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基本原理:
http://www.labbookpages.co.uk/audio/beamforming.html
IntroductionThe diagram below shows the sensitivity patterns for two different microphone setups. The lefthand diagram shows the pattern for an ideal omnidirectional microphone. It shows that the microphonehas equal sensitivity to signals from all directions. The right hand image shows a focusedsensitivity pattern aiming for maximum sensitivity in a single direction, whilst all other direction havereduced sensitivity, the goal is to create a sensitivity pattern that results in the abilityto 'listen' to signals coming from a single direction.
The beamforming effect can be achieved by using a simple linear array of microphones. Such anarray is illustrated below, in this case the array has three microphones. It is easy to see that thedirection from which a wave front originates has an effect on the time at which the signal meets each element inthe array. When arriving from -45° the signal reaches the left hand microphone first, whenarriving from perpendicular to the array (called broadside) the signal reaches each microphone atthe same time and when from +45° the right hand microphone receives the signal first.
If the array's output is created by summing all microphone signals, the maximum output amplitudeis achieved when the signal originates from a source perpendicular to the array; the signals arriveat the same time, they are highly correlated in time and reinforce each other. Alternatively, if thesignal originates from a non-perpendicular direction, they will arrive at different times so will beless correlated and will result in a lesser output amplitude.
Beam PatternA simple calculation can be used to determine the sensitivity of a microphonearray for signals coming from a particular direction. The image below shows an array with fourmicrophones. Each array is separated by a distance l (in metres). The angle of arrival is measured fromperpendicular to the array. The equation below calculates the array's gain for a single frequencyf, and an arrival angle θ. c denotes the speed of sound andN is the number of microphones.
The page on Wave Summation gives a full explanation on how this equation is derived.
Note: The equation makes a few assumptions; the signal source is sufficiently far from the array thatthe wavefront is effectively flat, also the there is no accounting for attenuation of the signal as it travels from source to the microphones.
The gain of the array is shown in the plots below. The output is normalised to the output thatwould be received from a single microphone. Therefore at an angle of 0 degrees (broadside) theoutput amplitude is equivalent to a omnidirectional microphone, resulting in a gain of 1 (or 0dB).
Beam Pattern, 4 Elements, 0.2m Spacing, 1kHz
| Beam Pattern in polar form
| The data for these plots was generated using the code below. It was then plotted using gnuplot. Twosets of gnuplot commands are also given below, one for the XY plot, the other for the polar plot.
Frequency ResponseThe sensitivity-plot calculation in the previous section was calculated for a single frequency.When dealing with a broadband source (such as speech) it is important to calculate an array'sfrequency response. The plot below shows the array's frequency response for the frequency range 0 to10000Hz. The most noticeable features are the gain maximas where the array's output is equal to thatat the perpendicular source direction. These are called grating lobes and are explained below. Their effect is a loss of directional filtering. Signal sources arriving fromnon-perpendicular directions will make it to the array's output in bands of frequencies.
Another interesting feature is the lack of directionality at low frequencies.
The code used to generate the data for this plot is show below. The gnuplot commands are also given.
Microphone Spacing & QuantityAn inspection of the delay-sum equation from the Beam Pattern section reveals that the beamformer's performance isdependant on the spacing and quantity of the array's elements. The table below illustrates how changing these parametersaffects the beamformer's spatial filtering performance.
| | | 5 Elements, 0.04m Spacing, 0.2m Aperture
| 15 Elements, 0.04m Spacing, 0.6m Aperture
| 25 Elements, 0.04m Spacing, 1m Aperture
| 5 Elements, 0.08m Spacing, 0.4m Aperture
| 15 Elements, 0.08m Spacing, 1.2m Aperture
| 25 Elements, 0.08m Spacing, 2m Aperture
| 5 Elements, 0.16m Spacing, 0.8m Aperture
| 15 Elements, 0.16m Spacing, 2.4m Aperture
| 25 Elements, 0.16m Spacing, 4m Aperture
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Grating LobesBelow is a beam pattern plot for a 4 element array with 0.2m spacing at a frequency of 4kHz. Theplot shows a number of extra lobes with a gain that matches the main lobe, these are called gratinglobes. Grating lobes are usually unwanted as they cause the array to pick up signals from directionsother than that of the main lobe without attenuation.
Grating lobes occur when the extra distance a signal wavefront must travel between array elementsis a multiple of the signal's wavelength. In this situation, the signals received by each elementare highly correlated and no signal attenuation occurs. This is illustrated in the right hand diagrambelow.
For a 1 dimensional linear array with equally spaced elements the positions of the grating lobesare easy to calculate. l is the element spacing, c is the speed of sound,f is the signal frequency and n is an integer that selects the gratinglobe.
| n | angle (degrees) | 0 | 0.0° | 1 | 25.388° | 2 | 59.037° |
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SteeringSo far the main lobe of the array's sensitivity pattern has been fixed to a single direction;perpendicular to the array. A powerful feature of the beamforming array is the ability toelectronically steer the beam pattern without physically moving the array. This is simply achieved byadding a delay stage to each of the array elements. The diagram below illustrates this configuration, that givesthe Delay-Sum architecture its name.
The idea is very simple, add a delay to each microphone such that the signals from a particulardirection are aligned before they are summed. By controlling these arrays, the main lobe directioncan be steered.
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开源项目:manyears 我就懒得翻译了
ManyEars Microphone Array-Based Audition for Mobile Robots
ManyEars implements real-time microphone array processing to perform sound source localisation, tracking and separation. It was designed for mobile robot audition in dynamic environments. This project was started at IntroLab, Universite de Sherbrooke, Sherbrooke, Quebec, Canada.
Features- Real-Time
- Sound Source Localisation
- Sound Source Tracking
- Sound Source Separation
- Tuning GUI
- Microphone Array
- Beamforming
https://github.com/introlab/manyears
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