701,
`the teachings of which are incorporated herein by reference.
`Cardioid signals can be formed from two omnidirectional
`microphones by including a delay (T) before the subtraction
`(which is equal to the propagation time (dlc) between micro
`phones for Sounds impinging along the microphone pair
`axis).
`FIG. 4 shows directivity patterns for the back-to-back car
`dioids of FIG. 3. The solid curve is the forward-facing car
`dioid, and the dashed curve is the backward-facing cardioid.
`A practical way to realize the back-to-back cardioid
`arrangement shown in FIG. 3 is to carefully choose the spac
`ing between the microphones and the sampling rate of the
`A/D converter to be equal to some integer multiple of the
`required delay. By choosing the sampling rate in this way, the
`cardioid signals can be made simply by combining input
`signals that are offset by an integer number of samples. This
`approach removes the additional computational cost of inter
`polation filtering to obtain the required delay, although it is
`relatively simple to compute the interpolation if the sampling
`
`DETAILED DESCRIPTION
`
`15
`
`Differential Microphone Arrays
`A differential microphone is a microphone that responds to
`spatial differentials of a scalar acoustic pressure field. The
`order of the differential components that the microphone
`responds to denotes the order of the microphone. Thus, a
`microphone that responds to both the acoustic pressure and
`the first-order difference of the pressure is denoted as a first
`order differential microphone. One requisite for a micro
`phone to respond to the spatial pressure differential is the
`implicit constraint that the microphone size is Smaller than
`the acoustic wavelength. Differential microphone arrays can
`be seen directly analogous to finite-difference estimators of
`continuous spatial field derivatives along the direction of the
`microphone elements. Differential microphones also share
`strong similarities to Superdirectional arrays used in electro
`magnetic antenna design. The well-known problems with
`implementation of Superdirectional arrays are the same as
`those encountered in the realization of differential micro
`phone arrays. It has been found that a practical limit for
`differential microphones using currently available transduc
`ers is at third-order. See G. W. Elko, “Superdirectional Micro
`phone Arrays. Acoustic Signal Processing for Telecommu
`nication, Kluwer Academic Publishers, Chapter 10, pp. 181
`237, March, 2000, the teachings of which are incorporated
`herein by reference and referred to herein as “Elko-1.”
`First-Order Dual-Microphone Array
`FIG. 1 illustrates a first-order differential microphone 100
`having two closely spaced pressure (i.e., omnidirectional)
`microphones 102 spaced at a distanced apart, with a plane
`wave S(t) of amplitude S and wavenumber k incident at an
`angle 0 from the axis of the two microphones.
`The output m,(t) of each microphone spaced at distanced
`for a time-harmonic plane wave of amplitude S and fre
`quency coincident from angle 0 can be written according to
`the expressions of Equation (1) as follows:
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`m(r)=Sejatika cos(9)2
`(1)
`The output E(0,t) of a weighted addition of the two micro
`phones can be written according to Equation (2) as follows:
`
`55
`
`E(6, t) = win (t) + win2 (t)
`
`(2)
`
`60
`
`where w and w are weighting values applied to the first and
`second microphone signals, respectively.
`If kd-3L, then the higher-order terms (“h.o.t.” in Equation
`(2)) can be neglected. If w=-w, then we have the pressure
`
`65
`
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`

`US 8,942,387 B2
`
`5
`rate cannot be easily set to be equal to the propagation time of
`Sound between the two sensors for on-axis propagation.
`By combining the microphone signals defined in Equation
`(1) with the delay and subtraction as shown in FIG. 3, a
`forward-facing cardioid microphone signal can be written
`according to Equation (5) as follows:
`(5)
`C(kd,0)=-2iS sin(kd. 1+cos 0/2).
`Similarly, the backward-facing cardioid microphone signal
`can similarly be written according to Equation (6) as follows:
`(6)
`If both the forward-facing and backward-facing cardioids
`are averaged together, then the resulting output is given
`according to Equation (7) as follows:
`
`5
`
`10
`
`15
`
`(7)
`2)cos(kd/2 cos 0).
`For Small k.d. Equation (7) has a frequency response that is a
`first-order high-pass, and the directional pattern is omnidirec
`tional.
`The subtraction of the forward-facing and backward-fac
`ing cardioids yields the dipole response of Equation (8) as
`follows:
`
`(8)
`(kd/2 cos 0).
`A dipole constructed by simply Subtracting the two pressure
`microphone signals has the response given by Equation (9) as
`follows:
`
`(9)
`E(kd.0)=-2iS sin(Ikd/2) cos 0).
`One observation to be made from Equation (8) is that the
`dipole's first zero occurs at twice the value (kd=27t) of the
`cardioid-derived omnidirectional and cardioid-derived
`dipole term (kd. Tt) for signals arriving along the axis of the
`microphone pair.
`FIG. 5 shows the frequency responses for signals incident
`along the microphone pair axis (0–0) for a dipole micro
`phone, a cardioid-derived dipole microphone, and a cardioid
`derived omnidirectional microphone. Note that the cardioid
`derived dipole microphone and the cardioid-derived
`omnidirectional microphone have the same frequency
`response. In each case, the microphone-element spacing is 2
`cm. At this angle, the Zero occurs in the cardioid-derived
`dipole term at the frequency where kd=27t.
`Adaptive Differential Beamformer
`FIG. 6 shows the configuration of an adaptive differential
`microphone 600 as introduced in G. W. Elko and A. T.
`Nguyen Pong, “A simple adaptive first-order differential
`microphone.” Proc. 1995 IEEE ASSP Workshop on Applica
`tions of Signal Proc. to Audio and Acoustics, October 1995,
`referred to herein as “Elko-2. As represented in FIG. 6, a
`plane-wave signal s(t) arrives at two omnidirectional micro
`phones 602 at an angle 0. The microphone signals are
`sampled at the frequency 1/T by analog-to-digital (A/D) con
`verters 604 and filtered by anti-aliasing low-pass filters 606.
`In the following stage, delays 608 and subtraction nodes 610
`form the forward and backward cardioid signals C(n) and
`C(n) by Subtracting one delayed microphone signal from the
`other undelayed microphone signal. As mentioned previ
`ously, one can carefully select the spacing dand the sampling
`rate 1/T such that the required delay for the cardioid signals is
`an integer multiple of the sampling rate. However, in general,
`one can always use an interpolation filter (not shown) to form
`any general required delay although this will require more
`computation. Multiplication node 612 and subtraction node
`614 generate the unfiltered output signaly(n) as an appropri
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`55
`
`60
`
`65
`
`6
`ate linear combination of C(n) and C(n). The adaptation
`factor (i.e., weight parameter) B applied at multiplication
`node 612 allows a solitary null to be steered in any desired
`direction. With the frequency-domain signal S(co) X,
`is
`(nT)e", the frequency-domain signals of Equations (10)
`and (11) are obtained as follows:
`
`Cecio, d)=S(j)ešo-e (":"),
`Cacio, d)=S(j)-e J's co-ed'"
`
`.kd
`
`cost
`
`cost
`
`and hence
`
`Y(ico, d) = -ji; 2iS (ico).
`sinci -- cost) Bird cost)
`
`(10)
`
`(11)
`
`A desired signal S(co) arriving from straight on (0-0) is
`distorted by the factor sin(kd). For a microphone used for a
`frequency range from about kd=27t:100 HZ-T to kd-JL/2, first
`order recursive low-pass filter 616 can equalize the men
`tioned distortion reasonably well. There is a one-to-one rela
`tionship between the adaptation factor B and the null angle 0,
`as given by Equation (12) as follows:
`
`sin- (1 + cost)
`2
`p3 = kd
`sin
`(1 - cosé)
`
`(12)
`
`Since it is expected that the sound field varies, it is of
`interest to allow the first-order microphone to adaptively
`compute a response that minimizes the output under a con
`straint that signals arriving from a selected range of direction
`are not impacted. An LMS or Stochastic Gradient algorithm is
`a commonly used adaptive algorithm due to its simplicity and
`ease of implementation. An LMS algorithm for the back-to
`back cardioid adaptive first-order differential array is given in
`U.S. Pat. No. 5,473,701 and in Elko-2, the teachings of both
`of which are incorporated herein by reference.
`Subtraction node 614 generates the unfiltered output signal
`y(n) according to Equation (13) as follows:
`
`Squaring Equation (13) results in Equation (14) as follows:
`y(t)=c, f(t)-2?c.(t)ca(t)+fce(t).
`(14)
`The steepest-descent algorithm finds a minimum of the error
`surface Ey(t) by stepping in the direction opposite to the
`gradient of the Surface with respect to the adaptive weight
`parameter B. The steepest-descent update equation can be
`written according to Equation (15) as follows:
`
`dELy(t)
`d p3
`
`(15)
`
`where u is the update step-size and the differential gives the
`gradient of the error surface Ey(t) with respect to B. The
`quantity that we want to minimize is the mean of y(t) but the
`LMS algorithm uses the instantaneous estimate of the gradi
`
`Page 20 of 38
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`

`US 8,942,387 B2
`
`7
`ent. In other words, the expectation operation in Equation
`(15) is not applied and the instantaneous estimate is used.
`Performing the differentiation yields Equation (16) as fol
`lows:
`
`dy(t)
`
`(16)
`
`10
`
`15
`
`Thus, we can write the LMS update equation according to
`Equation (17) as follows:
`
`Typically the LMS algorithm is slightly modified by nor
`malizing the update size and adding a regularization constant
`e. Normalization allows explicit convergence bounds foru to
`be set that are independent of the input power. Regularization
`stabilizes the algorithm when the normalized input power in
`c. becomes too small. The LMS version with a normalized LL
`is therefore given by Equation (18) as follows:
`
`f31 = f3, +24ty(t)
`
`25
`
`(18)
`
`8
`FIG. 7 shows a block diagram of the back end 700 of a
`frequency-selective first-order differential microphone. In
`FIG. 7, subtraction node 714, low-pass filter 716, and adap
`tation block 718 are analogous to subtraction node 614, low
`pass filter 616, and adaptation block 618 of FIG. 6. Instead of
`multiplication node 612 applying adaptive weight factor B.
`filters 712 and 713 decompose the forward and backward
`cardioid signals as a linear combination of bandpass filters of
`a uniform filterbank. The uniform filterbank is applied to both
`the forward cardioid signal c(n) and the backward cardioid
`signal c(n), where m is the Subband index number and G2 is
`the frequency.
`In the embodiment of FIG. 7, the forward and backward
`cardioid signals are generated in the time domain, as shown in
`FIG. 6. The time-domain cardioid signals are then converted
`into a Subband domain, e.g., using a multichannel filterbank,
`which implements the processing of elements 712 and 713. In
`this embodiment, a different adaptation factor B is generated
`for each different subband, as indicated in FIG. 7 by the
`“thick” arrow from adaptation block 718 to element 713.
`In principle, we could directly use any standard adaptive
`filter algorithm (LMS, FAP, FTF, RLS ...) for the adjustment
`of h(n), but it would be challenging to easily incorporate the
`constraint H(CO)s1. Therefore and in view of a computation
`ally inexpensive Solution, we realize H(CO) as a linear com
`bination of band-pass filters of a uniform filterbank. The
`filterbank consists of M complex band-passes that are modu
`lated versions of a low-pass filter W(c)). That filter is com
`monly referred to as prototype filter. See R. E. Crochiere and
`L. R. Rabiner, Multirate Digital Signal Processing, Prentice
`Hall, Englewood Cliffs, N.J., (1983), and P. P. Vaidyanathan,
`Multirate Systems and Filter Banks, Prentice Hall, Engle
`wood Cliffs, N.J., (1993), the teachings of both of which are
`incorporated herein by reference. Since h(n) and H(()) have
`to be real, we combine band-passes with conjugate complex
`impulse responses. For reasons of simplicity, we choose Mas
`a power of two so that we end up with M/2+1 channels. The
`coefficients for f3, ... B
`control the position of the null or
`minimum in the different subbands. The B's form a linear
`combiner and will be adjusted by an NLMS-type algorithm.
`It is desirable to design W(co) such that the constraint
`H(CO)51 will be met automatically for all frequencies kd,
`given all coefficients fare smaller than or equal to one. The
`heuristic NLMS-type algorithm of the following Equations
`(19)-(21) is apparent:
`
`30
`
`35
`
`40
`
`45
`
`where the brackets (“K.>'') indicate a time average. One prac
`tical issue occurs when there is a desired signal arriving at
`only 0–0. In this case, B becomes undefined. A practical way
`to handle this case is to limit the power ratio of the forward
`to-back cardioid signals. In practice, limiting this ratio to a
`factor of 10 is sufficient.
`The intervals fe0.1 and Belo) are mapped onto
`0e 0.571, t) and 0e0,0.57t, respectively. For negative B, the
`directivity pattern does not contain a null. Instead, for Small
`|BI with -1 <B<0, a minimum occurs at 0=TL: the depth of
`which reduces with growing B|. For B=-1, the pattern
`becomes omnidirectional and, for B-1, the rear signals
`bec