Compression
A Look At A Sample
Let's consider a 16-bit audio sample:
00 010100000101 01Sample consists of
Headroom: Not recorded at maximum amplitude to avoid clipping
Signal: The actual audio
Noise: The low-order bits are typically garbage
The signal and noise blend together
As signals are manipulated, more noise creeps up into the signal bits because addition and multiplication
Clipping
Artifact of fixed-range representation of PCM sample: floating-point samples are basically unclippable
If the amplitude to be represented goes over the max possible value or under the min, what to do?
Not much except clamp (clip) the sample as close as you can get it
Net effect: tops clipped off waves
This happens in analog systems also because max/min voltages
Discontinuity introduces harmonics: bad distortion
This is why headroom
Noise
Several kinds of common audio noise
Uniform "white noise": easy to make with a computer
"Pink noise" that rolls off linearly with frequency ("1/f noise", "flicker noise")
"Brownian noise" ("1/f^2 noise") from random walk in time domain
Check out this Wikipedia article on noise colors
Audio Compression — Model and Residue
Idea: Build a simplified model of the audio signal — requires less space to represent.
Maybe the model is good enough for purpose: lossy compression
Otherwise send the model along with the residue — the difference between the model and the true signal: lossless compression
The residue might be a bit compressible too
Audio Compression — Model
Goal: build a simple parameterized approximate model of the audio signal
Time domain model
Audio signals tend to be "smooth" continuous and have continuous derivatives
Model the signal as lines or polynomials or splines
Frequency domain model
Audio signals tend to be periodic; frequencies tend to vary slowly
Model the spectrum with quantization in frequency and amplitude
Phase is confusing
Audio Compression — Residue
The residue can often look like noise
Still, the amplitude of the residue should be small relative to the signal amplitude
Common compression schemes — Huffman coding, Rice coding, arithmetic coding — take advantage of frequency distribution of residue
Lossless vs Lossy Compression
Lossless (e.g. FLAC) is going to be limited for a lot of kinds of sounds. The fancier the model, the more kinds of sounds that can be compressed well
Doing lossy well is harder, because mustn't throw away stuff that wrecks the sound. Psychoacoustics is needed. Tends to be done in frequency domain; models are generalized