Equal power crossfade I am working on an audio system where I need to implement an equal power crossfade between two signals over a specified number of samples. Initially I implemented a linear fade but this creates a dip in the middle of the crossfade which I don't want. I tried a few other methods that I found on Google but they either make a dip in another part of the curve or even make the sound louder.

If I have float samples ranging from -1.0 to 1.0 and I want to crossfade between them over the course of x samples, keeping the perceived volume the same over the entire crossfade, what would be the correct formula for calculating the curve? Preferably I want to have a value like 0.001 represent the minimum level that the fade in starts at and the fade out goes to. 1.0 should be the maximum. Thanks in advance for any advice!
if the two audio signals are totally uncorrelated, the the squares of the two crossfade gains should add to 1.  so, to prevent that dip, your crossfade function will look more like $\sqrt{\frac{1}{2}(1+t)}$ and $\sqrt{\frac{1}{2}(1-t)}$ rather than $\frac{1}{2}(1+t)$ and $\frac{1}{2}(1-t)$  for $-1 \le t \le +1$.  note, for constant power crossfades, at the midpoint of the crossfade ($t=0$), both crossfade gains are at $\sqrt{\frac{1}{2}} \approx 0.707$ rather than at $\frac{1}{2}$.  that's what addresses the dip you want to avoid.

if your two audio signals are somewhere between totally uncorrelated and totally correlated, you need to determine the degree of correlation (that's what cross-correlation is all about), and then the crossfade functions can be determinied analytically.  i have posted to music-dsp a little theory about it.  it's not perfectly rigorous, but i think it works.