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

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

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

4. Continuous vs. 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

5. 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
(Pohlmann pg. 27)
Proof in Couch pg

6. 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
High fs: Large guard band, Allows varispeedLow fs: Reduces transmission and storage BW
Critical Sampling: When a signal is sampled at exactly twice its highest frequency. Never done in audio

7. 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

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

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

10. Sampling Process waveform is periodically sampled
A band limited waveform amplitude modulates an impulse train. The spectrum of an impulse train is 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.

11. Sampling Process
the sampled signal

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

13. 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

14. 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

15. Aliasing
a high frequency waveform is put into the sampler

16. Aliasing
the waveform is periodically sampled

17. Aliasing
the sampled signal

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

19. Aliasing Aliasing also happens in visual media...
If you watch a film of a spinning wheel, it can seem to stop or go backwards

20. 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
giving a ‘quantity’

21. Quantization Process
sampled waveform
any amplitude is possible

22. Quantization Process
amplitude is rounded to the closest quantization interval

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

24. 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

25. 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
6dB of dynamic range per bit

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

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

28. 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!

30. 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
Error is +/- 1/2 Q with a rectangular PDF (equal chance)

31. Quantization Error Quantization noise is not random, but
based on signal
Distortion produces harmonics which can aliasMultiple input freq. can cause intermodulation distortionQuantization error can create Aliasing (frequencies not present in source) even though it occurs after the sample process

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

33. Pros Randomizes granulation distortion, changing it to random noise
encodes low-level signals via PWMear averages PWM signal to resolve signalWith dither, resolution is below least significant bit!

34. Con
Raises noise floor slightly

35. 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

36. Analog vs. Digital Deterioration