principles of digital audio

1. Principles of Digital Audio

2. The principles which underlie almost all digital audio applications, be they digital synthesis, sampling, digital recording or CD playback are based on the following concepts………

3. Digital audio terms sample; sampling rate; sample size (bit depth) analogue-to-digital converter; digital-to-analogue converter Nyquist theorem aliasing jitter dither quantizing or digital noise transient

4. The quality of digital sound Is affected by: - Sample rate Sample resolution A/D and D/A converters Quantization error Jitter

5. Sounds from the real world can be recorded and digitized using an Analog-to-Digital Converter (A/DC). This digital audio is simply sound represented with numbers. The sound is processed as binary data (i.e. 0s and 1s). Digitizing sound

7. The sample rate refers to the number of times the incoming sound is sampled by the A/D converter. Typical rates are 44.1 kHz (CD quality), 48 kHz (DAT) and 96 kHz (hard-disc recorders). E.G. when recording at 44.1 kHz the sound would be sampled 44,100 times per second. This sounds like a lot – except for a factor called the Nyquist frequency………………..

8. Nyquist theory According to the Nyquist theory (named after Harry Nyquist), the highest reproducible frequency of a digital system is 1/2 the sampling rate, often called the Nyquist frequency. E.G. if a sound is recorded at 44.1 kHz then the highest frequency that can be accurately represented is 22.05 kHz (about the top end of human hearing). Any frequencies above this will be cut off and be digitally represented at a much lower frequency than the original – this process is called aliasing.

9. Aliasing

10. AMAZING FACT! If you think this is all becoming a bit dry and boring WAKE UP! All recent machines and devices that you probably use to play and listen to music – i.e. CDs, DVDs, DATs, MP3s – are built upon these principles of digital sound. Now read on………………..

11. Sample Resolution Sample resolution refers to the number of bits of digital information contained in each sample. The number of bits – or bit depth - signifies the number of levels of gradation of sound within a single sample. An analogy can be seen with photos: -

12. The CD standard is 16 bits, although most professional recorders handle 24 bits. Recording audio at 24 bits requires more hard-disc space than 16 bits (as more information about each sample of sound is recorded and needs storage space) The sample rate is the number of "snapshots" of audio that are sampled every second. The continuous audio stream is digitally encoded in a similar way to a movie camera capturing motion by recording a frame of image many times per second. The higher the sample rate (and bit depth), the closer one can come to accurately representing the original sound.

13. Sample Resolution Graph

14. A/D and D/A converters The analogue-to-digital and digital-to-analogue converters do just that. E.G. suppose you have a 24 bit converter and a 48 kHz sample rate. When the A/D converter senses an audio signal it measures that signal 48,000 times a second. Each one of the 48,000 “snapshots” is given a value between -8,395,008 and +8,305,008 (24 bit resolution has 16,790,016 possible levels). The digital recorder reads these numbers, and the D/A converters translates these numbers back into an analogue signal. Got that!?!

15. Quantization error Even with 48,000 snapshots per second, some time still exists when the sound doesn’t get sampled. Even with 16 million (24 bit) possible values there’s still a point when those values may not accurately represent the signal’s position on the waveform graph, as the samples are rounded up or down to the nearest number. This rounding is called the quantization error.

17. Digital noise The greater the quantization error the greater the amount of digital noise The solution to reducing digital noise is to use larger sample sizes or bit depth

18. Jitter Sound sampled at 44.1 kHz (CD quality) should take place once every 44,100th of a second. In reality there are small timing errors which occur –known as jitter. Does this make a big difference? Because it’s related to the timing of the snapshot of sound, it can change the recorded frequencies just a little. Typical jitter times goes between 1.0 x 10 (-9) secs (a NANO second) and 1.0 x 10 (-7) secs – it’s what makes the difference between a ‘pro’ sound and a ‘consumer’ sound.

19. Soundcards The soundcard is set to the required sample rate. Sound is processed using (i) low-pass filter (cuts off very high frequencies which it can’t handle) (ii) anti-aliasing filter After each sample the A/DC looks at the ‘filtered’ sound and sees how loud it is at that exact moment in time and transforms that loudness level into the nearest digital number