MUSC 365
Basics of Digital Audio Module (revised)
Analog = continuous
Analog = continuous


•   sound or audio waveform
Analog = continuous


•   sound or audio waveform

•   continuous time and amplitude
Analog = continuous


•   sound or audio waveform

•   continuous time and amplitude

•   infinite possibilities within a g...
Digital = discrete
Digital = discrete


•   time and amplitude are discrete
Digital = discrete


•   time and amplitude are discrete

•   only certain values are allowed
Continuous vs. Discrete
          Continuous                          Discrete

All numbers (including fractions)         ...
Sampling
Sampling

•   the process of making discrete time
Sampling

•   the process of making discrete time

•   Amplitude of a waveform is captured (sampled) at regularly spaced
 ...
Sampling

•   the process of making discrete time

•   Amplitude of a waveform is captured (sampled) at regularly spaced
 ...
Sampling Rate (ƒs)
Sampling Rate (ƒs)

•   The sample rate determines the bandwidth of the system
Sampling Rate (ƒs)

•   The sample rate determines the bandwidth of the system

•   A signal of bandwidth BW may be LOSSLE...
Sampling Rate (ƒs)

•   The sample rate determines the bandwidth of the system

•   A signal of bandwidth BW may be LOSSLE...
Sampling Rate (ƒs)
Sampling Rate (ƒs)

•   Common sample rates:
Sampling Rate (ƒs)

•   Common sample rates:

    •   44.1kHz for audio only (CD, MP3, etc)
Sampling Rate (ƒs)

•   Common sample rates:

    •   44.1kHz for audio only (CD, MP3, etc)

    •   48kHz for video/film (...
Sampling Rate (ƒs)

•   Common sample rates:

    •   44.1kHz for audio only (CD, MP3, etc)

    •   48kHz for video/film (...
Nyquist Frequency
Nyquist Frequency


•   half the sampling frequency (ƒs / 2)
Nyquist Frequency


•   half the sampling frequency (ƒs / 2)

•   Highest frequency possible in a digital system
Nyquist Frequency


•   half the sampling frequency (ƒs / 2)

•   Highest frequency possible in a digital system

    •   ...
Sampling Process - Input
Sampling Process - Input


•   Initial audio input
Sampling Process - Input


•   Initial audio input

•   frequencies above ƒs / 2
    have been removed
Sampling Process
Sampling Process


•   waveform is periodically
    sampled
Sampling Process
Sampling Process



•   the sampled signal
Sampling Process - Reconstruction
Sampling Process - Reconstruction


•   the sampled signal is
    reconstructed (made
    continuous)
Sampling Process - Reconstruction


•   the sampled signal is
    reconstructed (made
    continuous)

•   “connecting-the...
Sampling Process
Sampling Process

•   There is only waveform
    that satisfies 2 conditions:
Sampling Process

•   There is only waveform
    that satisfies 2 conditions:

    •   it passes thru all the
        sampl...
Sampling Process

•   There is only waveform
    that satisfies 2 conditions:

    •   it passes thru all the
        sampl...
Aliasing
Aliasing


•   Input signal must be bandlimited (frequencies above ƒs / 2 removed)
Aliasing


•   Input signal must be bandlimited (frequencies above ƒs / 2 removed)

•   If it is not, frequencies above ƒs...
Aliasing


•   Input signal must be bandlimited (frequencies above ƒs / 2 removed)

•   If it is not, frequencies above ƒs...
Aliasing
Aliasing


•   a high frequency
    waveform is put into the
    sampler
Aliasing
Aliasing


•   the waveform is
    periodically sampled
Aliasing
Aliasing



•   the sampled signal
Aliasing
Aliasing

•   after the signal is
    reconstructed to a
    continuous waveform,
Aliasing

•   after the signal is
    reconstructed to a
    continuous waveform,

•   but it is not what was
    input!
Aliasing
Aliasing


•   Aliasing also happens in visual media...
Aliasing


•   Aliasing also happens in visual media...

•   If you watch a film of a spinning wheel, it can seem to stop o...
Quantization
Quantization

•   the process of making discrete Amplitude
Quantization

•   the process of making discrete Amplitude

•   the amplitude range is broken up into a fixed number of lev...
Quantization

•   the process of making discrete Amplitude

•   the amplitude range is broken up into a fixed number of lev...
Quantization Process
Quantization Process


•   sampled waveform
Quantization Process


•   sampled waveform

•   any amplitude is possible
Quantization Process
Quantization Process


•   amplitude is rounded to
    the closest quantization
    interval
Quantization Process
Quantization Process


•   this close-up shows that
    there is some error in
    the quantization process
Quantization Process
Quantization Process


•   the smaller the intervals, the smaller the error will be
Quantization Process


•   the smaller the intervals, the smaller the error will be

•   since the range (maximum to minim...
Quantization Process


•   the smaller the intervals, the smaller the error will be

•   since the range (maximum to minim...
Quantization
Quantization

•   number of levels based on word length (number of bits per sample)
Quantization

•   number of levels based on word length (number of bits per sample)

•   # of levels = 2 # of bits
Quantization

•   number of levels based on word length (number of bits per sample)

•   # of levels = 2 # of bits

•   Ad...
Quantization

•   number of levels based on word length (number of bits per sample)

•   # of levels = 2 # of bits

•   Ad...
Quantization

•   number of levels based on word length (number of bits per sample)

•   # of levels = 2 # of bits

•   Ad...
Dynamic Range
Dynamic Range


•   Loudest to quietest
Dynamic Range


•   Loudest to quietest

•   6dB of dynamic range per bit
Dynamic Range
Dynamic Range

•   8 bits = 28 = 256 = 48dB
Dynamic Range

•   8 bits = 28 = 256 = 48dB

•   12 bits = 212 = 4,096 = 72dB
Dynamic Range

•   8 bits = 28 = 256 = 48dB

•   12 bits = 212 = 4,096 = 72dB

•   16 bits = 216 = 65,536 = 96dB
Dynamic Range

•   8 bits = 28 = 256 = 48dB

•   12 bits = 212 = 4,096 = 72dB

•   16 bits = 216 = 65,536 = 96dB

•   20 b...
Dynamic Range

•   8 bits = 28 = 256 = 48dB

•   12 bits = 212 = 4,096 = 72dB

•   16 bits = 216 = 65,536 = 96dB

•   20 b...
Incredible accuracy
Incredible accuracy

•   Imagine a stack of paper 22 feet high.
Incredible accuracy

•   Imagine a stack of paper 22 feet high.

    •   The thickness of a sheet of paper is the accuracy...
Incredible accuracy

•   Imagine a stack of paper 22 feet high.

    •   The thickness of a sheet of paper is the accuracy...
Quantization Error
Quantization Error

•   Distortion power relative to number of intervals, independent of
    amplitude of signal
Quantization Error

•   Distortion power relative to number of intervals, independent of
    amplitude of signal

•   Erro...
Quantization Error

•   Distortion power relative to number of intervals, independent of
    amplitude of signal

•   Erro...
Quantization Error

•   Distortion power relative to number of intervals, independent of
    amplitude of signal

•   Erro...
Quantization Error
Quantization Error


•   Quantization noise is not random, but
Quantization Error


•   Quantization noise is not random, but

•   based on signal
Dither
Dither


•   Noise added to the signal to de-correlate the signal from the
    quantizer
Pros
Pros


•   Randomizes granulation distortion,
Pros


•   Randomizes granulation distortion,

•   changing it to random noise
Con
Con



•   Raises noise floor slightly
Analog vs. Digital Deterioration
Analog vs. Digital Deterioration

•   In Analog, noise steadily deteriorates the signal-to-noise ratio
Analog vs. Digital Deterioration

•   In Analog, noise steadily deteriorates the signal-to-noise ratio

•   In Digital, au...
Analog vs. Digital Deterioration

•   In Analog, noise steadily deteriorates the signal-to-noise ratio

•   In Digital, au...
Analog vs. Digital Deterioration
365 digital basics after
365 digital basics after
365 digital basics after
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  • (Pohlmann pg. 27)
    Proof in Couch pg. 90-91
  • (Pohlmann pg. 27)
    Proof in Couch pg. 90-91
  • (Pohlmann pg. 27)
    Proof in Couch pg. 90-91
  • High fs: Large guard band, Allows varispeed
    Low fs: Reduces transmission and storage BW
    Critical Sampling: When a signal is sampled at exactly twice its highest frequency. Never done in audio
  • High fs: Large guard band, Allows varispeed
    Low fs: Reduces transmission and storage BW
    Critical Sampling: When a signal is sampled at exactly twice its highest frequency. Never done in audio
  • High fs: Large guard band, Allows varispeed
    Low fs: Reduces transmission and storage BW
    Critical Sampling: When a signal is sampled at exactly twice its highest frequency. Never done in audio









  • A band limited waveform amplitude modulates an impulse train. The spectrum of an impulse train is sinewaves @ multiples of Fs. Modulated spectrum is waveform spectrum (bandlimited) repeated around multiples of Fs (with upper and lower sidebands). If impulses have some width, then the total spectrum is superimposed with the |Sin (x)/x| curve.














  • http://www.youtube.com/watch?v=C8_6NRXfRVE
  • http://www.youtube.com/watch?v=C8_6NRXfRVE
  • giving a ‘quantity’
  • giving a ‘quantity’
  • giving a ‘quantity’







  • 6dB of dynamic range per bit
  • 6dB of dynamic range per bit
  • 6dB of dynamic range per bit
  • 6dB of dynamic range per bit
  • 6dB of dynamic range per bit











  • Error is +/- 1/2 Q with a rectangular PDF (equal chance)
  • Error is +/- 1/2 Q with a rectangular PDF (equal chance)
  • Error is +/- 1/2 Q with a rectangular PDF (equal chance)
  • Error is +/- 1/2 Q with a rectangular PDF (equal chance)
  • Distortion produces harmonics which can alias
    Multiple input freq. can cause intermodulation distortion
    Quantization error can create Aliasing (frequencies not present in source) even though it occurs after the sample process
  • Distortion produces harmonics which can alias
    Multiple input freq. can cause intermodulation distortion
    Quantization error can create Aliasing (frequencies not present in source) even though it occurs after the sample process

  • encodes low-level signals via PWM
    ear averages PWM signal to resolve signal
    With dither, resolution is below least significant bit!
  • encodes low-level signals via PWM
    ear averages PWM signal to resolve signal
    With dither, resolution is below least significant bit!






  • 365 digital basics after

    1. 1. MUSC 365 Basics of Digital Audio Module (revised)
    2. 2. Analog = continuous
    3. 3. Analog = continuous • sound or audio waveform
    4. 4. Analog = continuous • sound or audio waveform • continuous time and amplitude
    5. 5. Analog = continuous • sound or audio waveform • continuous time and amplitude • infinite possibilities within a given range
    6. 6. Digital = discrete
    7. 7. Digital = discrete • time and amplitude are discrete
    8. 8. Digital = discrete • time and amplitude are discrete • only certain values are allowed
    9. 9. Continuous vs. Discrete Continuous Discrete All numbers (including fractions) Only integers distance down my street number of houses on my street time it takes to cook an egg number of eggs a chicken lays volume of applesauce number of apples in a basket
    10. 10. Sampling
    11. 11. Sampling • the process of making discrete time
    12. 12. Sampling • the process of making discrete time • Amplitude of a waveform is captured (sampled) at regularly spaced intervals
    13. 13. Sampling • the process of making discrete time • Amplitude of a waveform is captured (sampled) at regularly spaced intervals • the rate of repeat of this regularly spaced interval is called the sample rate
    14. 14. Sampling Rate (ƒs)
    15. 15. Sampling Rate (ƒs) • The sample rate determines the bandwidth of the system
    16. 16. Sampling Rate (ƒs) • The sample rate determines the bandwidth of the system • A signal of bandwidth BW may be LOSSLESSLY sampled if the sampling rate ƒs ≥ 2 • BW
    17. 17. Sampling Rate (ƒs) • The sample rate determines the bandwidth of the system • A signal of bandwidth BW may be LOSSLESSLY sampled if the sampling rate ƒs ≥ 2 • BW • Input must be bandlimited to half the sampling rate
    18. 18. Sampling Rate (ƒs)
    19. 19. Sampling Rate (ƒs) • Common sample rates:
    20. 20. Sampling Rate (ƒs) • Common sample rates: • 44.1kHz for audio only (CD, MP3, etc)
    21. 21. Sampling Rate (ƒs) • Common sample rates: • 44.1kHz for audio only (CD, MP3, etc) • 48kHz for video/film (DVD, etc)
    22. 22. Sampling Rate (ƒs) • Common sample rates: • 44.1kHz for audio only (CD, MP3, etc) • 48kHz for video/film (DVD, etc) • double (2x) and quadruple (4x) those rates
    23. 23. Nyquist Frequency
    24. 24. Nyquist Frequency • half the sampling frequency (ƒs / 2)
    25. 25. Nyquist Frequency • half the sampling frequency (ƒs / 2) • Highest frequency possible in a digital system
    26. 26. Nyquist Frequency • half the sampling frequency (ƒs / 2) • Highest frequency possible in a digital system • 22.05kHz for ƒs = 44.1kHz
    27. 27. Sampling Process - Input
    28. 28. Sampling Process - Input • Initial audio input
    29. 29. Sampling Process - Input • Initial audio input • frequencies above ƒs / 2 have been removed
    30. 30. Sampling Process
    31. 31. Sampling Process • waveform is periodically sampled
    32. 32. Sampling Process
    33. 33. Sampling Process • the sampled signal
    34. 34. Sampling Process - Reconstruction
    35. 35. Sampling Process - Reconstruction • the sampled signal is reconstructed (made continuous)
    36. 36. Sampling Process - Reconstruction • the sampled signal is reconstructed (made continuous) • “connecting-the-dots”
    37. 37. Sampling Process
    38. 38. Sampling Process • There is only waveform that satisfies 2 conditions:
    39. 39. Sampling Process • There is only waveform that satisfies 2 conditions: • it passes thru all the sample points, and
    40. 40. Sampling Process • There is only waveform that satisfies 2 conditions: • it passes thru all the sample points, and • it does not have frequencies above ƒs / 2
    41. 41. Aliasing
    42. 42. Aliasing • Input signal must be bandlimited (frequencies above ƒs / 2 removed)
    43. 43. Aliasing • Input signal must be bandlimited (frequencies above ƒs / 2 removed) • If it is not, frequencies above ƒs / 2 are folded back into audio band
    44. 44. Aliasing • Input signal must be bandlimited (frequencies above ƒs / 2 removed) • If it is not, frequencies above ƒs / 2 are folded back into audio band • This artifact is called aliasing
    45. 45. Aliasing
    46. 46. Aliasing • a high frequency waveform is put into the sampler
    47. 47. Aliasing
    48. 48. Aliasing • the waveform is periodically sampled
    49. 49. Aliasing
    50. 50. Aliasing • the sampled signal
    51. 51. Aliasing
    52. 52. Aliasing • after the signal is reconstructed to a continuous waveform,
    53. 53. Aliasing • after the signal is reconstructed to a continuous waveform, • but it is not what was input!
    54. 54. Aliasing
    55. 55. Aliasing • Aliasing also happens in visual media...
    56. 56. Aliasing • Aliasing also happens in visual media... • If you watch a film of a spinning wheel, it can seem to stop or go backwards
    57. 57. Quantization
    58. 58. Quantization • the process of making discrete Amplitude
    59. 59. Quantization • the process of making discrete Amplitude • the amplitude range is broken up into a fixed number of level, also called quantization intervals
    60. 60. Quantization • the process of making discrete Amplitude • the amplitude range is broken up into a fixed number of level, also called quantization intervals • amplitude is measured and assigned to the closest interval
    61. 61. Quantization Process
    62. 62. Quantization Process • sampled waveform
    63. 63. Quantization Process • sampled waveform • any amplitude is possible
    64. 64. Quantization Process
    65. 65. Quantization Process • amplitude is rounded to the closest quantization interval
    66. 66. Quantization Process
    67. 67. Quantization Process • this close-up shows that there is some error in the quantization process
    68. 68. Quantization Process
    69. 69. Quantization Process • the smaller the intervals, the smaller the error will be
    70. 70. Quantization Process • the smaller the intervals, the smaller the error will be • since the range (maximum to minimum) is fixed,
    71. 71. Quantization Process • the smaller the intervals, the smaller the error will be • since the range (maximum to minimum) is fixed, • more levels will mean smaller levels
    72. 72. Quantization
    73. 73. Quantization • number of levels based on word length (number of bits per sample)
    74. 74. Quantization • number of levels based on word length (number of bits per sample) • # of levels = 2 # of bits
    75. 75. Quantization • number of levels based on word length (number of bits per sample) • # of levels = 2 # of bits • Adding bit doubles the number of levels,
    76. 76. Quantization • number of levels based on word length (number of bits per sample) • # of levels = 2 # of bits • Adding bit doubles the number of levels, • which cuts the error in half
    77. 77. Quantization • number of levels based on word length (number of bits per sample) • # of levels = 2 # of bits • Adding bit doubles the number of levels, • which cuts the error in half • reduces error by 6dB
    78. 78. Dynamic Range
    79. 79. Dynamic Range • Loudest to quietest
    80. 80. Dynamic Range • Loudest to quietest • 6dB of dynamic range per bit
    81. 81. Dynamic Range
    82. 82. Dynamic Range • 8 bits = 28 = 256 = 48dB
    83. 83. Dynamic Range • 8 bits = 28 = 256 = 48dB • 12 bits = 212 = 4,096 = 72dB
    84. 84. Dynamic Range • 8 bits = 28 = 256 = 48dB • 12 bits = 212 = 4,096 = 72dB • 16 bits = 216 = 65,536 = 96dB
    85. 85. Dynamic Range • 8 bits = 28 = 256 = 48dB • 12 bits = 212 = 4,096 = 72dB • 16 bits = 216 = 65,536 = 96dB • 20 bits = 220 = 1,048,576 = 120dB
    86. 86. Dynamic Range • 8 bits = 28 = 256 = 48dB • 12 bits = 212 = 4,096 = 72dB • 16 bits = 216 = 65,536 = 96dB • 20 bits = 220 = 1,048,576 = 120dB • 24 bits = 224 = 16,777,216 = 144dB
    87. 87. Incredible accuracy
    88. 88. Incredible accuracy • Imagine a stack of paper 22 feet high.
    89. 89. Incredible accuracy • Imagine a stack of paper 22 feet high. • The thickness of a sheet of paper is the accuracy of a 16-bit quantization interval!
    90. 90. Incredible accuracy • Imagine a stack of paper 22 feet high. • The thickness of a sheet of paper is the accuracy of a 16-bit quantization interval! • Now imagine a stack of paper a mile high. The thickness of a sheet of paper is the accuracy of a 24-bit quantization interval!
    91. 91. Quantization Error
    92. 92. Quantization Error • Distortion power relative to number of intervals, independent of amplitude of signal
    93. 93. Quantization Error • Distortion power relative to number of intervals, independent of amplitude of signal • Error changes perceptively with input level
    94. 94. Quantization Error • Distortion power relative to number of intervals, independent of amplitude of signal • Error changes perceptively with input level • High level signal has un-correlated error (random noise)
    95. 95. Quantization Error • Distortion power relative to number of intervals, independent of amplitude of signal • Error changes perceptively with input level • High level signal has un-correlated error (random noise) • Low level signal has correlated error – distortion, not noise-like
    96. 96. Quantization Error
    97. 97. Quantization Error • Quantization noise is not random, but
    98. 98. Quantization Error • Quantization noise is not random, but • based on signal
    99. 99. Dither
    100. 100. Dither • Noise added to the signal to de-correlate the signal from the quantizer
    101. 101. Pros
    102. 102. Pros • Randomizes granulation distortion,
    103. 103. Pros • Randomizes granulation distortion, • changing it to random noise
    104. 104. Con
    105. 105. Con • Raises noise floor slightly
    106. 106. Analog vs. Digital Deterioration
    107. 107. Analog vs. Digital Deterioration • In Analog, noise steadily deteriorates the signal-to-noise ratio
    108. 108. Analog vs. Digital Deterioration • In Analog, noise steadily deteriorates the signal-to-noise ratio • In Digital, audio quality is independent of transmission/storage quality
    109. 109. Analog vs. Digital Deterioration • In Analog, noise steadily deteriorates the signal-to-noise ratio • In Digital, audio quality is independent of transmission/storage quality • Until we reach a point of catastrophic failure, when the data can no longer be received correctly
    110. 110. Analog vs. Digital Deterioration

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