soundstage_extender

NODE

Extends the stereo image from where the mix put it. Wide sounds go further out and the ones at the edges go past the speakers, while center sounds and the ambience stay where they are.

Parameters

FIELD	WHAT IT DECIDES	RANGE	REQUIRED
amount	How far sounds inside the speakers are extended outward (0.0 = not at all, 1.0 = most). Center and fully-panned positions stay where they are.	0 〜 1	no
outside_deg	How far sounds at the edges are pushed beyond the speakers [deg] (0 = never leave the speakers).	0 〜 60	no
push_from	Where the outward push starts, as a fraction of the speaker angle (smaller = more sounds go outside).	0.1 〜 0.9	no
speaker_angle_deg	Half-angle between the listener's front and each speaker [deg] (30 for an equilateral triangle).	10 〜 60	no
xtc_beta	Regularization of the crosstalk canceller. Larger is gentler (less boost in the speaker feeds) and pushes less far.	0.01 〜 1	no

{
  "amount": 1,
  "outside_deg": 45,
  "speaker_angle_deg": 30,
  "type": "soundstage_extender"
}

How it is computed

per STFT bin (the window is 1024 samples at 48 kHz in length, hop 1/4):

1. smooth the L/R covariance over about 30 ms
2. u = its principal eigenvector = [cos ψ, sin ψ · e^(jφ)]
   c = (λ1 - λ2) / (λ1 + λ2)    how much the bin is one direct sound
3. p = uᴴ x  (direct)          a = x - u · p  (ambience)
4. the pan position from ψ is extended by amount,
   and pushed out by outside_deg from push_from to the edge;
   it moves in proportion to c
5. inside the speakers: p is re-panned at the new angle
   outside: feeds = (Hᴴ H + β I)⁻¹ Hᴴ · d(θ)
   H = speakers to ears, d = ears for a source at θ (spherical head)
6. out = re-placed p + a

Nothing is moved below about 200 Hz or above 20 kHz. The push past the speakers works between about 200 Hz and 9 kHz, where the spherical head model (Brown and Duda) holds. With amount and outside_deg at 0, the output is the input, one window late.

Using it

It only moves what is already wide.
Center sounds and the ambience are left alone. A sound panned halfway goes further out and a sound at the edge goes past the speaker, so the left to right order of the mix stays the same.
The outside image needs the sweet spot.
It is computed for a head centered between the speakers at speaker_angle_deg. A few centimeters off still works; about 10 cm off and the image falls back inside the speakers. It does nothing useful on headphones.
It adds one window of delay.
About 21 ms, or 23 ms for material in the 44.1 kHz family. Adding or removing the node while playing leaves a gap of that length. Changing its values does not.
Sounds that overlap move less.
When two sounds share a frequency at the same moment, the bin points between them and neither reaches its target. The error is always on the short side: nothing is pushed further than asked.
Do not combine it with crosstalk_canceller.
Both cancel crosstalk. Used together, the cancellation is applied twice.