1. MUSC 365
Basics of Digital Audio Module (revised)

2. Analog = continuous

3. Analog = continuous
• sound or audio waveform

4. Analog = continuous
• sound or audio waveform
• continuous time and amplitude

5. Analog = continuous
• sound or audio waveform
• continuous time and amplitude
• infinite possibilities within a given range

6. Digital = discrete

7. Digital = discrete
• time and amplitude are discrete

8. Digital = discrete
• time and amplitude are discrete
• only certain values are allowed

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. Sampling

11. Sampling
• the process of making discrete time

12. Sampling
• the process of making discrete time
• Amplitude of a waveform is captured (sampled) at regularly spaced
intervals

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. Sampling Rate (ƒs)

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

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. 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. Sampling Rate (ƒs)

19. Sampling Rate (ƒs)
• Common sample rates:

20. Sampling Rate (ƒs)
• Common sample rates:
• 44.1kHz for audio only (CD, MP3, etc)

21. Sampling Rate (ƒs)
• Common sample rates:
• 44.1kHz for audio only (CD, MP3, etc)
• 48kHz for video/film (DVD, etc)

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. Nyquist Frequency

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

25. Nyquist Frequency
• half the sampling frequency (ƒs / 2)
• Highest frequency possible in a digital system

26. Nyquist Frequency
• half the sampling frequency (ƒs / 2)
• Highest frequency possible in a digital system
• 22.05kHz for ƒs = 44.1kHz

27. Sampling Process - Input

28. Sampling Process - Input
• Initial audio input

29. Sampling Process - Input
• Initial audio input
• frequencies above ƒs / 2
have been removed

30. Sampling Process

31. Sampling Process
• waveform is periodically
sampled

32. Sampling Process

33. Sampling Process
• the sampled signal

34. Sampling Process - Reconstruction

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

36. Sampling Process - Reconstruction
• the sampled signal is
reconstructed (made
continuous)
• “connecting-the-dots”

37. Sampling Process

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

39. Sampling Process
• There is only waveform
that satisfies 2 conditions:
• it passes thru all the
sample points, and

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. Aliasing

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

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. 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. Aliasing

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

47. Aliasing

48. Aliasing
• the waveform is
periodically sampled

49. Aliasing

50. Aliasing
• the sampled signal

51. Aliasing

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

53. Aliasing
• after the signal is
reconstructed to a
continuous waveform,
• but it is not what was
input!

54. Aliasing

55. Aliasing
• Aliasing also happens in visual media...

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. Quantization

58. Quantization
• the process of making discrete Amplitude

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. 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. Quantization Process

62. Quantization Process
• sampled waveform

63. Quantization Process
• sampled waveform
• any amplitude is possible

64. Quantization Process

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

66. Quantization Process

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

68. Quantization Process

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

70. Quantization Process
• the smaller the intervals, the smaller the error will be
• since the range (maximum to minimum) is fixed,

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. Quantization

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

74. Quantization
• number of levels based on word length (number of bits per sample)
• # of levels = 2 # of bits

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. 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. 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. Dynamic Range

79. Dynamic Range
• Loudest to quietest

80. Dynamic Range
• Loudest to quietest
• 6dB of dynamic range per bit

81. Dynamic Range

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

83. Dynamic Range
• 8 bits = 28 = 256 = 48dB
• 12 bits = 212 = 4,096 = 72dB

84. Dynamic Range
• 8 bits = 28 = 256 = 48dB
• 12 bits = 212 = 4,096 = 72dB
• 16 bits = 216 = 65,536 = 96dB

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. 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. Incredible accuracy

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

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. 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!

92. Quantization Error

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

94. Quantization Error
• Distortion power relative to number of intervals, independent of
amplitude of signal
• Error changes perceptively with input level

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)

96. 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

97. Quantization Error

98. Quantization Error
• Quantization noise is not random, but

99. Quantization Error
• Quantization noise is not random, but
• based on signal

100. Dither

101. Dither
• Noise added to the signal to de-correlate the signal from the
quantizer

102. Pros

103. Pros
• Randomizes granulation distortion,

104. Pros
• Randomizes granulation distortion,
• changing it to random noise

105. Con

106. Con
• Raises noise floor slightly

107. Analog vs. Digital Deterioration

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

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

110. 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

111. Analog vs. Digital Deterioration