This MATLAB code analyzes two audio signals (.wav files) by: 1. Reading in the signals and extracting the right channel of each stereo recording. 2. Cutting the signals to the same length for comparison. 3. Calculating the fast Fourier transform (FFT) and plotting the power spectra of the cut signals. 4. Comparing the signals by calculating the mean squared error (MSE) and determining if they are the same or not based on a threshold.

1. Contents
 Matlab Code:
 signal into left and right, stereo records
 time for right signal only (stereo) for original signals
 find new length
 find new time
 find new frequency
 perform fft and plot of the cut orignal signal
 Zoom in to signal baseline noise signal
 plot two signals
 plot fft compare
 calculate and compare two signals
 corlation
Matlab Code:
Author: Minh Anh Nguyen (minhanhnguyen@q.com) This script will perform the following
tasks:
%1. read in two "wav" files, plot the signals of these files
%2. fft
% 3. compare input signals, and display a message on the screen whether or
not the signals are the same.
% the MSE must be 0, for both signals are the same.
% The script will read in a stereo data (right channel)
close all;% Close all figures (except those of imtool.)
clear all; % Erase all existing variables.
clc;% Clear the command window.
fontSize = 20;
fontSize1 = 14;
fontSize2 = 12;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Please edit files
% set folder
folder = 'C:UsersMinh anhDesktopmicrophone-project-demo';
%%Open WAV file:
sound1=audioread('.good 2.wav');
[y1,fs1]=audioread('.good 2.wav');
sound2=audioread('.good 3.wav');
[y2,fs2]=audioread('.good 3.wav');
% sound2=audioread('.upper_channel 2.wav');
% [y2,fs2]=audioread('.upper_channel 2.wav');
% sound2=audioread('.upper_channel_bide 1.wav');
% [y2,fs2]=audioread('.upper_channel_bide 1.wav');

2. % sound2=audioread('.lower_channel 1.wav');
% [y2,fs2]=audioread('.lower_channel 1.wav');
% sound2=audioread('.pin1.wav');
% [y2,fs2]=audioread('.pin1.wav');
sound1_baseline_noise=audioread('.good 2_noise.wav');
[y1_basenoise,fs1_basenoise]=audioread('.good 2_noise.wav');
%
sound2_baseline_noise=audioread('.good 3_noise.wav');
[y2_basenoise,fs2_basenoise]=audioread('.good 3_noise.wav');
% sound2_baseline_noise=audioread('upper_channel 2_noise.wav');
% [y2_basenoise,fs2_basenoise]=audioread('.upper_channel 2_noise.wav');
% sound2_baseline_noise=audioread('upper_channel_bide 1_noise.wav');
% [y2_basenoise,fs2_basenoise]=audioread('.upper_channel_bide 1_noise.wav');
% sound2_baseline_noise=audioread('lower_channel 1_noise.wav');
% [y2_basenoise,fs2_basenoise]=audioread('.lower_channel 1_noise.wav');
% sound2_baseline_noise=audioread('.pin1_noise.wav');
% [y2_basenoise,fs2_basenoise]=audioread('.pin1_noise.wav');
signal into left and right, stereo records
size(y1);
left1=y1(:,1);
right1=y1(:,2);
[MR1,NR1] = size(right1);
size(y2);
left2=y2(:,1);
right2=y2(:,2);
[MR2,NR2] = size(right2);
time for right signal only (stereo) for original signals
Nl = length(right1); % number of points to analyze
lsl = size (right1); % find the length of the data per second
nbits = 2^(length(right1));
t1l = (0:1:length(right1)-1)/fs1;
fx = fs1*(0:Nl/2-1)/Nl; %Prepare freq data for plot
T1 = 1/fs1; % period between each sample
N = Nl;
N2 = length(right2);
ls2 = size (right2); % find the length of the data per second
nbits2 = 2^(length(right2));
t2 = (0:1:length(right2)-1)/fs2;
fx2 = fs2*(0:N2/2-1)/N2; %Prepare freq data for plot
T2 = 1/fs2; % period between each sample
% baseline noise is removed from signals

3. size(y1_basenoise);
left1_basenoise=y1_basenoise(:,1);
right1_basenoise=y1_basenoise(:,2);
[MR1_basenoise,NR1_basenoise] = size(right1_basenoise);
size(y2_basenoise);
left2_basenoise=y2_basenoise(:,1);
right2_basenoise=y2_basenoise(:,2);
[MR2_basenoise,NR2_basenoise] = size(right2_basenoise);
t1_basenoise = (0:1:length(right1_basenoise)-1)/fs1_basenoise;
t2_basenoise = (0:1:length(right2_basenoise)-1)/fs2_basenoise;
%%cut signal to the same length for comparing
voice1 = right1(fs1*1 : fs1*40);
voice2 = right2(fs2*1 : fs2*40);
find new length
N2x = length(voice2);
N1x = length(voice1);
find new time
t1x = (0:1:length(voice1)-1)/fs1;
t2x = (0:1:length(voice2)-1)/fs2;
find new frequency
f2x = fs2*(0:N2x/2-1)/N2x;
f1x = fs1*(0:N1x/2-1)/N1x;
perform fft and plot of the cut orignal signal
NFFT1x = 2 ^ nextpow2(N1x);
Y1x = fft(voice1, NFFT1x)/ N1x;
f1xx = (fs1/ 2 * linspace(0, 1, NFFT1x / 2+1))'; % Vector containing
frequencies in Hz
STFFT1x = ( 2 * abs(Y1x(1: NFFT1x / 2+1))); % Vector containing corresponding
amplitudes
NFFT2x = 2 ^ nextpow2(N2x);
Y2x = fft(voice2, NFFT2x) / N2x;
f2xx = (fs2 / 2 * linspace(0, 1, NFFT2x / 2+1))'; % Vector containing
frequencies in Hz
STFFT2x = ( 2 * abs(Y2x(1: NFFT2x / 2+1))); % Vector containing corresponding
amplitudes
% plot of the cut orginal signal
figure; subplot (2,2,1); plot(t1x, voice1);xlim([0,40]); ylim([-2,2]);
%str1=sprintf('Correct loading with sampling rate = %d Hz, number sample =
%d', fs1, N1x);

4. str1=sprintf('Correct loading signal');
title(str1,'Fontsize', fontSize2);
xlabel('Time (sec)','Fontsize', fontSize1); ylabel('Amplitude','Fontsize',
fontSize1); grid on;
subplot (2,2,2); plot(t2x, voice2); xlim([0,40]); ylim([-2,2]);
%str2=sprintf(' User loading with sampling rate = %d Hz, number sample = %d',
fs2, N2x);
str2=sprintf('User loading signal');
title(str2,'Fontsize', fontSize2); xlabel('Time (sec)','Fontsize',
fontSize1); ylabel('Amplitude','Fontsize', fontSize1); grid on;
% plot of the fft cut signal2
%subplot (2,2,3); plot(f1xx, STFFT1x); xlim([0,1500]); ylim([0,.09]);
figure;
plot(f1xx, STFFT1x); xlim([0,1500]); ylim([0,.09]);
str1ft1=sprintf('Single-sided Power spectrum for Correct loading');
title(str1ft1,'Fontsize', fontSize2);
ylabel ('Magnitude','Fontsize', fontSize1); xlabel ('Frequency
[Hz]','Fontsize', fontSize1); grid on;
% display markers at specific data points on DFT graph
indexmin1 = find(min(STFFT1x) == STFFT1x);
xmin1 = f1xx(indexmin1);
ymin1 = STFFT1x(indexmin1);
indexmax1 = find(max(STFFT1x) == STFFT1x);
xmax1 = f1xx(indexmax1);
ymax1 = STFFT1x(indexmax1);
strmax1 = ['Frequency = ',num2str(xmax1),' Hz',' ','Magnitude=',
num2str(ymax1),''];
text(xmax1,ymax1,strmax1,'HorizontalAlignment','Left');
%subplot (2,2,4); plot(f2xx, STFFT2x); xlim([0,1500]); ylim([0,.09]);
figure; plot(f2xx, STFFT2x); xlim([0,1500]); ylim([0,.09]);
str1ft2=sprintf('Single-sided Power spectrum for User loading');
title(str1ft2,'Fontsize', fontSize2);
ylabel ('Magnitude', 'Fontsize', fontSize1); xlabel ('Frequency
[Hz]','Fontsize', fontSize1); grid on;
% display markers at specific data points on DFT graph
indexmin2 = find(min(STFFT2x) == STFFT2x);
xmin2 = f2xx(indexmin2);
ymin2 = STFFT2x(indexmin2);
indexmax2 = find(max(STFFT2x) == STFFT2x);
xmax2 = f2xx(indexmax2);
ymax2 = STFFT2x(indexmax2);
strmax2 = ['Frequency = ',num2str(xmax2),' Hz',' ','Magnitude =',
num2str(ymax2),' '];
text(xmax2,ymax2,strmax2,'HorizontalAlignment','Left');

6. Zoom in to signal baseline noise signal
figure; subplot(3,2,1); plot(t1_basenoise,right1_basenoise); xlim([0,10]);
ylim([-2,2]);
str1=sprintf('Correct loading with Zoom in');
title(str1,'Fontsize', fontSize1);
xlabel('Time (secs)','Fontsize', fontSize1); ylabel('Amplitude','Fontsize',
fontSize1); grid on;
subplot(3,2,3); plot(t2_basenoise,right2_basenoise,'r'); xlim([0,10]);
ylim([-2,2]);
str2=sprintf('User loading with Zoom in');
title(str2, 'Fontsize', fontSize1);
xlabel('Time (secs)','Fontsize', fontSize1); ylabel('Amplitude','Fontsize',
fontSize1); grid on;

7. plot two signals
figure, plot(t1_basenoise,right1_basenoise,
t2_basenoise,right2_basenoise,'r'); xlim([0,10]); ylim([-2,2]);
str2=sprintf('Comparing two loading signals with Zoom in ');
title(str2, 'Fontsize', fontSize1);
xlabel('Time (secs)','Fontsize', fontSize1); ylabel('Amplitude','Fontsize',
fontSize1); grid on;
legend ('Correct loading signal', 'User loading signal', 'Fontsize',
fontSize);
Warning: Using an integer to specify the legend location is not supported.
Specify the legend location with respect to the axes using the 'Location'
parameter.
Warning: Ignoring extra legend entries.

8. plot fft compare
figure, plot(f1xx, STFFT1x,f2xx, STFFT2x,'r'); xlim([0,1500]); ylim([0,.09]);
str1ft3=sprintf('Comparing FFT for two loading signals');
title(str1ft3,'Fontsize', fontSize1);
ylabel ('Magnitude', 'Fontsize', fontSize1); xlabel ('Frequency
[Hz]','Fontsize', fontSize1); grid on;
indexmax3 = find(max(STFFT2x) == STFFT2x);
xmax3 = f2xx(indexmax3);
ymax3 = STFFT2x(indexmax3);
strmax3 = ['Frequency = ',num2str(xmax3),' Hz',' ','Magnitude= ',
num2str(ymax3),' '];
legend ('Correct loading signal', 'User loading signal','Fontsize',
fontSize);
Warning: Using an integer to specify the legend location is not supported.
Specify the legend location with respect to the axes using the 'Location'
parameter.
Warning: Ignoring extra legend entries.

9. calculate and compare two signals
Calculate the MSE
D= voice1 - voice2;
MSE=mean(D.^2);
%msgbox(strcat('MSE value is= ',mat2str(),' MSE'));
%msgbox(strcat('MSE value is= ',mat2str(MSE)));
%if MSE ==0;
%if MSE <= 0.00135; %%v this will work
if MSE <= 5.2731e-09 ; %%v this will work
disp('Signal are the same');
else
% msgbox(strcat('MSE value is= ',mat2str(MSE)));
disp('Signal are not the same');
msgbox('Centrifuge loading error. Please check bearings are seated
properly');
end
% %% play back play back the audio files
% disp('Playing (correctly loaded).');
% sound(y1,fs1);
% pause; %create a 2 second pause
%
%

10. % disp('Playing the user loading.');
% sound(y2,fs2);
% pause
%%Calculate variance, mean and standard deviation of sounds
D1c= STFFT1x - STFFT2x;
MSEfft=mean(D1c.^2);
disp(['MSEfft' num2str(MSEfft)]);
mean1= sum(right1)/N;
mean2= sum(right2)/N2;
stdev1 = sqrt ((sum(right1-mean1).^2)/2);
stdev2 = sqrt ((sum(right2-mean2).^2)/2);
% var(right1(1:length(right2))-right2) %for the whole signal y1-y2
var(voice1(1:length(voice2))-voice2); %for the voice
fprintf('digital statitics of voice 1 a same length signalnn');
fprintf('mean of voice 1:%fn', mean(voice1));
fprintf('standard deviation of voice 1:%fn', std(voice1));
fprintf('variance of voice 1:%fn', std(voice1)^2);
fprintf('average power of voice 1:%fn', mean(voice1.^2));
fprintf('average magnitude of voice 1:%fn', mean(abs(voice1)));
% prod1 = sound1(1:N-1) * sound1(2:N);
% crossing1 = length (find(prod1<0));
% fprintf(' zero crossing of sound 1:% 0.fn', crossing1);
%
fprintf('ndigital statitics of voice 2nn');
fprintf('mean of voice 2:%fn', mean(voice2));
fprintf('standard deviation of voice 2:%fn', std(voice2));
fprintf('variance of voice 2:%fn', std(voice2)^2);
fprintf('average power of voice 2:%fn', mean(voice2.^2));
fprintf('average magnitude of voice 2:%fn', mean(abs(voice2)));
% prod1 = sound1(1:N-1) * sound1(2:N);
% crossing1 = length (find(prod1<0));
% fprintf(' zero crossing of sound 1:% 0.fn', crossing1);
%
% % var(right1(1:length(right2))-right2) %for the whole signal y1-y2
% var(voice1(1:length(voice2))-voice2); %for the voice
%
%
Signal are the same
MSEfft0
digital statitics of voice 1 a same length signal
mean of voice 1:-0.000105
standard deviation of voice 1:0.251742
variance of voice 1:0.063374
average power of voice 1:0.063374
average magnitude of voice 1:0.197595

11. digital statitics of voice 2
mean of voice 2:-0.000105
standard deviation of voice 2:0.251742
variance of voice 2:0.063374
average power of voice 2:0.063374
average magnitude of voice 2:0.197595
correlation
[C1, lag1] = xcorr(abs((fft(voice1))),abs((fft(voice2)) ));
figure, plot(lag1/fs1,C1);
ylabel('Amplitude'); grid on
title('Cross-correlation between Correct and User loading files')
% %% plot orginal signal. for debug. %% team does not like long length
% %% perform fft and plot of orignal signal
% %
% figure; subplot (2,2,1); plot(t1, sound1);
% title ('Signal of sound 1 , frequency = 44100 Hz and number sample =
2742270');
% xlabel('time (sec)'); ylabel('relative signal strength'); grid on;
% %
% subplot (2,2,2); plot(t2, sound2);
% title ('Signal of sound 2, frequency = 44100 Hz and number sample =
2674665');
% xlabel('time (sec)'); ylabel('relative signal strength'); grid on;
% %% fft of orignal signal
% NFFT1 = 2 ^ nextpow2(N);
% Y1 = fft(y1, NFFT1)/ N;
% f1 = (fs1 / 2 * linspace(0, 1, NFFT1 / 2+1))'; % Vector containing
frequencies in Hz
% STFFT1 = ( 2 * abs(Y1(1: NFFT1 / 2+1))); % Vector containing corresponding
amplitudes
% subplot (2,2,3); plot(f1, STFFT1); title ('Single-sided Power spectrum for
Sound1');
% %subplot (2,2,3); plot(abs(fft(sound1))); title ('plot fft of Sound 1');
%plot Magnitude of fft
% ylabel ('Magnitude |y(f)|'); xlabel ('frequency [Hz]'); grid on;
%
% NFFT2 = 2 ^ nextpow2(N2);
% Y2 = fft(y2, NFFT2) / N2;
% f2 = (fs2 / 2 * linspace(0, 1, NFFT2 / 2+1))'; % Vector containing
frequencies in Hz
% STFFT2 = ( 2 * abs(Y2(1: NFFT2 / 2+1))); % Vector containing corresponding
amplitudes
% subplot (2,2,4); plot(f2, STFFT2); title ('Single-sided Power spectrum for
Sound2');
% % subplot (2,2,4); plot(abs(fft(sound2))); title ('plot fft of Sound2');
% ylabel ('Magnitude |y(f)|'); xlabel ('frequency [Hz]'); grid on;

12. Published with MATLAB® R2016a