## A Look At A Sample

• Let's consider a 16-bit audio sample:

00 010100000101 01

• Sample 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

## 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