# Uncorrelated sinuoids

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zozo on 29 May 2012
How can I create two uncorrelated sinusoidal signals of same frequency (say 900Hz)?
f1=900; %frequency in Hertz
t_duration=1;% duration of signal (seconds)
fs=10000; %FS sampling freq of the signal Hz
t = 0:1/fs:t_duration-1/fs;
s=10*sin(2*pi*f1*t); %source signal
j= 20*sin(2*pi*f1*t); %jammer signal
What changes should be made in above code to make 's' and 'j' uncorrelated?

Walter Roberson on 29 May 2012
You cannot. Two pure sine waves of the same frequency are always correlated. They differ in at most 1/2 a sample period or (phrasing another way) differ only in phase.
To get the signals uncorrelated, at least one needs to be modulated, or they need to be incommensurate frequencies (must be irrational relative to each other.)
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Geoff on 29 May 2012
Not really. 900 and 950 will create a complex waveform with a frequency of 50Hz. It really depends on what 'uncorrelated' means in the field you are applying this too (radio communications, presumably)
Walter Roberson on 30 May 2012
A signal that was (900 + Pi) Hz would be uncorrelated to a signal that was at (900 + exp(1)) Hz, at least when measured over a sufficiently long time frame.

Geoff on 29 May 2012
By 'uncorrelated', you just mean out-of-phase, right? This is about as simple as wave generation gets.
Just work out how much of the wavelength to offset it by. Let's say you want a quarter wavelength:
lambda = 0.25;
phase = 2*pi*lambda / f1;
j = 20*sin(2*pi*f1*t + phase);