Suppose I have a signal (that is not normalized) and some random noise value to add to it (also not normalized). And suppose the proportion to the signal and the noise must be maintained. Both the signal and the noise are 1xN lists.
In matlab I can normalize the combined signal by: signal_new = signal + noise; signal_new = signal_new/rms(signal_new);
Is this mathematically the same? I believe it is by superposition. signal_new = signal/rms(signal + noise) + noise/rms(signal + noise);
Now suppose I have a normalized signal: clean_signal = signal/rms(signal)
and I only have access to 'clean_signal' and the 'noise' signal. Now the noise signal is not normalized but it is proportional to the original signal.
How can I replicate the equation in (1) with what I have from (2). In pseudo math how can I find 'signal_new': signal_new = clean_signal/XX+ noise/YY;
Thank you.