# Equal power crossfades functions.



## tomaslobosk (Jun 18, 2015)

I'm having serious doubts about equal power crossfades functions, Big Bob's equal power crossfades are made with sine and cosine functions (B), while in Cubase, equal power crossfades are more like square root functions (A)

In both cases f(0.5)=0.7071, so WTF :lol: 







I would love to hear some good answers!

Greetings, 

Tomás.


----------



## d.healey (Jun 18, 2015)

What's the question?


----------



## tomaslobosk (Jun 18, 2015)

Sorry, my bad, hehe which one of these is actually an equal-power crossfade?


----------



## olajideparis (Jun 19, 2015)

Do not over think this, use whatever fade type and length creates a seamless edit.


----------



## tomaslobosk (Jun 19, 2015)

Thanks for your reply!... I was thinking this issue in a more mathematical aproach :(


----------



## Big Bob (Jun 19, 2015)

The _mathematical_ distinction of equal power xfade curves is that at any X position, the sum of the squares of the two Y values must be some constant value. 

Of course to use them for crossfading, one of the curves must swiing from zero to some max value while the other swings from the same max value to zero. Sin/Cos curves satisfy this relationship because they have the right shape *and* the Sin squared plus the Cos squared always equals 1.0 at any X.

In real life whether EQPXF will produce a constant volume or not will depend on the relative coherency of the two signals. For example, the left and right channels of true stereo source are apt to be very incoherent whereas two copies of the same pure sound source will be nearly 100% coherent. For very incoherent channels, EQPXF will produce the most uniform volume xfade. For very coherent channels, Linear Xfade will be best. Most real-world channels will be somewhere in between.

Rejoice,

Bob


----------



## tomaslobosk (Jun 20, 2015)

Amazing explanation Bob, thank you very much!  

Both A and B curves satisfies this condition!

BTW Bob, what do you mean with the right shape?, if both cases satisfies f(x)^2+g(x)^2=k, what makes one XFade better than the other?


----------



## Big Bob (Jun 20, 2015)

> BTW Bob, what do you mean with the right shape?, if both cases satisfies f(x)^2+g(x)^2=k, what makes one XFade better than the other?



Primarily, as I already stated, the curves should be smooth with one up-trending and the other down-trending and need to swing between 0 and max and vice versa. Not only must the midpoint crossover be at 0.707 (square-root of two over two) but both the up-curve and the down-curve must 'head that way' in a cooperative fashion insofar as fading out one sound and fading in the other.

An absurd example of a true equal-power xfade function that would be useless is:

Va = 0.707 and Vb = 0.707 across the entire xfade X-axis range. ie two straight lines with a height independent of X. The power would be constant over the entire xfade range but what good would it be :lol: 

In the end, what sounds good to the ear and accomplishes the desired objective is what's important.

Rejoice,

Bob


----------



## tomaslobosk (Jun 20, 2015)

Thank you Bob!, everything is clear now.


----------

