Digital Audio

1
Digital Audio

• What do we mean by digital?
• How do we produce, process, and playback?
• Why is physics important?
• What are the limitations and possibilities?

2
Digital vs. Analog

• Discrete data
• Reproducible with 100 fidelity
• Can be stored using any digital medium
• Frequency and amplitude ranges limited by
  digitization

• Continuous data
• Reproduction introduces new noise
• Storage limited by physical size
• Virtually unlimited frequency and amplitude ranges

3
Physics of Digitization

• Sound (pressure wave) is transduced into an
  electrical signal (usually voltage)
• Signal read by A-D converter to discrete values
• Time sequence of signal values encoded in a
  computer

4
Sampling Basics

• Sample Rate Frequency interval of the time
  sequence of encoded values
• Sample Depth (or Bit Depth) Number of bits used
  to encode each value
• Bit Rate (Sample Rate) x (Bit Depth)
• For example, CD Quality audio is 44.1kHz at 16
  bits 7.065E5 bps per channel, or 1411 kbps total

5
Sample Rate (Sample Frequency)

• Sample Period 0.5s
• Sample Rate 1/0.5s 2Hz

6
Sample Rate Matters!(Mathematica Demo 1)
7
What do the samples actually represent?
8
Nyquist-Shannon Sampling Theorem

• If a function x(t) contains no frequencies
  higher than B, it is completely determined by
  giving its ordinates at a series of points spaced
  1/(2B) seconds apart.
• A necessary condition for digitizing a signal so
  that it can be faithfully reconstructed is that
  the sample rate is at least twice as high as the
  highest frequency present in the signal.

9
What can go wrong?

• Aliasing High frequencies contribute signal
  components that are perceived as lower
  frequencies (Mathematica Demo 2)

10
Bit Depth

• Number of bits used to represent each sampled
  value
• Available discrete values n2b
• Here there are only 5 discrete values, so 3 bits
  per sample

11
Dynamic Range

• Ability to represent small and large amplitude
  signals in the same scheme
• Clipping Large signals are cut off, introducing
  high harmonics
• Masking Small signals are drowned out

12
Signal-to-Noise Ratio (S/N)

• Ratio of meaningful signal power to unwanted
  signal power
• In sound, the audible power (decibels) is
  skewed from the actual power
• Best case scenario noise is in the first bit
• S/N (dB) 10 Log (2b) 3.01b (per channel)
• Human ear sensitivity covers a range of more than
  120dB! (40 bits)

13
Digital Audio Compression

• Analog signals are practically incompressible
• Raw audio signals are similarly hard to reduce
  using standard (lossless) file compression
  (Shannon Information Theory)
• Psycho-acoustic models may be helpful! (lossy)

14
MP3 Codec

• Divide the file into packets and find the Fourier
  power spectrum via DFT
• Throw out easily masked frequencies to reach
  desired bit rate
• Dither regions with different dynamic ranges or
  where the bit depth must be lowered to match
  desired bit rate
• Perform traditional redundancy compression
• (ratatat samples)

15
Discrete Fourier Transform

• Frequency Limit ½ Sample Frequency (Nyquist)
• Frequency Resolution 1/Signal Period
  (Mathematica 3)
• Usually frequency resolution is much sharper than
  the ear can detect

16
Dithering
17
Digital Signal Processing (DSP)

• Non-linear (ie, atemporal)
• Real-time effects subject to latency and
  buffering memory
• Filters and envelopes extremely
  difficult/expensive to achieve with analog
  techniques
• Easier non-destructive editing
• Perfect fidelity in copying

18
Some Common DSP Effects

• Vocoder vs Autotune (Daft Punk)
• Delay/Echo (U2, David Gray)
• Filter/Flange (Foster the People, Dizzy Gillespie)

19
Digital Synthesis (If you can write an equation,
you can hear it!)

• Sound engineering for movies/TV
• Arbitrary mathematical functions can be generated
  (Mathematica 4)
• Sounds not identifiable by the ear/brain
• (Chem Bros and Skrillex samples)