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Hello,

I have two time domain signals, e.g.:

y1= 3*cos(10*t+180*pi/180);

y2= 2*cos(10*t+60*pi/180);

What is the correct procedure for calculating the residual of these two signals? The current code I am using is below, where I am simply subtracting the two signals to get the residual signal. I am not sure if the residual is correct and whether the affect of phase difference is taken into account in this calculation.

clear all ;

close all;

clc;

t= 0:0.001:1;

% first signal vector (larger magnitude)

y1= 3*cos(10*t+0*pi/180);

% seond signal vector (smaller magnitude)

y2= 2*cos(10*t+180*pi/180);

% residualI tried

y3=y1-y2;

%% plots

figure

plot(t,y1)

hold on

plot(t, y2)

hold on

plot(t,y3)

legend ('y1', 'y2', 'residual')

Furthermore, the residual signal should be of smaller amplitude then the parent signals, isnt it so? I realise that can be achived by simply adding the signals instead of subtracting(y3= y1+y2 gives the figure below) them but is that the correct way?

Daniel M
on 16 Oct 2019

Edited: Daniel M
on 16 Oct 2019

Daniel M
on 16 Oct 2019

The residuals, as it stands, would be res = x1-x2; However, I suspect that would not give you a satisfying result, and you would prefer to subtract the two signals as if they were in phase. Then what you need to do is find the phase difference between the two signals. (Here we know it because we have the equation for the signal, but in the general case we will not). To do this, you can curve fit your signals, or use fzero, as in this example:

Once you have the phase, you can shift one of your signals by that phase amount, then subtract them to get the residuals. Shifting the phase can be done using the fft, but can also be done in the time domain by just padding one of your signals, if you know the relationship between time and your index.

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