How to prepare input for the MUSIC DOA algorithm using real world audio signal (NOT simulation)

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tachung chi 2021-1-15

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https://ww2.mathworks.cn/matlabcentral/answers/718075-how-to-prepare-input-for-the-music-doa-algorithm-using-real-world-audio-signal-not-simulation

评论： Remya Prabhakaran 2022-5-18

Hi,

I am working on using the MUSIC algorithm to calculate DOA of ultrasonic sound input. I have the configuration of the microphone array and the number of microphone is 7. Therefore, the received audio signal would be something like [7xN] in real values, where N is the number of samples collected in a fixed time duration.

The matlab function/example I am refering to is: https://www.mathworks.com/help/phased/ref/phased.musicestimator2d-system-object.html.

Now, I am able to define the phased.URA object using the array configuration (microphone spacing, positions..and so on). The problem is: I do not know how to convert the input signal into the matrix generated by the collectPlaneWave function in the demo. Specifically, the output of collectPlaneWave is a complex matrix while my audio input is a [7xN] real-valued matrix.

Thanks in advance!

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Answer 1

Priyanka Rai 2021-2-2

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https://ww2.mathworks.cn/matlabcentral/answers/718075-how-to-prepare-input-for-the-music-doa-algorithm-using-real-world-audio-signal-not-simulation#answer_612443

This might help you:

https://www.mathworks.com/help/phased/ug/music-super-resolution-doa-estimation.html

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Answer 2

Colin Waters 2022-3-24

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No, that link does not help. The description fails to specify the data types (real, complex) and matrix shapes for the variables, e.g. x(t).

There is a way to get the complex x(t) matrix (hence complex covariance matrix) if the signal is narow band and plane wave. Assume you have a plane wave (e^i[k dot r - wt] model) propagating across the sensor array and you have them placed to avoid spatial aliasing etc.

For each of the (real) time series from each sensor, choose one sensor as a reference. You can do an FFT to get the frequency of the narrow band signal. Then do the cross spectrum for each pair, using the reference sensor time series. This gets you the phase differences at the relevant frequency between the reference and each of the other sensor time series. This phase difference is the k dot r for each sensor pair and you know the r vector from the location of the sensors, measured from the reference sensor.

You can then generate the complex time series at each sensor, using the phase differences as k dot r in the signal model. Then you can get the complex covariance etc.

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Colin Waters 2022-5-11

Firstly, an FFT of 1024 input real values only gives 512 unique complex values, the other 512 are complex conjugate so add nothing new.

Secondly, choose one frequency bin. The covariance matrix for that one frequency is a 6 x 6 (complex) matrix - called the 'spectral matrix' by some.

Put the 6 complex values from the same frequency bin at all 6 microphone data streams (the FFT of these) into a 6 x 1 complex vector. Then calculate the outer product to get the spectral matrix ( 6 x 6 complex). The diagonal elements should be real values.

Remya Prabhakaran 2022-5-18

Hi @Colin Waters

I tried different ways to implement the same you mentioned. Iam attaching my code here will you please help me to find what is wrong here.

clear all;

close all;

clc

load('audio_mic6.mat','audio111');

frame_1024 = audio111(1:1024,:);

N=6; %% number of elements

FS=16000; %% sampling rate

Radius=0.03856; % radius

L=1024; %number of samples

Fn =FS/2;

fft_sig = fft(frame_1024);

abs_fft_sig = abs(fft_sig);

energy_db = 20*log(abs_fft_sig);

minimum_db = -50; %% setting a minimum energy

Fv = linspace(0, 1, fix(L/2)+1)*Fn;

Iv = 1:numel(Fv);

for k1=1:6

for k =1:513

if(energy_db(k,k1) < minimum_db ) %% comparing the energy

gain =0;

else

gain =1;

end

abs_fft_sig(k,k1)=gain*abs_fft_sig(k,k1);

end

%% Finding peaks for each channel to find the dominant frequency

[pks1,locs1] = findpeaks((abs_fft_sig(1:513,1)));

[pks2,locs2] = findpeaks((abs_fft_sig(1:513,2)));

[pks3,locs3] = findpeaks((abs_fft_sig(1:513,3)));

[pks4,locs4] = findpeaks((abs_fft_sig(1:513,4)));

[pks5,locs5] = findpeaks((abs_fft_sig(1:513,5)));

[pks6,locs6] = findpeaks((abs_fft_sig(1:513,6)));

a=Fv(locs1)

b=Fv(locs2)

c1=Fv(locs3)

d=Fv(locs4)

e=Fv(locs5)

f=Fv(locs6)

%% Spectral matrix creation

mat_creation = fft_sig(4,:);

mat = (mat_creation)';

spectral_matrix = mat *(mat_creation);

fc= 156.25; %% common peak from each channel

%% Eigen value decomposition

[eigenvec eigenval] = eigs(spectral_matrix,N)

eigv=eigenvec(:,1+1:6)

c=343;

lambda = c/fc;

p=zeros(361,361);

%% P music spectrum for UCA

ph =(0:0.5:360);

th =(0:0.5:360);

for i = 1:length(th)

for j = 1:length(ph)

k=1:1:1*N;

theta=th(i)*pi/180;

phi = ph(j)*pi/180;

% phase = exp(-1j*2*pi*0.03864*(0:N-1)'*sind(theta)/lambda);

phase =((2*pi*0.03864)/lambda)*(sin(theta)*cos(phi-((2*pi*(k'))/N)));

aa=exp(1i*phase);

p(i,j)=10*log(abs(1/((aa'*eigv)*(eigv'*aa))));

end

[f,idx]=maxk(p(:),1);

doa=ph(ceil(idx/length(th)));

doa1=th(mod(idx,length(ph)));

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How to prepare input for the MUSIC DOA algorithm using real world audio signal (NOT simulation)

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