Design of Circular Differential Microphone Arrays by Jacob Benesty, Jingdong Chen, Israel Cohen

By Jacob Benesty, Jingdong Chen, Israel Cohen

Recently, we proposed a very novel and effective strategy to layout differential beamforming algorithms for linear microphone arrays. because of this very versatile process, any order of differential arrays should be designed. additionally, they are often made strong opposed to white noise amplification, that's the most inconvenience in all these arrays. the opposite recognized challenge with linear arrays is that digital steerage will not be feasible.

during this booklet, we expand these kind of primary principles to round microphone arrays and convey that we will be able to layout small and compact differential arrays of any order that may be electronically advised in lots of diversified instructions and provide a very good measure of keep watch over of the white noise amplification challenge, excessive directional achieve, and frequency-independent reaction. We additionally current a few useful examples, demonstrating that differential beamforming with round microphone arrays is one of the top applicants for purposes related to speech enhancement (i.e., noise relief and dereverberation). the majority of the fabric awarded is new and should be of serious curiosity to engineers, scholars, and researchers operating with microphone arrays and their functions in all kinds of telecommunications, safety and surveillance contexts.

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2 dB. 4 depict the different second-order and third-order directivity patterns discussed above for θs = 0. 19). To make the analysis of a CDMA similar to an LDMA, we assume that θs = 0. Then, we can simplify the notation by writing h (ω, θs ) = h (ω). We will discuss the more general case of any steering angle later on. , we must have B [h (ω) , θ] = B [h (ω) , −θ] . 36) 24 2 Problem Formulation 120◦ 90◦ 0 dB 120◦ 60◦ −20 dB −30 dB 30◦ −20 dB 150◦ −40 dB 0◦ 330◦ 210◦ 120◦ 270◦ (a) 90◦ 0 dB 180◦ 0◦ 210◦ 330◦ 300◦ 240◦ 60◦ 120◦ −10 dB −20 dB 150◦ −30 dB 30◦ 300◦ 90◦ 0 dB 60◦ −10 dB −30 dB 30◦ −40 dB 0◦ 210◦ 330◦ 270◦ (c) 270◦ (b) −20 dB 150◦ −40 dB 180◦ 240◦ 30◦ −30 dB −40 dB 180◦ 240◦ 60◦ −10 dB −10 dB 150◦ 90◦ 0 dB 180◦ 0◦ 210◦ 330◦ 240◦ 300◦ 270◦ (d) 300◦ Fig.

As expected, this white noise gain is worse than the one corresponding to the first-order dipole. 0 f (kHz) (d) Fig. 3 The white noise gain of the second-order dipole (with four microphones), as a function of frequency, for different values of δ: (a) δ = 1 cm, (b) δ = 2 cm, (c) δ = 3 cm, and (d) δ = 5 cm. We observe from simulations that a second-order dipole with a good compromise between the directivity factor and the white noise gain should be designed with an interelement spacing between 2 and 3 cm.

2 First-Order Cardioid In the first-order cardioid, there is a one at the angle θs = 0 and a null at the angle θs + π. 9). 4 shows the patterns of the first-order cardioid with three microphones for several frequencies and two values of δ (1 and 2 cm). These patterns are identical to the ideal pattern given in Fig. 2(b). 5 gives plots of Gdn,1 [h (ω)] [where h (ω) corresponds to the firstorder cardioid filter with three microphones], as a function of frequency, for different values of δ. This directivity factor is close to 5 dB for small values of δ but it decreases quite quickly in high frequencies when δ increases.

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