3 ms·

tl;dr: the algorithm splits the audio into blocks (default is 4096 samples per block). Then a polynomial is used to approximate the wave for the block, and resi

by jsbg 4y ago

tl;dr: the algorithm splits the audio into blocks (default is 4096 samples per block). Then a polynomial is used to approximate the wave for the block, and residuals are calculated for each sample by subtracting the approximation. The residuals, because their magnitude is smaller than the original signal, require fewer bits to encode. Hence the smaller file without loss of information.

aidos 4y ago
Nice. Not dissimilar from what jpeg2000 does (from memory - correct me if I’m wrong!). They use the previous pixel values in order to “guess” the next value and then store the delta, which tends to be a smaller number on average, giving better compression.
- mistrial9 4y ago
  proximity in a 2D image has neighbors in north-south-east-west (NSEW) on a 2D grid, not just pixel neighbors per-scanline (row of bytes); proximity in a sound file has harmonics and transitions of some plural set of signal, but the sound file neighbors are roughly at a point in time. corrections welcome
  - robotresearcher 4y ago
    True. The fact of locality in real-world 2D images means you can predict a pixel's value by picking any neighboring pixel, or indeed any nearby pixel, with worsening performance with L2 distance. There's no reason I can think of to prefer a direction, except for convenience in the data structure.
cryptonector 4y ago
Plus the use of Rice codes for encoding the residuals in as few bits as possible.
derefr 4y ago
Curious to me why only such a simple representation (polynomial) is used for the approximation. Couldn't you get a much better approximation (⇒ more compressible residual) in about the same amount of storage space + CPU decoding effort, using a formula based on e.g. wavelet LUTs as your primitive (plus maybe a larger block size)? Are there other, more advanced lossless encodings that do this? And if so, why didn't they catch on compared to FLAC? For that matter, is there a lossless format that just embeds a regular lossy encoding of the audio as the approximation, and then computes+stores the residual relative to that? (I'm guessing that this wouldn't work well for some reason, but I'm not sure what that reason would be.) (ETA: the other later lossless audio formats that I'm personally aware of — ALAC, Monkey's Audio, and WavPack — all seem to use linear prediction. Seemingly they were all designed under the presumption of the constraint that the encode step must be able to be done in hardware / with fixed-sized memory buffers; rather than allowing that you can load the whole PCM audio file into memory and do things like FFT to it. Possibly made sense in the late 90s, when a PC's RAM wasn't much larger than five minutes of uncompressed audio. Doesn't really make sense today. Maybe we're due for a new lossless audio encoding?)
- hcs 4y ago
  I just ran across MPEG-4 SLS [1] (née "AAZ" for "Advanced Audio Zip", aka HD-AAC), which is a lossless format on top of AAC's MDCT, and which is patented, unfortunately. That led me to other coders: DTS-HD Master Audio [2] (née DTS++) and OptimFROG DualStream [3]. OptimFROG's DualStream mode is similar to WavPack's hybrid mode, and DTS-HD MA uses DTS Coherent Acoustics (based on ADPCM), so none of these are based on a perceptual lossy codec besides MPEG-4 SLS. (Sorry to keep replying here, I keep stumbling on interesting things after the edit window closes) [1] https://en.wikipedia.org/wiki/MPEG-4_SLS https://en.wikipedia.org/wiki/MPEG-4_SLS [2] https://en.wikipedia.org/wiki/DTS-HD_Master_Audio https://en.wikipedia.org/wiki/DTS-HD_Master_Audio [3] http://losslessaudio.org/DualStream.php http://losslessaudio.org/DualStream.php
- hcs 4y ago
  > is there a lossless format that just embeds a regular lossy encoding of the audio as the approximation, and then computes+stores the residual relative to that? It's not "regular lossy", but WavPack does allow separating lossy from the residual in hybrid mode. I think this is rarely done with DCT-based stuff because there's so much potential imprecision in the decoders.
black_knight 4y ago
As always with compression there is no magic. There are wav files that are smaller than the equivalent flac file (perhaps even the majority of possible WAV files are shorter than their equivalent FLAC). But it so happens that the sounds we actually want to store are very well approximated by polynomials.
drawingthesun 4y ago
Would applying a lossless compression algorithm to the data such as zip or 7z after the algorithm you describe reduce the file even size even more? Wondering if FLAC already does this or if such a feature could be added?
- tgv 4y ago
  These methods perform poorly on audio, so even worse on compressed audio. Just try it on a wav and a flac file.
liftm 4y ago
Sounds quite simple already. I still wonder if for FLAC there's an equivalent of what QOI is to PNG.

by jsbg 4y ago

aidos 4y ago

Nice. Not dissimilar from what jpeg2000 does (from memory - correct me if I’m wrong!). They use the previous pixel values in order to “guess” the next value and then store the delta, which tends to be a smaller number on average, giving better compression.

mistrial9 4y ago
proximity in a 2D image has neighbors in north-south-east-west (NSEW) on a 2D grid, not just pixel neighbors per-scanline (row of bytes); proximity in a sound file has harmonics and transitions of some plural set of signal, but the sound file neighbors are roughly at a point in time. corrections welcome
- robotresearcher 4y ago
  True. The fact of locality in real-world 2D images means you can predict a pixel's value by picking any neighboring pixel, or indeed any nearby pixel, with worsening performance with L2 distance. There's no reason I can think of to prefer a direction, except for convenience in the data structure.

cryptonector 4y ago

Plus the use of Rice codes for encoding the residuals in as few bits as possible.

derefr 4y ago

Curious to me why only such a simple representation (polynomial) is used for the approximation. Couldn't you get a much better approximation (⇒ more compressible residual) in about the same amount of storage space + CPU decoding effort, using a formula based on e.g. wavelet LUTs as your primitive (plus maybe a larger block size)? Are there other, more advanced lossless encodings that do this? And if so, why didn't they catch on compared to FLAC? For that matter, is there a lossless format that just embeds a regular lossy encoding of the audio as the approximation, and then computes+stores the residual relative to that? (I'm guessing that this wouldn't work well for some reason, but I'm not sure what that reason would be.) (ETA: the other later lossless audio formats that I'm personally aware of — ALAC, Monkey's Audio, and WavPack — all seem to use linear prediction. Seemingly they were all designed under the presumption of the constraint that the encode step must be able to be done in hardware / with fixed-sized memory buffers; rather than allowing that you can load the whole PCM audio file into memory and do things like FFT to it. Possibly made sense in the late 90s, when a PC's RAM wasn't much larger than five minutes of uncompressed audio. Doesn't really make sense today. Maybe we're due for a new lossless audio encoding?)

hcs 4y ago
I just ran across MPEG-4 SLS [1] (née "AAZ" for "Advanced Audio Zip", aka HD-AAC), which is a lossless format on top of AAC's MDCT, and which is patented, unfortunately. That led me to other coders: DTS-HD Master Audio [2] (née DTS++) and OptimFROG DualStream [3]. OptimFROG's DualStream mode is similar to WavPack's hybrid mode, and DTS-HD MA uses DTS Coherent Acoustics (based on ADPCM), so none of these are based on a perceptual lossy codec besides MPEG-4 SLS. (Sorry to keep replying here, I keep stumbling on interesting things after the edit window closes) [1] https://en.wikipedia.org/wiki/MPEG-4_SLS https://en.wikipedia.org/wiki/MPEG-4_SLS [2] https://en.wikipedia.org/wiki/DTS-HD_Master_Audio https://en.wikipedia.org/wiki/DTS-HD_Master_Audio [3] http://losslessaudio.org/DualStream.php http://losslessaudio.org/DualStream.php
hcs 4y ago
> is there a lossless format that just embeds a regular lossy encoding of the audio as the approximation, and then computes+stores the residual relative to that? It's not "regular lossy", but WavPack does allow separating lossy from the residual in hybrid mode. I think this is rarely done with DCT-based stuff because there's so much potential imprecision in the decoders.

black_knight 4y ago

As always with compression there is no magic. There are wav files that are smaller than the equivalent flac file (perhaps even the majority of possible WAV files are shorter than their equivalent FLAC). But it so happens that the sounds we actually want to store are very well approximated by polynomials.

drawingthesun 4y ago

Would applying a lossless compression algorithm to the data such as zip or 7z after the algorithm you describe reduce the file even size even more? Wondering if FLAC already does this or if such a feature could be added?

tgv 4y ago
These methods perform poorly on audio, so even worse on compressed audio. Just try it on a wav and a flac file.

liftm 4y ago

Sounds quite simple already. I still wonder if for FLAC there's an equivalent of what QOI is to PNG.