I have two audio signals that I want to mix at various mixing ratios. Initially, I simply went for something like
$y(t) = \alpha \cdot x_1(t) + (1-\alpha) \cdot x_2(t)$
where $\alpha$ is the ratio between zero and one and $x_1$ and $x_2$ are the two signals.
However, I have seen a few panning curves that did not mix signals linearly. They told me that a linear mix would change the overall loudness while mixing.
Is there something to that or is a linear mix the correct way to do it?