Transcript Digital Audio Powerpoint

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?
Digital vs. Analog
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Discrete data
Continuous data
Reproducible with
100% fidelity
Reproduction
introduces new
noise
Can be stored
using any digital
medium
Frequency and
amplitude ranges
limited by
digitization
Storage limited by
physical size
Virtually unlimited
frequency and
amplitude ranges
Physics of Digitization
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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
Sampling Basics
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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
Sample Rate (Sample Frequency)
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Sample Period =
0.5s
Sample Rate =
1/0.5s = 2Hz
Sample Rate Matters!
(Mathematica Demo 1)
What do the samples actually
represent?
Nyquist-Shannon Sampling Theorem
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“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.
What can go wrong?
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Aliasing: High frequencies contribute signal
components that are perceived as lower
frequencies (Mathematica Demo 2)
Bit Depth
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Number of bits
used to represent
each sampled value
Available discrete
values n=2b
Here there are only
5 discrete values,
so 3 bits per
sample
Dynamic Range
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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”
Signal-to-Noise Ratio (S/N)
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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)
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Human ear sensitivity covers a range of
more than 120dB! (~40 bits)
Digital Audio Compression
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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)
MP3 Codec
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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)
Discrete Fourier Transform
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Frequency Limit = ½
Sample Frequency
(Nyquist)
Frequency
Resolution =
1/Signal Period
(Mathematica 3)
Usually frequency
resolution is much
sharper than the ear
can detect
Dithering
Digital Signal Processing (DSP)
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Non-linear (ie, atemporal)
Real-time effects subject to latency and
buffering memory
Filters and envelopes extremely
difficult/expensive to achieve with analog
techniques
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Easier non-destructive editing
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Perfect fidelity in copying
Some Common DSP Effects
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Vocoder vs Autotune (Daft Punk)
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Delay/Echo (U2, David Gray)
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Filter/Flange (Foster the People, Dizzy
Gillespie)
Digital Synthesis (If you can write an
equation, you can hear it!)
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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)