Mix First-Order Ambisonics to Stereo in FFmpeg

First-order Ambisonics (FOA) uses four channels to capture a complete three-dimensional soundfield, but standard playback systems require a two-channel stereo downmix. By synthesizing virtual cardioid microphones pointed at left and right angles, FFmpeg's pan filter can decode four-channel Ambisonics into standard stereo without needing external plugins. This guide explains how to calculate the matrix coefficients and execute the FFmpeg commands for both modern AmbiX and legacy FuMa Ambisonic formats.

Understanding Ambisonic Channel Orders

Before applying the pan filter, you must identify whether your source audio is in AmbiX (standard for YouTube and modern spatial audio) or FuMa (traditional Ambisonics). Each uses a different channel assignment:

  • AmbiX (ACN / SN3D):
    • Channel 0 (c0): \(W\) (Omnidirectional)
    • Channel 1 (c1): \(Y\) (Left / Right)
    • Channel 2 (c2): \(Z\) (Up / Down)
    • Channel 3 (c3): \(X\) (Front / Back)
  • FuMa (Traditional):
    • Channel 0 (c0): \(W\) (Omnidirectional)
    • Channel 1 (c1): \(X\) (Front / Back)
    • Channel 2 (c2): \(Y\) (Left / Right)
    • Channel 3 (c3): \(Z\) (Up / Down)

Decoding via Virtual Microphones

A standard stereo downmix synthesizes two virtual cardioid microphones angled at \(\pm 45^\circ\) from the center front (\(\pm 90^\circ\) stereo aperture). The mathematical formula for a virtual cardioid combines the omnidirectional component (\(W\)), the forward component (\(X\)), and the lateral component (\(Y\)). The vertical component (\(Z\)) is discarded for horizontal stereo.

For normalized AmbiX:

  • Left (\(c0\) output): \(0.5 \times W + 0.3535 \times X + 0.3535 \times Y\)
  • Right (\(c1\) output): \(0.5 \times W + 0.3535 \times X - 0.3535 \times Y\)

FFmpeg Command for AmbiX (ACN/SN3D)

In AmbiX, \(W\) is c0, \(Y\) is c1, and \(X\) is c3. Run the following command to downmix to stereo:

ffmpeg -i input_ambix.wav -af "pan=stereo|c0=0.5*c0 + 0.3535*c3 + 0.3535*c1|c1=0.5*c0 + 0.3535*c3 - 0.3535*c1" output_stereo.wav

Explanation of the Filter:

  • pan=stereo: Defines the target output layout as a 2-channel stereo file.
  • c0=...: Sums 50% omni (c0), ~35.4% front (c3), and ~35.4% left (c1) to create the left stereo output.
  • c1=...: Sums 50% omni (c0), ~35.4% front (c3), and subtracts ~35.4% left (yielding right) to create the right stereo output.

FFmpeg Command for FuMa

In FuMa, \(W\) is attenuated by \(3\text{ dB}\) (\(\approx 0.707\)), \(X\) is c1, and \(Y\) is c2. Adjust the coefficients accordingly:

ffmpeg -i input_fuma.wav -af "pan=stereo|c0=0.7071*c0 + 0.5*c1 + 0.5*c2|c1=0.7071*c0 + 0.5*c1 - 0.5*c2" output_stereo.wav

Preventing Clipping

Summing multiple audio channels together can increase the overall amplitude and cause digital clipping if the source is mastered close to \(0\text{ dBFS}\). To avoid distortion, append the volume filter or the loudnorm filter after the pan filter:

ffmpeg -i input_ambix.wav -af "pan=stereo|c0=0.5*c0 + 0.3535*c3 + 0.3535*c1|c1=0.5*c0 + 0.3535*c3 - 0.3535*c1,loudnorm" output_stereo.wav