By Jacob Benesty, Jingdong Chen, Israel Cohen
Recently, we proposed a totally novel and effective solution to layout differential beamforming algorithms for linear microphone arrays. because of this very versatile method, any order of differential arrays should be designed. in addition, they are often made strong opposed to white noise amplification, that is the most inconvenience in these kind of arrays. the opposite famous challenge with linear arrays is that digital steerage is not feasible.
during this ebook, we expand these kind of primary rules to round microphone arrays and express that we will layout small and compact differential arrays of any order that may be electronically urged in lots of diverse instructions and provide an excellent measure of regulate of the white noise amplification challenge, excessive directional achieve, and frequency-independent reaction. We additionally current a few functional examples, demonstrating that differential beamforming with round microphone arrays is one of the most sensible applicants for functions regarding speech enhancement (i.e., noise aid and dereverberation). the vast 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, safeguard and surveillance contexts.
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Extra info for Design of Circular Differential Microphone Arrays
M B [h (ω) , −θ] = ∗ Hm (ω) ej cos (−θ − ψm ) ∗ Hm (ω) ej cos (θ + ψm ) . 36) is veriﬁed if and only if cos (θ − ψM−m+2 ) . 40) 26 2 Problem Formulation Hm+1 (ω) = HM−m+1 (ω) , m = 1, 2, . . , M − 1. 41) We observe that in the ﬁlter h (ω) of length M , only its ﬁrst M 2 + 1 coefﬁcients need to be optimized, where x is the integer part of x. This also means that only M 2 + 1 independent constraints are possible. As a result, with a UCA of M microphones, we can design any diﬀerential array up to the order M at the steering angle θs = 0.
14 The white noise gain of the ﬁrst-order hypercardioid (with three 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. 0 f (kHz) (d) Fig. 15 The white noise gain of the ﬁrst-order supercardioid (with three 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. From all the extensive simulations presented in this chapter, we can conclude that any ﬁrst-order directivity pattern can be designed with a 3-element UCA, which can perfectly steer in three diﬀerent directions.
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 Second-Order Cardioid In the second-order cardioid, there is a one at the angle θs = 0 and two nulls at the angles θs + π/2 and θs + π. We see that θ2,1 = π/2, θ2,2 = π, β2,1 = 0, and β2,2 = 0. 6). 4 shows the patterns of the second-order cardioid with four microphones for several frequencies and two values of δ (1 and 2 cm).