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Visualization of Wideband Beamformer Performance

This example shows how to plot the response of an acoustic microphone element and an array of microphone elements to validate the performance of a beamformer. The array must maintain an acceptable array pattern throughout the bandwidth.

Create an 11-element uniform linear array (ULA) of microphones using cosine antenna elements as microphones. The phased.CosineAntennaElement System object™ is general enough to be used as a microphone element as well because it creates or receives a scalar field. You need to change the response frequencies to the audible range. In addition make sure the PropagationSpeed parameter in the array pattern methods are set to the speed of sound in air.

c = 340;
freq = [1000 2750];
fc = 2000;
numels = 11;
microphone = phased.CosineAntennaElement('FrequencyRange',freq);
array = phased.ULA('NumElements',numels,...
   'ElementSpacing',0.5*c/fc,'Element',microphone);

Plot the response pattern of the microphone element over a set of frequencies.

plotFreq = linspace(min(freq),max(freq),15);
pattern(microphone,plotFreq,[-180:180],0,'CoordinateSystem','rectangular',...
    'PlotStyle','waterfall','Type','powerdb')

Figure contains an axes object. The axes object with title Azimuth Cut (elevation angle = 0.0°) contains an object of type surface.

This plot shows that the element pattern is constant over the entire bandwidth.

Plot the response pattern of an 11-element array over the same set of frequencies.

pattern(array,plotFreq,[-180:180],0,'CoordinateSystem','rectangular',...
    'PlotStyle','waterfall','Type','powerdb','PropagationSpeed',c)

Figure contains an axes object. The axes object with title Azimuth Cut (elevation angle = 0.0°) contains an object of type surface.

This plot shows that the element pattern mainlobe decreases with frequency.

Apply a subband phase shift beamformer to the array. The direction of interest is 30° azimuth and 0° elevation. There are 8 subbands.

direction = [30;0];
numbands = 8;
beamformer = phased.SubbandPhaseShiftBeamformer('SensorArray',array,...
   'Direction',direction,...
   'OperatingFrequency',fc,'PropagationSpeed',c,...
   'SampleRate',1e3,...
   'WeightsOutputPort',true,'SubbandsOutputPort',true,...
   'NumSubbands',numbands);
rx = ones(numbands,numels);
[y,w,centerfreqs] = beamformer(rx);

Plot the response pattern of the array using the weights and center frequencies from the beamformer.

pattern(array,centerfreqs.',[-180:180],0,'Weights',w,'CoordinateSystem','rectangular',...
    'PlotStyle','waterfall','Type','powerdb','PropagationSpeed',c)

Figure contains an axes object. The axes object with title Azimuth Cut (elevation angle = 0.0°) contains an object of type surface.

The above plot shows the beamformed pattern at the center frequency of each subband.

Plot the response pattern at three frequencies in two-dimensions.

centerfreqs = fftshift(centerfreqs);
w = fftshift(w,2);
idx = [1,5,8];
pattern(array,centerfreqs(idx).',[-180:180],0,'Weights',w(:,idx),'CoordinateSystem','rectangular',...
    'PlotStyle','overlay','Type','powerdb','PropagationSpeed',c)
legend('Location','South')

Figure contains an axes object. The axes object with title Azimuth Cut (elevation angle = 0.0°) contains 3 objects of type line. These objects represent 1.500 kHz, 2.000 kHz, 2.375 kHz.

This plot shows that the main beam direction remains constant while the beamwidth decreases with frequency.