Device and method for estimating direction of arrival

Abstract

A device for estimating Direction of Arrival (DOA) of sound from Q≥1 sound sources is provided. The device is configured to obtain a phase difference matrix, which includes measured phase difference values, each of the measured phase difference values being a measured value of a phase difference between two microphone units for a frequency bin in a range of frequencies of the sound. The device is further configured to generate a replicated phase difference matrix by replicating the measured phase difference values to other potential sinusoidal periods, calculate a DOA value for each phase difference value in the replicated phase difference matrix, and determine, as Q DOA results, the Q most prominent peak values in a histogram generated based on the calculated DOA values.

Claims

1. A device for estimating Direction of Arrival (DOA) of sound from Q >1 sound sources, the device being a component in a system comprising a plurality of microphone units, the device being configured to: obtain a phase difference matrix including measured phase difference values, each of the measured phase difference values being a measured value of a phase difference between two microphone units of the plurality of microphone units for a frequency bin in a range of frequencies of the sound, generate a replicated phase difference matrix by replicating the measured phase difference values to other potential sinusoidal periods, calculate a DOA value for each phase difference value in the replicated phase difference matrix, generate a first histogram from the calculated DOA values, select, as Q+q DOA candidates, Q+q most prominent peak values in the first histogram, wherein q=2, generate a second histogram based on the selected Q+q DOA candidates, and determine, as Q DOA results, Q most prominent peak values in the second histogram.

2. The device according to claim 1, wherein the device is further configured to: generate the replicated phase difference matrix by replicating the measured phase difference values based on a minimum aliasing frequency defined by $f_{a0}=\frac{c}{2\Delta d}$ wherein Δd denotes a distance between the two microphone units and c is a speed of the sound.

3. The device according to claim 2, wherein: the measured phase difference values in the phase difference matrix are wrapped into [−π, π], and the device is configured to generate the replicated phase difference matrix according to $C=.Math.\frac{f_i-f_{a_0}}{2f_{a_0}}.Math.$ $C_s=\left(-C,-C+1,\mathrm{.Math.},0,\mathrm{.Math.},C\right)$ $\mu \left(i,j\right)={\mu }_0\left(i\right)+2\pi C_s\left(j\right)$ $i=1,\mathrm{.Math.}N;j=1,\mathrm{.Math.}\left(2C+1\right)$ wherein μ.sub.0 denotes the phase difference matrix, μ denotes the replicated phase difference matrix, i is a frequency bin index corresponding to frequency f.sub.i, j is a replication index, and [*] denotes a ceiling function.

4. The device according to claim 3, wherein the device is further configured to: calculate the DOA values based on the formula $\theta \left(i,j\right)=\arcsin \frac{\mu \left(i,j\right)}{2\pi f\Delta d}$ wherein θ(i,j) denotes the DOA value for frequency bin index i and replication index j, μ denotes the replicated phase difference matrix and Δd denotes a distance between the two microphone units.

5. The device according to claim 1, wherein the device is further configured to: remove complex calculated DOA values, before generating the first histogram.

6. The device according to claim 1, wherein, for generating the second histogram, the device is configured to: determine, for each selected DOA candidate, its related DOA values from the calculated DOA values, generate third histograms from each selected DOA candidate and its related DOA values, and generate the second histogram by merging the third histograms of all selected DOA candidates.

7. The device according to claim 6, wherein the device is further configured to: merge the third histograms of all selected DOA candidates to generate the second histogram by, for each histogram index, using the maximum value from all the third histograms as the value of the second histogram for that histogram index.

8. The device according to claim 6, wherein the device is further configured to: determine the related DOA values of a DOA candidate by determe, as its related phase difference values, the phase difference values in the replicated phase difference matrix that are in supposed correct sinusoidal periods, and calculate its related DOA values from its related phase difference values.

9. The device according to claim 6, wherein the device is further configured to: apply a soft mask to the peak values in each of the third histograms, before merging the third histograms into the second histogram, wherein the soft mask is designed as a peak filter with a smaller width at a DOA of 0° and larger widths at DOAs of ±90°.

10. The device according to claim 9, wherein the device is further configured to: apply a low-pass filter to the second histogram, before determining the Q DOA results.

11. The device according to claim 1, wherein: each microphone unit of the two microphone units includes an array of one or more microphones, and the one or more measured phase difference values of the phase difference matrix are obtained from measured phase differences between the one or more microphones of one of the microphone units and the one or more microphones of the other one of the microphone units.

12. An apparatus for determining Direction of Arrival (DOA) of sound from Q>1 sound sources, the apparatus comprising: a device configured to: obtain a phase difference matrix including measured phase difference values, each of the measured phase difference values being a measured value of a phase difference between two microphone units of a plurality of microphone units for a frequency bin in a range of frequencies of the sound, generate a replicated phase difference matrix by replicating the measured phase difference values to other potential sinusoidal periods, calculate a DOA value for each phase difference value in the replicated phase difference matrix, generate a first histogram from the calculated DOA values, select, as Q+q DOA candidates, Q+q most prominent peak values in the first histogram, wherein q=2, generate a second histogram based on the selected Q+q DOA candidates, and determine, as Q DOA results, Q most prominent peak values in the second histogram and a sound receiver, including the two microphone units, configured to receive the sound, generate the phase difference matrix, and provide the phase difference matrix to the device.

13. A method of estimating Direction of Arrival (DOA) of sound from Q >1 sound sources, in a system comprising a plurality of microphone units, the method comprising: obtaining a phase difference matrix including measured phase difference values, each of the measured phase difference values being a measured value of a phase difference between two microphone units of the plurality of microphone units for a frequency bin in a range of frequencies of the sound, generating a replicated phase difference matrix by replicating the measured phase difference values to other potential sinusoidal periods, calculating a DOA value for each phase difference value in the replicated phase difference matrix, generating a first histogram from the calculated DOA values, selecting, as Q+q DOA candidates, Q+q most prominent peak values in the first histogram, wherein q=2, generating a second histogram based on the selected Q+q DOA candidates, and determining, as Q DOA results, Q most prominent peak values in the second histogram.

14. The device according to claim 10, wherein the low-pass filter is a Gaussian filter with a standard deviation σ according to $\sigma =\arccos \left(1-\frac{c}{f_s\Delta d}\right)$ wherein f.sub.s denotes the sampling rate.

15. The apparatus according to claim 12, wherein the device is further configured to: generate the replicated phase difference matrix by replicating the measured phase difference values based on a minimum aliasing frequency defined by $f_{a0}=\frac{c}{2\Delta d}$ wherein Δd denotes a distance between the two microphone units and c is a speed of the sound.

16. The apparatus according to claim 15, wherein: the measured phase difference values in the phase difference matrix are wrapped into [−π, π], and the device is configured to generate the replicated phase difference matrix according to $C=.Math.\frac{f_i-f_{a_0}}{2f_{a_0}}.Math.$ $C_s=\left(-C,-C+1,\mathrm{.Math.},0,\mathrm{.Math.},C\right)$ $\mu \left(i,j\right)={\mu }_0\left(i\right)+2\pi C_s\left(j\right)$ $i=1,\mathrm{.Math.}N;j=1,\mathrm{.Math.}\left(2C+1\right)$ wherein μ.sub.0 denotes the phase difference matrix, μ denotes the replicated phase difference matrix, i is a frequency bin index corresponding to frequency f.sub.i, j is a replication index, and [*] denotes a ceiling function.

17. The method according to claim 13, further comprising: generating the replicated phase difference matrix by replicating the measured phase difference values based on a minimum aliasing frequency defined by $f_{a0}=\frac{c}{2\Delta d}$ wherein Δd denotes a distance between the two microphone units and c is a speed of the sound.

18. The method according to claim 17, wherein: the measured phase difference values in the phase difference matrix are wrapped into [−π, π], and the method further comprises: generating the replicated phase difference matrix according to $C=.Math.\frac{f_i-f_{a_0}}{2f_{a_0}}.Math.$ $C_s=\left(-C,-C+1,\mathrm{.Math.},0,\mathrm{.Math.},C\right)$ $\mu \left(i,j\right)={\mu }_0\left(i\right)+2\pi C_s\left(j\right)$ $i=1,\mathrm{.Math.}N;$ $j=1,\mathrm{.Math.}\left(2C+1\right)$ wherein μ.sub.0 denotes the phase difference matrix, μ denotes the replicated phase difference matrix, i is a frequency bin index corresponding to frequency f.sub.i, j is a replication index, and [*] denotes a ceiling function.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The above described aspects and implementation forms of embodiments of the present invention will be explained in the following description of specific embodiments in relation to the enclosed drawings, in which:

(2) FIG. 1 shows a device and a method according to embodiments of the invention.

(3) FIG. 2 shows a device and an apparatus according to embodiments of the invention.

(4) FIG. 3 shows a device according to an embodiment of the invention.

(5) FIG. 4 shows technical details of a device according to an embodiment of the invention.

(6) FIG. 5 shows technical details of a device according to an embodiment of the invention.

(7) FIG. 6 shows a comparison between a histogram produced by a device according to an embodiment of the invention and a conventional histogram.

(8) FIG. 7 shows technical details of a device according to an embodiment of the invention.

(9) FIG. 8 shows technical details of a device according to an embodiment of the invention.

(10) FIG. 9 shows technical details of a device according to an embodiment of the invention.

(11) FIG. 10 shows technical details of a device according to an embodiment of the invention.

(12) FIG. 11 shows a comparison between a DOA histogram produced by a device according to an embodiment of the invention and a conventional device.

(13) FIG. 12 shows a comparison between a DOA histogram produced by a device according to an embodiment of the invention and a conventional device.

(14) FIG. 13 illustrates a spatial aliasing problem.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(15) FIG. 1 shows a device 100 according to an embodiment of the invention, which is configured for estimating DOA of sound from Q≥1 sound sources 202. FIG. 2 shows a specific scenario, in which the device 100 may be used. Namely, the device 100 may be part of an apparatus 200 according to another embodiment of the invention for determining the DOA. As shown, this apparatus 200 may also include a sound receiver 201 for receiving the sound from the sound sources 202 (here one sound source 202 is shown, i.e. Q=1). Notably, the device 100 may also be separate from, and for example connected to, such a sound receiver 201. The sound receiver 201 may include microphones or microphone arrays 203 and may include a pre-processing unit 204.

(16) The device 100 of FIG. 1 is configured to obtain a phase difference matrix μ.sub.0, which includes measured phase difference values. Each of the measured phase difference values is a measured value of a phase difference between the two microphone units 203 for a frequency bin in a range of frequencies of the sound. The device 100 may for instance obtain the phase difference matrix from the sound receiver 201, particularly the pre-processing unit 204, which transforms the sound recorded by the microphones 203 into the phase difference matrix μ.sub.0.

(17) The device 100 is further configured to generate a replicated phase difference matrix μ by replicating the measured phase difference values in the obtained phase difference matrix μ.sub.0 to other potential sinusoidal periods.

(18) Then, the device 100 is configured to calculate a DOA value for each phase difference value in the replicated phase difference matrix μ, i.e. it calculate a DOA matrix θ. Finally, the device 100 is configured to determine, as Q DOA results, the Q most prominent peak values in a histogram generated based on the calculated DOA values θ.

(19) The device 100 is thereby configured to carry out a method according to an embodiment of the invention. As shown in FIG. 1, this method includes a step of obtaining 111 the phase difference matrix μ.sub.0, which includes measured phase difference values, each of the measured phase difference values being a measured value of a phase difference between two microphone units 203 for a frequency bin in a range of frequencies of the sound. It then includes a step of generating 112 a replicated phase difference matrix μ by replicating the measured phase difference values to other potential sinusoidal periods, a step of calculating 113 a DOA value for each phase difference value in the replicated phase difference matrix μ, and finally a step of determining 114, as Q DOA results, the Q most prominent peak values in a histogram generated based on the calculated DOA values θ.

(20) The position of the device 100 in the sound source localization is shown in FIG. 2. The device 100 takes μ.sub.0 as an input, and outputs the at least one estimated DOA θ. In FIG. 2, the device 100 is part of the apparatus 200, in which the sound receiver 201 includes the two microphone units 203 and is configured to receive the sound, generate the phase difference matrix μ.sub.0, and provide the phase difference matrix μ.sub.0 to the device 100.

(21) A more detailed overview of a device 100 according to an embodiment of the invention, which builds on the embodiment of the device 100 in FIG. 1, is shown in FIG. 3. Different functions of the device 100 are shown with respect to boxes 301 to 309, and can generally be categorized as a post-processing for phase difference matrix replication and refining.

(22) In box 301, the phase difference matrix μ.sub.0 is obtained, and the replicated phase difference matrix μ is generated by replicating the measured phase difference values to other potential sinusoidal periods. In box 302, DOA values θ are calculated from the replicated phase difference matrix μ. That is, a DOA value θ is calculated for each phase difference value in the replicated phase difference matrix μ.

(23) In box 303, a DOA histogram h (denoted as first histogram) is generated from the calculated DOA values θ. In a simple implementation form of the device 100, the Q most prominent peak values in the first histogram h may be selected already at this point as Q DOA results. In an implementation form of the device 100, for improved robustness, more peaks in the histogram h are detected at box 304. In particular, here the Q+q most prominent peak values in the first histogram h may be detected as DOA candidates. q is preferably 2.

(24) In box 305, a binary masking may be applied, wherein the binary masking takes as input the Q+q peaks detected at box 304 and the DOA values θ calculated at box 302. Thus, in box 305 particularly related DOA values θ.sub.1, θ.sub.2 . . . θ.sub.i are determined and output. At box 306, further histograms (denoted as third histograms) are produced from each selected DOA candidate and its related DOA values, and are output as h.sub.1, h.sub.2 . . . h.sub.i. At box 307, soft masking is applied to these histograms to output soft-masked histograms H.sub.1, H.sub.2 . . . H.sub.i. That is, a soft mask to the peak values is applied in each of the third histograms. At box 308, these histograms H.sub.1, H.sub.2 . . . H.sub.i are then merged into one histogram H (denoted as second histogram) at box 308. The third histograms are particularly merged to generate the second histogram by, for each histogram index, using the maximum value from all the third histograms as the value of the second histogram for that histogram index (denoted by “maximum”).

(25) At box 309, an optional low-pass filtering is applied to the histogram H. Specifically, a Gaussian filter may be applied. Then, at box 309, the Q most prominent peak values in the second histogram are determined as the Q estimated DOA results θ, and are output.

(26) FIG. 4 shows in more detail the generation of the replicated phase difference matrix μ from the phase difference matrix μ.sub.0, as shown in box 301 of the device 100 of FIG. 3.

(27) The purpose of this step is to obtain a (replicated) phase difference matrix μ in all of the potential sinusoidal periods. Frequency bands below f.sub.a.sub.0 should be in the correct sinusoidal period, so that μ.sub.0 is not replicated to other sinusoidal periods for such frequencies. Frequency bands in [f.sub.a.sub.0, 3f.sub.a.] can maximally have 1 sinusoidal period out of the interval [−π, π]. Applying this rule to the higher frequency bands can be described as

(28) $\begin{array}{cc}C=.Math.\frac{f_i-f_a}{2f_a}.Math.C_s=\left(-C,-C+1,\mathrm{.Math.},0,\mathrm{.Math.},C\right)\mu \left(i,j\right)={\mu }_0\left(i\right)+2\pi C_s\left(j\right)i=1,\mathrm{.Math.}N;j=1,\mathrm{.Math.}\left(2C+1\right);& \left(4\right)\end{array}$
where └*┘ denotes floor process, and μ is the replicated matrix. μ now contains μ.sub.0 in the correct sinusoidal period and contains some errors introduced from this step.

(29) FIG. 4 shows specifically on the left-hand side the phase difference values in the replicated phase difference matrix μ in their dependence on the frequency. The bold lines in the graph denote the phase difference values, which are already contained in the phase difference matrix μ.sub.0. All other values in the graph are values replicated to other sinusoidal periods.

(30) FIG. 5 shows in more detail the calculation of the matrix of DOA values θ from the replicated phase difference matrix μ at box 302.

(31) Each phase difference value in the replicated phase difference matrix μ has a single corresponding DOA θ. μ is transformed to DOA θ including these θ as

(32) $\begin{array}{cc}\theta \left(i,j\right)=\arcsin \frac{c\mu \left(i,j\right)}{2\pi f_i\Delta d}& \left(5\right)\end{array}$
θ(i,j) denotes the DOA value for frequency bin index i and replication index j, and Δd denotes the distance between the two microphone units 203.

(33) FIG. 5 shows specifically on the left-hand side the DOA values in their dependence on frequency. The DOA values along the bold lines correspond to the phase difference values in the phase difference matrix μ.sub.0, while the other values result from the replication step.

(34) Now, {umlaut over (μ)} may define the phase differences in the correct sinusoidal periods, and the transformed corresponding value of DOAs may be defined as {dot over (θ)}. It is known that {dot over (θ)} is theoretically constant in clean (low noise) scenarios. This property can be expressed as

(35) $\begin{array}{cc}\stackrel{.}{\theta }\left(p\right)-\stackrel{.}{\theta }\left(q\right)=\arcsin \frac{c\stackrel{.}{\mu }\left(p\right)}{2\pi f_i\Delta d}-\arcsin \frac{c\stackrel{.}{\mu }\left(q\right)}{2\pi f_i\Delta d}=0& \left(6\right)\end{array}$

(36) By simplifying the above equation (6), the relationship of {dot over (μ)} between different frequencies can be determined as

(37) 0$\begin{array}{cc}\frac{\stackrel{.}{\mu }\left(p\right)}{f_i}=\frac{\stackrel{.}{\mu }\left(q\right)}{f_i}& \left(7\right)\end{array}$

(38) When the phase difference is in the wrong sinusoidal periods, {umlaut over (μ)}(i)={umlaut over (μ)}(i)+2nπ, (n≠0, n∈Z). The wrong estimated DOA is defined as {umlaut over (θ)}(i). {umlaut over (θ)}(i) is a complex number when the condition

(39) $\begin{array}{cc}\frac{\stackrel{.}{\mu }\left(i\right)}{2\pi }+n>\frac{f_i\Delta d}{c}& \left(8\right)\end{array}$
is met. For this reason, all of the complex values are preferably removed from θ.

(40) FIG. 6 shows in more detail, how then the remaining values are collected and transformed, at box 303, into the histogram h in [−90, 90] degree, wherein the length of h is denoted as N.sub.h.

(41) By taking the above equation (6) and the mentioned simplifications, the {umlaut over (θ)} differences relationship between different frequencies is obtained as

(42) $\begin{array}{cc}0<\arcsin \sqrt{\frac{\mathrm{cn}}{\Delta d}.Math.\frac{1}{f_{i_p}}-\frac{1}{f_{i_q}}.Math.}<.Math.\stackrel{\mathrm{.Math.}}{\theta }\left(p\right)-\stackrel{\mathrm{.Math.}}{\theta }\left(q\right).Math.<\arcsin \sqrt{\frac{c^2{n}^2}{\Delta d^2}.Math.\frac{1}{f_{i_p}^1}-\frac{1}{f_{\mathrm{iq}}^2}.Math.},p\ne q& \left(9\right)\end{array}$

(43) This proves that {umlaut over (θ)} is a monotonic variant along the frequency axis. Together with the constancy of {dot over (θ)}, when θ is transformed into the histogram h, the amplitudes of the correct peaks are higher than the peaks from {umlaut over (θ)}.

(44) FIG. 6 specifically compares a histogram of DOA values derived from the “raw” phase difference matrix μ.sub.0 (left-hand side) with the histogram h (here for Q=1) obtained from μ. The advantageous effect of the invention is clearly observable, namely that the prominence of the correct peak (here at a DOA of −54.9°) is significantly pronounced.

(45) If sound sources 202 are broadband signals, and the scenario is clean, the DOA results can be estimated by the positions of the peaks with the highest Q prominence. If the scenario is noisy, and/or some of the sound sources 202 are weak, the corresponding peaks may have less prominence than the peaks from {umlaut over (θ)}.

(46) To make the estimation carried out by the device 100 even more robust, in such a case, Q′=Q+q peaks may be taken from the histogram h as DOA candidates (practically, q is taken as 2, but it may also be another integer value, like 3 or higher).

(47) This is shown in FIG. 7, which illustrates in more detail the detecting of peaks in the histogram h at box 304. FIG. 7 shows specifically on the left-hand side, that in this case the (correct) peak at −54.9°, and two further peaks at −36.4° and −21.9°, respectively, are detected (wherein Q=1, and q=2). Then, further post-processing (specifically one or more masking steps) may be applied to preserve the correct peaks and to attenuate the peaks resulting from {umlaut over (θ)}.

(48) FIG. 8 shows particularly in more detail the binary masking carried out at box 305. FIG. 9 shows in more detail the soft masking carried out at box 307.

(49) To evaluate, whether the chosen peaks (DOA candidates) correspond to actual sound sources 202, and not aliasing peaks, each of the peaks is processed individually. The position of a k.sup.th peak is denoted as p.sub.k, and from equation (3), the corresponding aliasing frequency can be determined as f.sub.a.sub.k.

(50) With these frequency indexes, binary masks can be applied to select the DOA values of the phases in supposed correct sinusoidal periods for the corresponding peaks from θ. The process of selecting the related DOA values for a peak value may be described as

(51) $\begin{array}{cc}{\theta }_k\left(i\right)=\theta \left(i,.Math.\frac{f_{a_k}-f_i}{2f_i}.Math.\right)i=1,\mathrm{.Math.},N& \left(10\right)\end{array}$
where θ.sub.k includes the k.sup.th peak and its related DOA values.

(52) FIG. 8 shows the results of such binary masking. In particular, FIG. 8 shows (on the top-side) frequency dependent DOA values in a graph for each of the selected peaks (here the three peaks at −54.9°, −36.4° and −21.9° were selected, see FIG. 7). The DOA values along the bold values are the related DOA values of the respective peak (DOA candidate).

(53) θ.sub.k of each peak is then transformed into a histogram h.sub.k. That is a histogram h.sub.k is generated for the k.sup.th selected DOA candidate and its related DOA values, as is shown in FIG. 9 (on its top-side). In particular, FIG. 9 shows the three histograms for each of the selected DOA candidates, i.e. histograms corresponding to the respectively selected peaks and their corresponding DOA values. As shown in FIG. 8, for the first peak at −54.9° only DOA values on a horizontal line were related. Thus, there is only one sharp histogram peak.

(54) A soft mask M.sub.k may now be applied to the histogram h.sub.k related to the k.sup.th peak, in order to highlight the correct peaks. The mask may be the same or different for each peak. FIG. 9 shows in this respect (on its bottom-side) more details of the soft masking applied at box 307. The soft masking may be optionally combined with a low pass filtering. The histograms H.sub.1, H.sub.2 . . . H.sub.i shown on the bottom-side of FIG. 9 are after applying the soft mask to the respective histograms h.sub.1, h.sub.2 . . . h.sub.i on the top-side. It can be seen that the peaks corresponding to the selected DOA candidates are enhanced in the soft-masked histograms.

(55) Theoretically, the width of an aliasing peak is large. In contrast, the width of a correct peak p.sub.k is narrow at 0°, and increases when the peak is getting closer to ±90°. With this property, the soft mask may be designed as a peak filter with small width at 0° and large width at +90°. A practical soft mask with respect to the k.sup.th selected DOA candidate can preferably be designed like

(56) $\begin{array}{cc}{M}_k\left(i\right)=\frac{2p_k}{.Math.2i-N_h-2p_k.Math.\arcsin \sqrt{\left(\frac{1}{f_{\mathrm{ak}0}}-\frac{1}{f_{\mathrm{nh}}}\right)\frac{c}{\Delta d}}},i=1,\mathrm{.Math.},N_h& \left(11\right)\end{array}$
where f.sub.nh denotes the considered highest frequency.

(57) The soft masking is preferably applied by Schurproduct (°) according to
H.sub.k−h.sub.k° M.sub.k  (12)

(58) FIGS. 10 and 11 show in more detail the merging of the third histograms H.sub.1, H.sub.2 . . . H.sub.i into the second histogram H at box 308, and also the final low-pass filtering applied to the histogram H and the estimation of DOA results at box 309.

(59) The masked histograms from the peak candidates are merged to H by “maximum” according to
H(i)=max(H.sub.1(i), . . . ,H.sub.k(i), . . . H.sub.Q′(i))  (13)

(60) FIG. 10 shows the merged DOA histogram H.

(61) A low-pass filter is preferably further applied to this histogram H, more preferably Gaussian filter. Even more preferably, a Gaussian filter is suggested to be applied with a standard deviation a equal to the lowest localization resolution of the microphone setup. The reason to set this deviation is to balance the height of the peaks closer to 0° and 90°. Theoretically, the widths of the aliasing peaks are large while the widths of the correct peaks are narrow at 0°, and the widths of the correct peaks increase when the peaks are getting closer to ±90°. Therefore using the soft-mask in this way can help to detect the correct peaks more reliably. A simplified equation to obtain the lowest resolution is given as

(62) $\sigma =\arccos \left(1-\frac{c}{f_s\Delta d}\right)$
where f.sub.s denotes the sampling rate.

(63) Finally, Q peaks are selected by their peak prominence from the (optionally low-pass filtered) histogram H. The positions of the peaks are the DOA result output by the device 100.

(64) FIGS. 11 and 12 compare in this respect the histogram H of the device 100 with a histogram generated by a conventional device. FIG. 11 shows in particular the histogram of the conventional device for a sound source DOA of about −55° (Q=1) on the left-hand side, and the corresponding histogram H generated by the device 100 on the right-hand side. FIG. 12 shows further a histogram of a conventional device for multiple sound source DOAs of about −55°, −15° and 30° (Q=3) on the left-hand side, and the corresponding histogram H of the device 100 on the right-hand side. It can be seen that the peak at the correct DOA is much cleaner and much more pronounced in the histogram H produced by the device 100. Accordingly, the estimation of θ will be more accurate and robust, especially in noisy environments.

(65) As a consequence, the device 100 of embodiments of the invention enhances the robustness and accuracy of sound source localization that uses microphones or microphone arrays, especially when the distance between the microphones is large. A potential application for such a device 100 or for the apparatus 200 is, for example, in a distance speech pick up device, in a tablet, in a mobile phone, or in a teleconference device. In each application, the invention specifically reduces or eliminates the negative spatial aliasing effects.

(66) The invention has been described in conjunction with various embodiments as examples as well as implementations. However, other variations can be understood and effected by those persons skilled in the art and practicing the claimed invention, from the studies of the drawings, this disclosure and the independent claims. In the claims as well as in the description the word “comprising” does not exclude other elements or steps and the indefinite article “a” or “an” does not exclude a plurality. A single element or other unit may fulfill the functions of several entities or items described.