# Adjust the power of a digital signal to a given value

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?

• Right, units... It would be $sqrt(\text{var}(x)\cdot y(n)^2 / \text{var}(y))$, which simplifies to std(x)/std(y)... – Omegaman Jan 10 '16 at 1:13