06 Analogue and digital

Analogue and digital

We hear sound as a result of analogue physical vibrations in air pressure that are transferred to our eardrums
To record sound, we need to capture these vibrations in some way; analogue recording represents the change in sound pressure as e.g. a physical waveform in the groove of a record or a variation in magnetisation on tape
Nowadays, we convert the vibrations that make up sound into digital measurements by sampling the waveform
This means that we read its amplitude many times at a regular rate to get a very accurate idea of when it goes up and down, and list the binary numbers of each measurement
An analogue-to-digital converter (ADC) samples the analogue waveform and create the series of binary numbers
A digital-to-analogue converter (DAC) is used for the opposite purpose
When a digital signal picks up noise, it is still distinguishable as 0s or 1s; the noise doesn’t affect the reproduction
People still like analogue formats for a variety of reasons; words like warm / vintage are used and enthusiasts like the album artwork and having a physical rather than digital file.

Sampling a waveform means reading the amplitude regularly at a given rate – sample rate
This is the number of times we read the waveform every second, measured in Hertz; the more often samples are taken, the more accurately the readings recreate the waveform of the original analogue signal
If the sample rate isn’t high enough, the highest frequencies are not captured / roll off giving a muffled sound
Nyquist’s theorem states the sample rate must be double the highest frequency we want to capture; because humans can hear up to 20,000Hz, we must set our sample rate above 40000Hz or 40kHz (hence 44.1kHz on CD) to capture the audible frequency range
In old samplers, disk space / memory was at a premium – so lower sample rates were used to take up less space
If the sample rate is too low, aliasing can occur; inaudible frequencies above the Nyquist frequency are captured and incorrectly recreated – a new, lower frequency wave (artefact) is created in the audible frequency range
Audio interfaces use anti-aliasing filters (a type of LPF set at the highest desired audible frequency e.g. 20kHz)
If there are any samples that are taken at irregular intervals or the same issue occurs in playback, this is jitter.

The amplitude measurements we take can only be chosen from a certain number of values; the choices are given by the bit depth – any amplitude value that isn’t perfectly on a line is rounded up or down
The higher the bit depth, the more accurate the amplitude values are in reflecting the original analogue waveform; low bit depths have limited dynamic range and more noise / low signal-to-noise ratio – they sound grainy and metallic
We can calculate the number of amplitude measurements by working out 2 to the power of the bit depth.
For CD if we work out 2¹⁶, this gives us 65,536 possible amplitude measurements; if we step up to 24 bits, we see an increase in dynamic range to 144dB, and an increase in amplitude measurements to 16,777,216.
The bit depth relates to the dynamic range; each bit gives us around another 6dB of dynamic range
The bit depth on a CD is 16 bits so the dynamic range of a CD (16 bit) is around 96dB (16×6)
If the bit depth is low we encounter quantisation error, when a signal is rounded to an amplitude measurement a long way from the original
The higher the bit depth, the less of an issue quantisation error is
Dithering randomises quantisation error; this introduces a small amount of low level noise which pushes the level of some of the measurements up.

Keep this separate in your head to bit depth / sample rate; it is to do with streaming and not just digital audio
We have to transfer data when streaming digital audio, the bit rate is the number of bits transmitted per second
The more bits that are transmitted per second, the higher the quality of the streamed audio
If you were streaming an uncompressed recording with a low bit rate, it would still sound poor
If you streamed a low quality MP3 with a very high bit rate, the quality is limited by the original compression
Recordings with a high bit rate need more bandwidth as they transfer more audio data.

Analogue and digital hardware and software attributes

The differences between digital and analogue recordings

The advantages and disadvantages of analogue hardware and software

The advantages and disadvantages of digital hardware and software

Sampling theory and converters inc. Nyquist

Differences in the way noise affects analogue and digital recordings

Aliasing

Quantisation error and dithering

Digital consumer formats

MP3 / M4A, emerging technologies

Data bit rate

The specifications of digital recordings and how they affect sound quality

A/D and D/A conversion

Sample rate

Bit depth

Streaming bit rate

Uncompressed PCM audio formats

Data compressed formats e.g. MP3

The differences between lossless and lossy audio compression