Cancelling the background Noise by subtraction in frequency domain

Hi

these are the Audio Files that I am working on.

S1= the background Noise (Noise of drilling machine) , and S2= the background Noise + The targeted sound. Both of S1&S2 have the same length and same sampling F. Please listen to it.

I want to cancel the background noise in order to get only the targeted sound. In the Code below I plot both signals in time and frequency domain, after that I subtracted the fft(S2)- fft(S1) . I expected that should give me the targeted sound but i ended up having the same sound in S2.

My question is as follows:

1- Is this the best way to cancel the noise ?

2- Or should I use a frequency filter ? if yes what filter should I use ?

the Code :

    close all; clear all; clc;
  %%Analyse the audio
  [y, Fs] = audioread('S1.mp3');
  % Plot the Time Domain Representation
  t = (0:1/Fs:(length(y)-1)/Fs);
  subplot(2,2,1)
  plot(t,y)
  title('Time Domain - Background Noise')
  xlabel('Time (seconds)')
  ylabel('Amplitude')
  xlim([0 t(end)])

% Plot the Frequency Domain Representation
m = length(y);
x = fft(y, m);
f = (0:m-1)*(Fs/m);
amplitude = abs(x)/m;
subplot(2,2,2)
plot(f(1:(m/2)),amplitude(1:(m/2)))
title('Frequency Domain - Background Noise')
xlabel('Frequency')
ylabel('Amplitude')
xlim([0 20000])

%%Analyse the noise audio

[y_n, Fs_n] = audioread('S2.mp3');
% Plot the Time Domain Representation
t_n = (0:1/Fs_n:(length(y_n)-1)/Fs_n);
subplot(2,2,3)
plot(t_n,y_n)
title('Time Domain - Background Noise + Targeted Sound ')
xlabel('Time (seconds)')
ylabel('Amplitude')
xlim([0 t(end)])
% Plot the Frequency Domain Representation
a = length(y_n);
v = fft(y_n, a);
f_n = (0:a-1)*(Fs/a);
amplitude = abs(v)/a;
subplot(2,2,4)
plot(f_n(1:(a/2)),amplitude(1:(a/2)))
title('Frequency Domain - Background Noise + Targeted Sound ')
xlabel('Frequency')
ylabel('Amplitude')
xlim([0 20000])
%ylim([0 0.02])
%%SUBTRACTION IN Frequency domain 
% Plot the Frequency Domain Representation
a = length(y);
v = fft(y_n, a)-fft(y, a);
f_n = (0:a-1)*(Fs/a);
amplitude = abs(v)/a;
figure;
plot(f_n(1:(a/2)),amplitude(1:(a/2)))
title('Frequency Domain - Targeted Sound ')
xlabel('Frequency')
ylabel('Amplitude')
xlim([0 20000])
S=real(ifft(v));
sound(S);

[Carlos Alva]

Frequency subtraction works well however it is critical that the input samples line up, that is

S1 = Audio + S2

S2 = noise

Only in this condition you will see the benefit. The effort in this type of process is to insert and adjust delay lines (registers) to ensure the alignment before the summing junction, otherwise the spectrum of the noise will be added out of phase to the spectrum of the signal effectively putting it back in.

[Image Analyst]

Have you tried the wiener filter function?