Crossfade for files vs for speakers

Question

I'm fairly new to crossfading albeit having a fairly good understanding of the mathematics and physical units.

What I can't wrap my head around is as to whether there is a difference between crossfading between files and between physical speakers.

What I want to achieve is a constant loudness/volume level across the fade, leading to the questions:

• in order generate a 3rd mono WAV file C from two other mono WAV files A and B of equal loudness/volume, how do I guarantee that C.wav has the same loudness/volume as A.wav and B.wav individually? Do I choose equal power fading or equal gain fading?

• what is the method of choice for crossfading between two speakers, say the left and right one of a headphone, if I want the sound to "move" between the speakers with equal total loudness, do I have to use equal power fading or equal gain fading?

Answer 1

The answer depends on the degree of correlation between the signals. Correlated signals sum in amplitude, uncorrelated signals sum in power.

Most wave files are essentially uncorrelated, so for your first case constant-power fading is the best choice.

The second case (which is mainly a balance control) is more complicated. For headphones the two signals do not physically interact at all, but the loudness summing happens perceptually in your brain. Without going into too much detail of how this works: the best choice here is also constant-power fading.

Two loudspeakers in a room is another can of worms: At low frequencies the two loudspeaker signals at the listener position will sum in amplitude and at high frequencies they will sum in power. So the correct fading type depends on the frequency.

The "cutoff" frequency between the two states depends on the physical properties of the setup: distance between the speakers, acoustic properties of the room, listening distance etc. In most residential cases, it's fairly low, maybe 80Hz-160Hz. Hence most implementations will use a constant-power fade which gets the bulk of the spectrum correct. However this will result in the Left or Right location having roughly 3 dB less bass than the center position. That can be corrected using a dynamic low-shelf filter that's linked to the fading control.