If one normalized vector is subtracted from another normalized vector, is it necessary to normalize the result?

Hello

I was following the example:

https://www.mathworks.com/help/signal/ug/ocular-artifact-removal-from-electroencephalogram-signals-using-deep-learning-regression.html

I don't understand after prediction why the denoised signal is normalized.

Also, if I assume the noise was additive and subtract the normalized denoised signal from the normalized noisy signal to get the noise, do I need to normalize the noise signal?

Thanks in advance.

Answer 1

[Matt J]

If , it does not necessarily follows that . Example:

a=rand(1,5); a=a/norm(a);
b=rand(1,5); b=b/norm(b);

norm(a-b)

ans = 0.5268