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I have two signals: $x(n)$ is a white-noise signal with a given variance, $y(n)$ is the sum of white noise plus a sum of sinusoids. $$ x(n) = v_1(n) $$ $$ y(n) = \sum_{i=1}^{q} [ a_i \cos(\omega_i n) + b_i \sin(\omega_i n) ] + v_2(n) $$ $$ v_{1,2}(n) \sim W.N.(0,\sigma^2) $$

And that is how I generate the two signals on Matlab. Now I'd like to normalise $y(n)$ so that its power is the same as $x(n)$, how can I do that?

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Multiply y(n) by std(x)/std(y)

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  • $\begingroup$ To normalize power, shouldn't it be the ratio of variances? $\endgroup$
    – Omegaman
    Commented Jan 9, 2016 at 3:47
  • $\begingroup$ You would think so, but no. $\endgroup$
    – CMDoolittle
    Commented Jan 9, 2016 at 8:14
  • $\begingroup$ Right, units... It would be $sqrt(\text{var}(x)\cdot y(n)^2 / \text{var}(y))$, which simplifies to std(x)/std(y)... $\endgroup$
    – Omegaman
    Commented Jan 10, 2016 at 1:13

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