Principles of Digital Audio

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Principles of Digital Audio
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• 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

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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

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The quality of digital sound

• Is affected by -
• Sample rate
• Sample resolution
• A/D and D/A converters
• Quantization error
• Jitter

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Digitizing sound

• 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).

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• 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..

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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.

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Aliasing
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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..

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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 -

Graphic at 8 bits per pixel
Graphic at 4 bits per pixel
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• 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.

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Sample Resolution Graph
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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!?!

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Quantization error

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

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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

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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 its
  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
  its what makes the difference between a pro
  sound and a consumer sound.

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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 cant 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

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