Lesson 10 · Decoding 24-bit samples - Build a WAV/PCM Toolkit

Decoding 24-bit samples

Twenty-four-bit audio is studio quality but awkward - three bytes per sample, with no native integer that size, so you assemble it and sign-extend by hand. Today you decode it exactly.

The goal

Decode 24-bit signed little-endian samples, sign-extending the top bit.

Start here - the target

TO DO

Scenario: 24-bit little-endian bytes decode with sign extension

Giventhe twelve data bytes 00 00 00 FF FF 7F 00 00 80 FF FF FF

Whenthey are decoded as 24-bit signed little-endian samples

Thenthe samples are [0, 8388607, -8388608, -1]

And00 00 80 decodes to -8388608 (the negative edge), because bit 23 is the sign bit

Background

24-bit PCM gives more dynamic range than 16-bit and is common in recording and mastering, but no CPU has a 24-bit integer type. Each sample is three bytes, little-endian, so you assemble it into a wider integer: b[0] | b[1]<<8 | b[2]<<16, giving a value in 0 to 16777215. That is the unsigned reading; you still have to apply the sign.

The sign bit of a 24-bit value is bit 23. If the assembled value is >= 2^23 (8388608), the number is negative and you recover it by subtracting 2^24 (16777216) - the same two’s complement fix-up you would get for free from a native signed type, done manually. So 00 00 80 assembles to 0x800000 = 8388608, and subtracting 2^24 gives -8388608, the most negative 24-bit sample. The valid range is -8388608 to 8388607. Sign extension is the one thing to get right here; the byte assembly is just last lesson’s pattern with a third byte.

Make it work

// assemble three LE bytes, then sign-extend from bit 23
func decode24(b []byte) []int {
  var out []int
  for i := 0; i+2 < len(b); i += 3 {
    v := int(b[i]) | int(b[i+1])<<8 | int(b[i+2])<<16
    if v >= 1<<23 {   // top bit set -> negative
      v -= 1 << 24
    }
    out = append(out, v)
  }
  return out
}

CheckpointDONE

You can decode 24-bit signed samples with correct sign extension. Commit and stop here.