Amplification correlation for signal processing

I'm trying to write a program that takes two audio files and matches one to the other as best it can before subtracting it. To do this I've implemented a cross correlation function to handel time shift, but I am unsure how to do something similar to that for amplification. So if I were to give the program two audio files, one of which is just a quieter version of the other one the program should amplify the quieter one to match the other, then subtract and end up with silence. What functions could I used to acheive what I am looking for?

Answer 1

[Dimitris Kalogiros]

Suppose that you have two (discrete time) signals x[n] and y[n] where .

You can make them "unity energy" by using the following formulas:

Now these two signals x1[n] and y1[n] have equal power (=1) and you can correlate them as you've described.

Also, have a look at the following code:

clearvars;  clc; close all;

 % creation of signals
 N=1024;
 n=0:N-1;
 x=sin(2*pi*(2^-7).*n);
 y=2*sin(2*pi*(2^-7).*n+pi/4);
 
 % justify its power 
 x1=x/sqrt(mean(x.^2));
 y1=y/sqrt(mean(y.^2));
  
 %plots
 figure;
 subplot(2,1,1);
 plot(x); hold on;
 plot(y); grid on; zoom on;
 legend('x', 'y');
 
 subplot(2,1,2);
 plot(x1); hold on;
 plot(y1); grid on; zoom on;
 legend('x1', 'y1');

[Jonathan La Combe]

Thank you so much, this looks like just what I was looking for.

[Dimitris Kalogiros]

...then "accept" my answer

[Hamza Ashraf]

hi sir the above code reduces the signal y. i want to know how to increase amplitude of x to match y