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首页信号处理视角下的差分麦克风阵列设计与性能分析
信号处理视角下的差分麦克风阵列设计与性能分析
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《研究与设计不同阵列》一书旨在从信号处理的角度系统地探讨差分麦克风阵列的设计、实现和性能分析。本书的主要目标是建立一个严谨但易懂的理论框架,涵盖第一、二、三及N阶差分麦克风阵列的设计。作者提供了详尽的实例,如双极子、卡迪奥伊德、超卡迪奥伊德、次卡迪奥伊德和四极子等标准方向性图案的形成方法。通过这些示例,读者能够深入了解不同阶数阵列在指向性图谱、方向增益因子、白噪声增益以及点源处的增益方面的性能。 书中深入讨论了差分处理与自适应波束形成之间的内在联系,这有助于增强对差分麦克风阵列高方向性增益的理解。通过这种方式,读者能够学习如何设计抵抗白噪声放大效应的阵列,确保在实际应用中的稳定性。 此外,本书属于Springer Topics in Signal Processing系列的第六卷,由Jacob Benesty教授编写,他来自加拿大魁北克大学INRS-EMT。版权方面,所有内容受Springer-Verlag Berlin Heidelberg于2013年出版,强调保留所有权利,包括翻译、重印、再利用图像、朗诵、广播、微缩胶片复制等任何形式的复制,以及电子适应、计算机软件或未来开发出的类似或不同方法。然而,对于学术评论或特定用于计算机系统输入执行的短摘除外,仅供购买者个人使用。 《研究与设计不同阵列》是一本实用的指南,对于音频工程师、信号处理专家和研究者来说,它提供了一套完整的工具和技术,帮助他们在实际应用中设计和优化具有高性能的差分麦克风阵列系统。通过阅读这本书,读者不仅能掌握理论知识,还能学会如何在嘈杂环境中提高信号的捕捉和处理能力。
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10 1 Introduction
acoustic environment and then being corrupted by some unwanted noise. A
DMA consisting of M microphones is used to pick up the signals. To estimate
the source signal, the M noisy signals are partitioned into small overlapping
frames of a few milliseconds. Each frame is transformed into the short-time
Fourier transform (STFT) domain. In each subband, a differential beam-
former is designed and applied to the multichannel signals, thereby produc-
ing an estimate of the clean signal spectrum in this subband. Finally, the
time-domain clean speech estimate is constructed using the overlap-add or
overlap-save technique with the inverse STFT. Apparently, the most crucial
step in this paradigm is the design of the differential beamformers, which is
one of the main focuses of this book.
The problem addressed in this work is of great importance from both the
theoretical and practical viewpoints. From the theoretical side, it is essen-
tial to understand the theory and principles underlying DMAs from a signal
processing perspective. On the practical side, DMAs can be used in a wide
range of applications such as teleconferencing, hands-free communications,
3D sound recording, mobile phones, hearing aids, bluetooth headphones, and
navigation systems in cars, just to name a few. Therefore, it is important to
understand the design issues of DMAs and their limitations as well as the
way to circumvent those limitations.
1.3 Organization of the Book
The material in this book is organized into seven chapters, including this
one. In the next six chapters, we attempt to cover the most basic concepts
and fundamental techniques used in the design and implementation of the
different orders of DMAs and the associated beamforming algorithms. All
is explained from a signal processing perspective. The material discussed in
these chapters is as follows.
Chapter 2 presents the general formulation of a DMA design problem. It
also introduces several basic concepts that are important and useful in the
design and evaluation of a DMA including the steering vector (for a plane
wave with the conventional anechoic and farfield model), the beampattern,
the gain in SNR, the white noise gain, the directivity factor (the SNR gain in
diffuse noise), etc. In the design of a DMA, a particularly structured matrix
called the Vandermonde matrix generally appears (explicitly or implicitly) in
the formulation. This matrix and its inverse is also discussed.
The simplest form of a DMA is the first-order one that uses only two
omnidirectional sensors. If the two microphones are properly placed, many
beampatterns, such as the dipole, cardioid, subcardioid, hypercardioid, and
supercardioid, can be formed by processing the two microphones’ outputs.
Chapter 3 is dedicated to the design of first-order DMAs. It discusses how
to form different beampatterns and studies the performance associated with
1 Introduction
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11
References 11
each beampattern. It also illustrates the impact of the sensor spacing on the
performance.
Chapter 4 is concerned with the design and implementation of second-order
DMAs. It studies how to form the popularly used beampatterns such as the
dipole, two types of cardioid, quadrupole, hypercardioid, and supercardioid.
The performance of these beamformers in terms of the SNR gain in spatially
correlated and uncorrelated noise is also presented.
Chapter 5 investigates a family of third-order DMAs. Their beampatterns
have three distinct nulls, which can be viewed as three fundamental con-
straints. By properly adjusting these constraints, different beampatterns can
be formed, leading to different performance in suppressing noise impinging
at the array from different directions. As examples, we show how to design
the hypercardioid and supercardioid beampatterns and study their SNR gain
in white, diffuse, and point source noise. We also generalize this method to
the design of N th order DMAs with N distinct nulls.
The performance of a DMA in reducing noise depends on several factors
such as the order of the DMA and the characteristics of the noise. In general,
the higher the order of the DMA, the more effective is the array in suppressing
noise. However, a high-order DMA leads to huge white noise amplification,
which is a significant barrier that prevents using them. In Chapter 6, we
show how DMAs are related to the classical adaptive beamforming technique.
From this important and useful relationship, we then derive a minimum-norm
solution for the design of a general Nth-order DMA. Unlike the traditional
way of DMA design where exactly N + 1 sensors are required to design an
Nth order DMA, the proposed approach can use more than N + 1 sensors to
design an Nth order DMA. The advantage of this technique is its robustness
against white noise amplification. The more the number of microphones, the
more robust is the DMA.
In Chapter 7, we show that the patterns of DMAs can be obtained from
the general definition of the beampattern by approximating the exponential
function with its MacLaurin’s series expansion. In other words, a directional
pattern of order N can be obtained from the MacLaurin’s series of order N,
as long as this approximation holds. In this chapter, we also show how to
design differential arrays based on this approach and their relationship to
adaptive beamforming.
References
1. J. L. Flanagan, J. D. Johnson, R. Zahn, and G. W. Elko, “Computer-steered micro-
phone arrays for sound transduction in large rooms,” J. Acoust. Soc. Amer., vol. 75,
pp. 1508-1518, Nov. 1985.
2. M. Branstein and D. B. Ward, Eds., Microphone Arrays: Signal Processing Techniques
and Applications. Berlin, Germany: Springer-Verlag, 2001.
1.3 Organization of the Book
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12
12 1 Introduction
3. J. Benesty and Y. Huang, Eds., Adaptive Signal Processing: Applications to Real-
World Problems. Berlin, Germany: Springer-Verlag, 2003.
4. Y. Huang, J. Benesty, and J. Chen, Acoustic MIMO Signal Processing. Berlin, Ger-
many: Springer-Verlag, 2006.
5. J. Benesty, J. Chen, and Y. Huang, Microphone Array Signal Processing. Berlin, Ger-
many: Springer-Verlag, 2008.
6. D. B. Ward, R. C. Williamson, and R. A. Kennedy, “Broadband microphone arrays
for speech acquisition,” Acoust. Australia, vol. 26, pp. 17-20, Apr. 1998.
7. O. L. Frost, III, “An algorithm for linearly constrained adaptive array processing,”
Proc. IEEE, vol. 60, pp. 926–935, Aug. 1972.
8. J. Benesty, J. Chen, Y. Huang, and J. Dmochowski, “On microphone-array beamform-
ing from a MIMO acoustic signal processing perspective,” IEEE Trans. Audio, Speech,
Language Process., vol. 15, pp. 1053–1065, Mar. 2007.
9. B. Widrow, P. Mantey, L. Griffiths, and B. Goode, “Adaptive antenna systems,” Proc.
IEEE, vol. 55, pp. 2143–2159, Dec. 1967.
10. J. Capon, “High resolution frequency-wavenumber spectrum analysis,” Proc. IEEE,
vol. 57, pp. 1408–1418, Aug. 1969.
11. W. F. Gabriel, “Adaptive arrays–an introduction,” Proc. IEEE, vol. 64, pp. 239–272,
Feb. 1976.
12. R. A. Monzingo and T. W. Miller, Introduction to Adaptive Arrays. New York, NY:
Wiley, 1980.
13. T. J. Shan and T. Kailath, “Adaptive beamforming for coherence signals and inter-
ference,” IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-33, pp. 527–536,
1985.
14. H. Cox, R. M. Zeskind, and M. M. Owen, “Robust adaptive beamforming,” IEEE
Trans. Acoust., Speech, Signal Process., vol. ASSP-35, pp. 1365–1376, Oct. 1987.
15. H. F. Olson, “A uni-directional ribbon microphone,” J. Acoust. Soc. Am.
,vol.3,pp.
315, 1932.
16. H. F. Olson, “Gradient microphones,” J. Acoust. Soc. Am., vol. 17, pp. 192–198, Jan.
1946.
17. G. M. Sessler and J. E. West, “Directional transducers,” IEEE Trans. Audio Electroa-
coustic., vol. 19, pp. 19–23, Mar. 1971.
18. P. Graven and M. Gerzon, “Coincident microphone simlation covering three dimen-
sional space and yielding various directional outputs,” U.S. Patent 4,042,779, Aug.
1997.
19. J. Eargle, The Microphone Book. Burlington, MA: Focal Press, 2005.
20. G. W. Elko, “Steerable and variable first order differential microphone array,” U.S.
Patent 6,041,127, Apr. 1997.
21. G. W. Elko and A.-T. N. Pong, “A steerable and variable first-order differential mi-
crophone array,” in Proc. IEEE ICASSP, 1997, pp. 223–226.
22. G. W. Elko, “Superdirectional microphone arrays,” in Acoustic Signal Processing for
Telecommunication, S. L. Gay and J. Benesty, Eds. Boston, MA: Kluwer Academic
Publishers, 2000, Chapter 10, pp. 181–237.
23. G. W. Elko and J. Meyer, “Microphone arrays,” in Springer Handbook of Speech Pro-
cessing, J. Benesty, M. M. Sondhi, and Y. Huang, Eds. Berlin: Germany, Springer-
Verlag, 2008, Chapter 50, Part I, pp. 1021–1041.
24. M. Williamsen, “Design and measurement of a dipole microphone,” AudioXpress, vol.
7, pp. 1–8, 2009.
25. H. Teutsch and G. W. Elko, “First- and second-order adaptive differential microphone
arrays,” in Proc. IWAENC, 2001.
26. J. Pekonen, “Microphone techniques for spatial sound,” in Proc. Acoustics Seminar
on Spatial Sound Modeling, 2008.
27. T. D. Abhayapala and A. Gupta, “Higher order differential-integral microphone ar-
rays,” J.Acoust.Soc.Am., vol. 127, pp. EL227–EL233, May 2010.
1 Introduction
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13
References 13
28. M. Buck and M. R¨oßler, “First order differential microphone arrays for automotive
applications,” in Proc. IWAENC, 2001.
29. J. Bitzer, K.-D. Kammeyer, and K. U. Simmer, “An alternative implementation of the
superdirective beamformer,” in Proc. IEEE WASPAA, 1999.
30. M. Buck, “Aspects of first-order differential microphone arrays in the presence of sensor
imperfections,” European Trans. Telecommunications, vol. 13, pp. 115–122, Mar.-Apr.
2002.
31. E. De Sena, H. Hacihabibo˘glu, and Z. Cvetkovi´c, “On the design and implementa-
tion of higher-order differential microphones,” IEEE Trans. Audio, Speech, Language
Process., vol. 20, pp. 162–174, Jan. 2012.
32. V. Hamacher, J. Chalupper, J. Eggers, E. Fischer, U. Kornagel, H. Puder, and U.
Rass, “Signal processing in high-end hearing aids: state of the art, challenges, and
future trends,” EURASIP J. Applied Signal Process., vol. 2005, pp. 2915–2929, Jan.
2005.
33. R. Derkx, “Optimal azimuthal steering of a first-order supperdirectional microphone
response,” in Proc. IWAENC, 2008.
34. R. N. Miles, Y. Liu, Q. Su, and E. Cui, “A silicon directional microphone with second-
order directivity,” in Proc. inter. Congress Acoust., 2007.
35. M. Kolundˇzija, C. Faller, and M. Vetterli, “Spatiotemporal gradient analysis of differ-
ential microphone arrays,” J. Audio Eng. Soc., vol. 59, pp. 20–28, Jan.-Feb. 2011.
References
![](https://csdnimg.cn/release/download_crawler_static/12567199/bg14.jpg)
15
J. Benesty and J. Chen, Study and Design of Differential Microphone Arrays,
Springer Topics in Signal Processing 6, DOI: 10.1007/978-3-642-33753-6_2,
© Springer-Verlag Berlin Heidelberg 2013
Chapter 2
Problem Formulation
In this chapter, we explain some important aspects of beamforming and differ-
ential arrays. The problem of a DMA design is formulated while we progress
in defining some useful concepts. We start with the definition of the steering
vector for a plane wave with the conventional anechoic farfield model. We
give the general definition of the beampattern as well as its expression for
directional arrays. We then derive the gain in signal-to-noise ratio (SNR),
which can be very useful in the evaluation of DMAs under different types of
noise. Finally, we discuss the Vandermonde matrix, which always appears,
explicitly or implicitly, in the design of DMAs.
2.1 Signal Model
We consider a source signal (plane wave) that propagates in an acoustic
environment (anechoic farfield model) at the speed of sound, i.e., c = 340 m/s,
and impinges on a uniform linear sensor array consisting of M omnidirectional
microphones, where the distance between two successive sensors is equal to δ
(see Fig. 2.1). The direction of the source signal to the array is parameterized
by the angle θ. In this scenario, the corresponding steering vector (of length
M) is
d (ω, cos θ)=
1 e
−ωδ cos θ/c
···e
−(M − 1)ωδ cos θ/c
T
=
1
e
−ωτ
0
cos θ
1
···
e
−ωτ
0
cos θ
M−1
T
, (2.1)
where the superscript
T
is the transpose operator, =
√
−1 is the imaginary
unit, ω =2πf is the angular frequency, f>0 is the temporal frequency,
and τ
0
= δ/c is the delay between two successive sensors at the angle θ =0
◦
.
The acoustic wavelength is λ = c/f . In DMAs [1], it is always assumed that
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