# Time-Delay Beamforming of Microphone ULA Array

This example shows how to perform wideband conventional time-delay beamforming with a microphone array of omnidirectional elements. Create an acoustic (pressure wave) chirp signal. The chirp signal has a bandwidth of 1 kHz and propagates at a speed of 340 m/s at ground level.

Note: This example runs only in R2016b or later. If you are using an earlier release, replace each call to the function with the equivalent step syntax. For example, replace myObject(x) with step(myObject,x).

c = 340;
t = linspace(0,1,50e3)';
sig = chirp(t,0,1,1000);

Collect the acoustic chirp with a ten-element ULA. Use omnidirectional microphone elements spaced less than one-half the wavelength at the 50 kHz sampling frequency. The chirp is incident on the ULA with an angle of $6{0}^{\circ }$ azimuth and ${0}^{\circ }$ elevation. Add random noise to the signal.

microphone = phased.OmnidirectionalMicrophoneElement(...
'FrequencyRange',[20 20e3]);
array = phased.ULA('Element',microphone,'NumElements',10,...
'ElementSpacing',0.01);
collector = phased.WidebandCollector('Sensor',array,'SampleRate',5e4,...
'PropagationSpeed',c,'ModulatedInput',false);
sigang = [60;0];
rsig = collector(sig,sigang);
rsig = rsig + 0.1*randn(size(rsig));

Apply a wideband conventional time-delay beamformer to improve the SNR of the received signal.

beamformer = phased.TimeDelayBeamformer('SensorArray',array,...
'SampleRate',5e4,'PropagationSpeed',c,'Direction',sigang);
y = beamformer(rsig);

subplot(2,1,1)
plot(t(1:5000),real(rsig(1:5e3,5)))
axis([0,t(5000),-0.5,1])
title('Signal (real part) at the 5th element of the ULA')
subplot(2,1,2)
plot(t(1:5000),real(y(1:5e3)))
axis([0,t(5000),-0.5,1])
title('Signal (real part) with time-delay beamforming')
xlabel('Seconds')