Compression Methods

Stereo

• Idea: Left and right stereo channels are highly correlated

• Typical to take a stereo pair and turn it into a mono channel (l + r) / 2 and a side channel (l - r)

• The side channel is typically low amplitude, and so can be compressed easily

• Side benefit: mono channel is easily extracted

Downsampling

• Idea: Most audio has low amplitudes at higher frequencies

• Downsample the signal, transmit that

• Loss is pretty noticeable at high compression rates; maybe need some residue coding

• The signal path may be band-limited anyhow: embedded devices, guitar pedals, etc

• MP3 (discussed in a bit) is a surprisingly close cousin to this scheme

Companding

• Idea: Small differences in large amplitudes matter less. In particular, human hearing is log-amplitude

• To best represent a signal in a fixed number of bits, squash the encoding so that there are fewer codes for larger amplitudes

• Classic: 8-bit µ-Law, A-law

• µ-Law: 14 bits in, 8 bits out

  • Continuous

    $$y(t) = \mathrm{sgn}(x(t)) \frac{\ln(1 + \mu |x(t)|)}{\ln(1 + \mu)}$$

    where µ is 255

  • Discrete version is given by big approximation table

POTS

• US Plain Ol' Telephone Service compression is downsampling to 8000 sps and then µ-Law encoding to 8 bits, so 64000 bps

• Lossy, but turns out to be good enough to sound OK for voice

• Originally implemented entirely analog: the digital thing is a replicant

• Characteristic telephone sound is mostly this

FLAC

• Predict in time domain using polynomial model or Linear Predictive Code

• Encode residue using Rice codes (related to Huffman codes)

• Reliable compression of about 2×

• Remember: the noise must be compressed and recreated also

Lossy Compression ala MP3

• Good Ars Technica MP3 tutorial

• High-level view:

  • Split the input signal up into a bunch of frequency bands using a "polyphase filter"

  • In each band:

    • Use an FFT to figure out what's going on

    • Use a DCT to get a power spectrum (noise subframes are speshul)

    • Quantize the spectrum to reduce the number of bits (giving power errors due to noise)

    • Huffman-encode the quantized coefficients to get a compact representation

  • Combine all the compressed quantized coefficients to get a frame

• The details are quite complex: see something like Ogg Vorbis for a cleaner version