# Audio Buffers

Most systems for digital signal processing and music programming process audio in chunks, which are defined by a so called buffer size. These buffer sizes are usually powers of 2, usually ranging from $16$ samples - which can be considered a small buffer size - to $2048$ samples (and more). Most applications, like DAWs and hardware interfaces allow the user to select this parameter. Technically this means that a system collects (or buffers) single samples - for example from an ADC (analog-digital-converter) - until the buffer is filled. This compensates irregularities in the speed of execution for single operations and ensures a jitter-free processing.

## Latency

The choice of the buffer size $N$ is usually a trade-off between processor load and system latency. Small buffers require faster processing whereas large buffers keep the user waiting until a buffer has been filled. In combination with the sampling rate $f_s$, the buffer-dependent latency can be calculated as follows:

$$\tau = \frac{N}{f_s}$$

Round trip latency usually considers both the input and output buffers, thus doubling the latency. For a system running at $48\ \mathrm{kHz}$ with a buffer size of $128$ samples - a typical size for a decent prosumer setup - this results in a round trip latency of $5.5\ \mathrm{ms}$. This value is low enough to allow a perceptually satisfying interaction with the system. When exceeding the $10\ \mathrm{ms}$ threshold it is likely that percussions and other timing-critical instruments experience disrupting latency.

## Buffers in Programming

In higher level programming environments like PD, MAX, SuperCollider or Faust (depending on the way it is used), users usually do not need to deal with the buffer size. When programming in C or C++, most frameworks and APIs offer a processing routine which is based on the buffer size. This accounts for solutions like JUCE or the JACK API, but also when programming externals or extensions for the above mentioned higher level environments. These processing routines, also referred to as callback, are called by an interrupt once the the hardware is ready to process the next buffer.