CN118112501A - Sound source positioning method and device suitable for periodic signals and sound source measuring device - Google Patents
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Abstract
The invention discloses a sound source positioning method, equipment and a sound source measuring device applicable to periodic signals, which relate to a sound source positioning technology and comprise the following steps: grouping all microphones into different microphone pairs in pairs; calculating a first delay difference of the microphone pair by adopting a cross-correlation technology, and calculating a second delay difference of a preset angle set according to the microphone space coordinate, the horizontal angle scanning range and the pitch angle scanning range; calculating the frequency of the periodic signal, and performing period matching calculation on the first delay time difference and the second delay time difference by adopting the frequency of the periodic signal to calculate a third delay time difference subjected to period compensation; and carrying out minimum root mean square error calculation on all third delay differences in the third data set and the delay at each pair of preset angles, wherein a group of corresponding directions with the minimum errors are obtained as sound source directions. The scheme expands the application scene of the existing disclosed TDOA sound source localization technology aiming at the non-periodic signals.
Description
Technical Field
The present invention relates to a sound source positioning technology, and in particular, to a sound source positioning method, apparatus and sound source measuring device suitable for periodic signals.
Background
TDOA localization is a passive technique for locating and tracking a transmitting sound source by taking advantage of the time differences (or phase differences) of signal arrival of a plurality of spatially separated microphones. Because the calculation amount is small and the real-time performance is high, the method is widely applied to products such as intelligent sound box sound source positioning, gunshot positioning and the like, and the signals do not have obvious periodicity, so that the positioning effect is good. And for signals with obvious periodicity of the sine wave phase or phase difference, the sound source cannot be accurately positioned directly by applying the TDOA technology.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a sound source positioning method applicable to periodic signals.
The invention is solved by the following technical scheme:
a sound source localization method applicable to periodic signals comprises the following steps: grouping all microphones into different microphone pairs in pairs;
Calculating first delay differences of the microphone pairs by adopting a cross-correlation technology, and obtaining first data sets of all the first delay differences; calculating second delay differences under a preset angle according to the microphone space coordinates, the horizontal angle scanning range and the pitch angle scanning range to obtain second data sets of all the second delay differences;
The method comprises the steps of obtaining periodic signal frequency, performing periodic matching on a first delay time difference and a second delay time difference by using the periodic signal frequency, and calculating a third delay time difference to obtain a third data set of all third delay time differences subjected to periodic compensation;
And carrying out minimum root mean square error calculation on all third delay differences in the third data set and the second delay differences under each pair of preset angles, wherein a group of corresponding directions with the minimum error is the sound source direction.
Preferably, the method for calculating the first delay difference of the microphone pair by adopting the cross-correlation technology comprises the following steps:
applying a window function to the original waveform of the microphone according to a preset overlapping proportion to obtain windowed data of each frame;
And taking the data of the same frame from all the microphones, and performing cross-correlation analysis according to the composed microphone pairs to obtain the delay difference of each microphone pair, wherein the delay difference is the first delay difference.
Preferably, the method for calculating the first delay difference of the microphone pair by adopting the cross-correlation technology comprises the following steps:
By adopting a cross-spectrum analysis method, a cross-correlation function is obtained by calculating the cross spectrum of the microphone pair and executing inverse discrete Fourier transform, and the delay difference of the microphone pair is calculated at the position of finding the maximum value in the cross-correlation function and is the first delay difference.
Preferably, the method for calculating the first delay difference of the microphone pair by adopting the cross-correlation technology further comprises the following steps: the weighting function and/or the band-pass filter are added when the cross spectrum analysis method is adopted for calculation.
Preferably, the method for calculating the second delay difference under the preset angle according to the space coordinates of the microphone, the horizontal angle scanning range and the pitch angle scanning range comprises the following steps:
calculating a sound source arrival direction vector according to a preset horizontal angle and a preset pitch angle;
and calculating a second delay difference under a preset angle according to the arrival direction vector of the sound source and the space coordinate difference of the microphone pair.
Preferably, the method for acquiring the frequency of the periodic signal comprises the following steps: and estimating the periodic signal frequency by correcting the frequency spectrum according to the FFT frequency spectrum and window function characteristics of the microphone acquisition signal.
Preferably, the method for performing cycle matching on the first delay time difference and the second delay time difference by using the measured signal frequency to obtain a third delay time difference after cycle compensation includes:
Estimating the number of the whole period according to the following formula by using the second delay difference under each pair of preset angles:
in the above Expressed as a downward rounding,/>For the period compensated cross-correlation delay difference, a third delay difference,/>For the first delay difference without period compensation,/>Is the second delay difference at each pair of preset angles.
Preferably, the method for calculating the minimum root mean square error between all third delay differences in the third data set and the delay at each pair of preset angles, wherein a group of corresponding directions with the minimum obtained errors are sound source directions comprises the following steps:
Third delay difference Second delay difference/>, at each pair of preset anglesAnd (3) calculating the minimum root mean square error, namely the delay difference/>, with the minimum errorThe corresponding direction is the direction of the sound source/>Minimum root mean square error/>The calculation formula of (2) is as follows:
Minimum root mean square error The minimum value of (2) is calculated as follows:
Wherein E is all data Is a set of (3).
Preferably, the method further comprises the steps of judging whether signals acquired by the sensor are periodic signals or not, and if yes, calculating the frequency of the periodic signals; if not, the minimum root mean square error calculation is carried out on the first delay difference and the second delay difference under each pair of preset angles, and the obtained direction with the minimum error is the sound source direction.
Preferably, the method for judging whether the signal acquired by the sensor is a periodic signal or not comprises the following steps:
And windowing an original signal acquired by the microphone, performing FFT (fast Fourier transform) to obtain a frequency spectrum, calculating a shannon entropy index of the normalized frequency spectrum, and if the shannon entropy index is less than 0.1, indicating that the signal is a periodic signal, otherwise, judging that the signal is an aperiodic signal.
A computer device is also proposed, comprising a memory and a processor, the memory being adapted to store one or more computer programs, wherein the one or more computer programs are executed by the processor to implement a sound source localization method as applied to a periodic signal.
Also proposed is a sound source measuring apparatus comprising:
a plurality of microphones for collecting sound signals;
a memory for storing one or more computer programs,
And the processor is used for receiving the sound signals collected by the microphone, and calling one or more computer programs to execute and realize a sound source positioning method applicable to the periodic signals.
The invention has the beneficial effects that: the scheme expands the application scene of the existing disclosed TDOA sound source localization technology aiming at the non-periodic signals.
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In order to more clearly illustrate the embodiments of the invention or the technical solutions of the prior art, the drawings which are used in the description of the embodiments or the prior art will be briefly described, it being obvious that the drawings in the description below are only some embodiments of the invention, and that other drawings can be obtained according to these drawings without inventive faculty for a person skilled in the art.
FIG. 1 is a flow chart of a method of sound source localization for a periodic signal;
FIG. 2 is a schematic diagram of DOA vectors at a pair of horizontal and pitch angles;
FIG. 3 is a schematic representation of three-dimensional spatial coordinates of a microphone array;
FIG. 4 is a map of the XY plane of a microphone array;
FIG. 5 is a diagram of an original waveform of an aperiodic signal;
FIG. 6 is a schematic diagram of a sound source localization result of a voice signal obtained by using a conventional TDOA localization technique;
FIG. 7 is a waveform diagram of a periodic signal;
FIG. 8 is a schematic diagram of sound source localization results using conventional TDOA localization techniques;
FIG. 9 is a schematic diagram of the result of a sound source localization method using the periodic signal of the present application;
FIG. 10 is a flow chart of a prior art TDOA sound source localization technique.
Detailed Description
The present invention will be described in further detail with reference to the following examples, which are illustrative of the present invention and are not intended to limit the present invention thereto.
Example 1
In practical application, especially in the metering field, in order to calibrate performance indexes of a sound source positioning technology, a periodic signal such as a sine wave is generally required to be tested and verified, and based on the purpose and other conceivable sound source calibration technologies suitable for the periodic signal, the embodiment discloses a sound source positioning method suitable for the periodic signal, and expands application scenes of the TDOA sound source positioning technology.
A sound source localization method applicable to a periodic signal, as shown in fig. 1, includes the steps of:
grouping all microphones into different microphone pairs in pairs; calculating first delay differences of the microphone pairs by adopting a cross-correlation technology, and obtaining first data sets of all the first delay differences;
secondly, calculating second delay differences under a preset angle according to the space coordinates of the microphone, the horizontal angle scanning range and the pitch angle scanning range, and obtaining second data sets of all the second delay differences;
Calculating the periodic signal frequency, performing periodic matching on the first delay time difference and the second delay time difference by adopting the periodic signal frequency, and calculating a third delay time difference to obtain a third data set of all third delay time differences subjected to periodic compensation;
And (IV) carrying out minimum root mean square error calculation on all third delay differences in the third data set and the second delay differences under each pair of preset angles, wherein a group of corresponding directions with the minimum error is the sound source direction.
For the step (one), the method for calculating the first delay difference is that a window function is applied to the original waveform of the microphone according to a preset overlapping proportion, so as to obtain each frame of data after windowing; and taking the data of the same frame from all the microphones, and performing cross-correlation analysis according to the composed microphone pairs to obtain the delay difference of each microphone pair, wherein the delay difference is the first delay difference.
In order to improve the calculation efficiency of the cross-correlation, the cross-correlation is obtained by adopting inverse transformation (IDFT) of the cross spectrum of the microphone pair, and the delay difference is calculated through the maximum value position subscript of the cross-correlation. The cross-spectrum analysis method comprises the steps of obtaining a cross-correlation function by calculating a cross spectrum of a microphone pair and performing inverse discrete Fourier transform, and calculating a delay difference of the microphone pair at a position where the maximum value is found in the cross-correlation function, wherein the delay difference is a first delay difference.
Assuming that the number of microphones distributed in space is M, after sound source sounds, the original waveform collected by each microphone is x m, the original waveform of each channel is divided into frames according to a certain overlapping proportion, a window function is applied, and the data length of each frame is N.
M=1..m, n=0..n-1 (formula 1)
In the above-mentioned method, the step of,For one frame of sample data after windowing, b is the frame number, b=0, 1,2.,/>As window function, A is the step of each frame, if the overlapping proportion is op,/>。
The core of TDOA positioning technology is to calculate the delay difference between microphones, and combine M microphones according to a certain rulePairs of microphones that do not repeat. And taking data of the same frame from all microphones, and performing cross-correlation analysis according to the composed microphone pairs to obtain delay differences among the microphone pairs. Taking the microphone pair ij as an example, the cross correlation/>, between the microphone pairs ijDelay difference/>The calculation mode of (2) is as follows:
(equation 3)
(Equation 4)
. In the above, f s is the sampling frequency, c is the sound velocity,/>For the distance between microphone i and microphone j, the delay difference/>, calculated from the cross correlationShould be in (+/>)Between them.
Here, a preferred scheme is proposed, in which the weighting function is increased when calculated by the cross-spectrum analysis methodAnd/or bandpass filter/>. The scheme can add or delete the weighting function/>, according to the requirements of usersOr a band-pass filter, adding or deleting the weighting function and the band-pass filter. Wherein the weighting function/>, in equation 3Get/>And if other weighting functions are needed to be added, corresponding replacement is carried out.
(Equation 5)
In the formula (5), f 1 and f 2 are the upper and lower cut-off frequencies of the band-pass filter, and by combining the formula (3), the cross spectrum outside the cut-off frequency can be directly set to 0 to achieve the band-pass filtering effect.
Because of the periodicity of the sine wave signals, the delay difference obtained by cross-correlation is between a single period (-0.5/f sig0.5/fsig), f sig is the frequency of the periodic signalThe expression is as follows:
the data set is the first data set comprising all the first delay differences.
Step (II) comprises calculating a sound source arrival direction vector according to a preset horizontal angle and pitch angle collection; and calculating a second delay difference under a preset angle according to the arrival direction vector of the sound source and the space coordinate difference of the microphone pair.
Specifically: defining microphone coordinates located in space as. Assuming that the radiation direction of the sound source is (/ >)) Azimuth/>The scan range of (3) is (-180 180), pitch angle/>Is (-90) the interval of the scan angles is defined as/>And/>Then/>，/>. At a preset angle (/ >)) Directional Sound Source arrival Direction (DOA) vector/>Calculated using equation 6:
(equation 6)
From FIG. 2, it can be seen that a pair of pitch and horizontal angles represent the position or direction of a sound source, and thus, for each predetermined sound source direction, there is a set, i.e.A fixed delay difference.
(Equation 7)
A second delay difference at each pair of angles according to the definition of the microphone pairThe method comprises the following steps of:
windowing an original signal acquired by a microphone, and performing FFT (fast Fourier transform) to obtain a frequency spectrum And calculates normalized spectrum/>The shannon entropy index H of (1) if the shannon entropy index is <0.1, indicates that the signal is a periodic signal, otherwise the signal is considered to be an aperiodic signal.
(Equation 8)
Wherein p representsThe probability of occurrence of each element in the list.
If the signal is detected as a periodic signal, the frequency f sig of the detected signal can be determined according to the microphone FFT spectrumAnd the window function characteristics are obtained by correction. Taking hanning window as an example, the frequency f sig of the detected periodic signal is estimated by the formula (9):
(equation 9)
In the above-mentioned method, the step of,For the maximum amplitude in the FFT spectrum, k is the subscript corresponding to the maximum amplitude.
On the other hand, if the periodic signal is a known signal, f sig is directly applied.
The delay difference of the microphone pairs calculated according to the cross correlation of the periodic signals is in a single period, and the delay difference needs to be matched with the second delay difference of each pair of preset angles in period. And estimating the number of the whole period by using the delay difference under each pair of preset angles according to a formula 10 and a formula 11.
(Equation 10)
(Equation 11)
In the aboveRepresenting a rounding down. /(I)For the period compensated cross-correlation delay difference.
The cross-correlation delay difference to be subjected to period compensationSecond delay difference/>, at each pair of preset anglesMinimum root mean square error/>The calculation formula of (2) is as formula 12:
(equation 12)
Delay difference with minimal errorThe corresponding direction is the direction of the sound source/>The calculation formula is as formula 13:
(equation 13)
Wherein E is all dataIs a set of (3).
Embodiment 2 further discloses a sound source localization method applicable to both periodic signals and non-periodic signals, referring to fig. 1 and 10, comprising the steps of: grouping all microphones into different microphone pairs in pairs; calculating first delay differences of the microphone pairs by adopting a cross-correlation technology, and obtaining first data sets of all the first delay differences;
secondly, calculating second delay differences under a preset angle according to the space coordinates of the microphone, the horizontal angle scanning range and the pitch angle scanning range, and obtaining second data sets of all the second delay differences;
Judging whether the signals acquired by the sensor are periodic signals or not, if so, calculating the frequency of the periodic signals according to the steps (IV) and (V); if not, the minimum root mean square error calculation is carried out on the first delay difference and the second delay difference under each pair of preset angles, and the obtained direction with the minimum error is the sound source direction.
Calculating the periodic signal frequency, performing periodic matching on the first delay time difference and the second delay time difference by adopting the periodic signal frequency, and calculating a third delay time difference to obtain a third data set of all third delay time differences subjected to periodic compensation;
And fifthly, carrying out minimum root mean square error calculation on all third delay differences in the third data set and the second delay differences under each pair of preset angles, wherein a group of corresponding directions with the minimum error is obtained as sound source directions.
Step (III) can be further understood as judging whether the signals collected by the sensor are non-periodic signals, if yes, carrying out minimum root mean square error calculation on the first delay difference and the second delay difference under each pair of preset angles, and obtaining a group of corresponding directions with minimum errors as sound source directions;
if not, the sound source direction is calculated according to the steps (four) (five).
The cross-correlation delay difference of non-periodic signals does not need to be compensated for period, i.e。
Difference of first time delayAnd the time delay/>, under each pair of preset anglesPerforming minimum root mean square error calculation, minimum root mean square error/>The calculation formula of (a) is as follows (formula 14):
(equation 14)
Minimum root mean square errorThe minimum value of (2) is calculated as follows:
Wherein E is all data Is a set of (3).
It should be noted that, if the existing TDOA positioning technology is only aimed at the non-periodic signal, it is not necessary to determine whether the signal is a periodic signal, and equation 13 and equation 14 are directly adopted for calculation.
Further, the application discloses a microphone array consisting of 8 microphones, and the method disclosed by the application is used for respectively calculating the positioning results of the non-periodic signals and the periodic signals for comparison.
FIG. 3 is a schematic representation of three-dimensional spatial coordinates of a microphone array; fig. 4 is a map of the XY plane of the microphone array. Fig. 5 is an original waveform of an aperiodic signal (speech signal); FIG. 6 is a graph of the sound source localization of a speech signal obtained by using the conventional TDOA localization technique, and is accurate.
FIG. 7 is a waveform diagram of a periodic signal (e.g., sine wave, frequency 1 kHz); fig. 8 is a sound source localization result obtained by using the conventional TDOA localization technique, and it can be seen that the actual position of the sound source and the localized position are very different. Fig. 9 shows the calculation result of the sound source positioning method for the applicable periodic signal disclosed by the application, and the actual position of the sound source is almost the same as or very similar to the positioned position, so that the sound source positioning method for the applicable periodic signal provided by the application can be well adapted to the scene, and the problem that the existing TDOA positioning technology cannot position the periodic signal is solved.
Still further disclosed is a computer device comprising a memory for storing one or more computer programs, and a processor, wherein the one or more computer programs are executed by the processor to implement a sound source localization method for applying periodic signals as disclosed in embodiment 1 or embodiment 2.
Still further disclosed is a sound source measuring apparatus including:
a plurality of microphones for collecting sound signals;
a memory for storing one or more computer programs,
And the processor is used for receiving the sound signals collected by the microphone, and calling one or more computer programs to execute and realize the sound source positioning method applicable to the periodic signals disclosed in the embodiment 1 or the embodiment 2.
By way of example, the computer program may be divided into one or more modules/units stored in a memory and executed by a processor and the I/O interface transmission of data accomplished by an input interface and an output interface to accomplish the present invention, and one or more modules/units may be a series of computer program instruction segments capable of accomplishing specific functions for describing the execution of the computer program in a computer device.
The computer device may be a desktop computer, a notebook computer, a palm computer, a cloud server, or the like. The computer device may include, but is not limited to, a memory, a processor, and it will be appreciated by those skilled in the art that the present embodiments are merely examples of computer devices and are not limiting of computer devices, may include more or fewer components, or may combine certain components, or different components, e.g., a computer device may also include an input, a network access device, a bus, etc.
The Processor may be a central processing unit (Central Processing Unit, CPU), but may also be other general purpose processors, digital signal processors (DIGITAL SIGNAL Processor, DSP), application SPECIFIC INTEGRATED Circuit (ASIC), off-the-shelf Programmable gate array (Field-Programmable GATE ARRAY, FPGA) or other Programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory may be an internal storage unit of the computer device, such as a hard disk or a memory of the computer device. The memory may also be an external storage device of the computer device, such as a plug-in hard disk, a smart memory card (SMART MEDIA CARD, SMC), a Secure Digital (SD) card, a flash memory card (FLASH CARD) or the like, and further, the memory may also include an internal storage unit of the computer device and also include an external storage device, where the memory is used to store a computer program and other programs and data required by the computer device, and the memory may also be used to temporarily store the computer program and other programs and data in an output device, where the aforementioned storage medium includes a usb disk, a removable hard disk, a ROM of a read-only memory, a RAM of a random access memory, a disk or an optical disk, and other various media that can store program codes.
The foregoing is merely illustrative of specific embodiments of the present invention, and the scope of the present invention is not limited thereto, but any changes or substitutions within the technical scope of the present invention should be covered by the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (12)
1. A sound source localization method applicable to a periodic signal, comprising the steps of: grouping all microphones into different microphone pairs in pairs;
Calculating first delay differences of the microphone pairs by adopting a cross-correlation technology, and obtaining first data sets of all the first delay differences; calculating second delay differences of the preset angle set according to the microphone space coordinates, the horizontal angle scanning range and the pitch angle scanning range, and obtaining second data sets of all the second delay differences;
The method comprises the steps of obtaining periodic signal frequency, performing periodic matching on a first delay time difference and a second delay time difference by using the periodic signal frequency, and calculating a third delay time difference to obtain a third data set of all third delay time differences subjected to periodic compensation;
And carrying out minimum root mean square error calculation on all third delay differences in the third data set and the second delay differences under each pair of preset angles, wherein a group of corresponding directions with the minimum error is the sound source direction.
2. The method for sound source localization of a useful periodic signal according to claim 1, wherein the method for calculating the first delay difference of the microphone pair using a cross correlation technique comprises:
applying a window function to the original waveform of the microphone according to a preset overlapping proportion to obtain windowed data of each frame;
And taking the data of the same frame from all the microphones, and performing cross-correlation analysis according to the composed microphone pairs to obtain the delay difference of each microphone pair, wherein the delay difference is the first delay difference.
3. A method for sound source localization for a periodic signal as claimed in claim 1 or 2, wherein the method for calculating the first delay difference of the microphone pair using a cross correlation technique comprises:
By adopting a cross-spectrum analysis method, a cross-correlation function is obtained by calculating the cross spectrum of the microphone pair and executing inverse discrete Fourier transform, and the delay difference of the microphone pair is calculated at the position of finding the maximum value in the cross-correlation function and is the first delay difference.
4. A method of sound source localization for a periodic signal as defined in claim 3, wherein the method of calculating the first delay difference for the microphone pair using a cross correlation technique further comprises: the weighting function and/or the band-pass filter are added when the cross spectrum analysis method is adopted for calculation.
5. The method for sound source localization of applicable periodic signals according to claim 1, wherein the method for calculating the second delay difference at the preset angle according to the microphone space coordinates, the horizontal angle scanning range and the pitch angle scanning range comprises the steps of:
Calculating a sound source arrival direction vector according to a preset horizontal angle and pitch angle set;
and calculating a second delay difference under a preset angle according to the arrival direction vector of the sound source and the space coordinate difference of the microphone pair.
6. The method for sound source localization of a useful periodic signal according to claim 1, wherein the method for obtaining the frequency of the periodic signal comprises: and estimating the periodic signal frequency by correcting the frequency spectrum according to the FFT frequency spectrum and window function characteristics of the microphone acquisition signal.
7. The method for locating a sound source of a periodic signal according to claim 1, wherein the method for periodically matching the first delay difference and the second delay difference to obtain a third delay difference subjected to period compensation using the frequency of the signal to be measured comprises:
Estimating the number of the whole period according to the following formula by using the second delay difference under each pair of preset angles:
in the above Expressed as a downward rounding,/>For the period compensated cross-correlation delay difference, a third delay difference,/>For the first delay difference without period compensation,/>Is the second delay difference at each pair of preset angles.
8. The method for locating a sound source using a periodic signal according to claim 7, wherein the method for calculating the minimum root mean square error between all third delay differences in the third dataset and the second delay differences at each pair of preset angles, and the set of corresponding directions with the minimum error is the sound source direction, comprises:
Third delay difference Second delay difference/>, at each pair of preset anglesAnd (3) calculating the minimum root mean square error, namely the delay difference/>, with the minimum errorThe corresponding direction is the direction of the sound source/>Minimum root mean square error/>The calculation formula of (2) is as follows:
Minimum root mean square error The minimum value of (2) is calculated as follows:
where E is all data/> Is a set of (3).
9. The method for locating a sound source of a periodic signal according to claim 1, further comprising determining whether the signal collected by the sensor is a periodic signal, and if so, calculating the frequency of the periodic signal; if not, the minimum root mean square error calculation is carried out on the first delay difference and the second delay difference under each pair of preset angles, and the obtained direction with the minimum error is the sound source direction.
10. The method for sound source localization of a periodic signal according to claim 9, wherein the method for determining whether the signal collected by the sensor is a periodic signal comprises:
And windowing an original signal acquired by the microphone, performing FFT (fast Fourier transform) to obtain a frequency spectrum, calculating a shannon entropy index of the normalized frequency spectrum, and if the shannon entropy index is less than 0.1, indicating that the signal is a periodic signal, otherwise, judging that the signal is an aperiodic signal.
11. A computer device comprising a memory and a processor, the memory for storing one or more computer programs, wherein the one or more computer programs are executed by the processor to implement a method of sound source localization for periodic signals as claimed in any one of claims 1-10.
12. A sound source measuring apparatus, comprising:
a plurality of microphones for collecting sound signals;
a memory for storing one or more computer programs,
A processor for receiving sound signals collected by the microphone and for invoking one or more computer programs to execute and implement a method for sound source localization for a periodic signal as defined in any one of claims 1-10.
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