1. Digital Audio
• Representation of audio signal in digital
ITMA 09 form for processing by digital circuits (or
Introduction to Audio II computers).
Krates Ng
Fall 2008
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Binary numbers Can you convert the following
from binary to decimal?
• In the computer world, there is only “1” and “0”
(or “on” and “off”) hence the binary system. • 111
powers of 2 23 22 21 20
• 1011
Equivalent decimal values 8’s 4’s 2’s 1’s
Sample 4-bit binary 1 0 1 1
How to solve 8 + 0 + 2 + 1 = 11 (decimal)
• 1101
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Dec. to Bin. by long division Bits and Bytes
• e.g. 156(10) to Binary
2) 156 0 • 1 byte = 8 bits
Steps:
2) 78 0 1. Write the integer answer (quotient) under the long
2) 39 1 division symbol, and write the remainder (0 or 1)
to the right of the dividend. Word size Power of 2 No. of values
2) 19 1 2. Continue downwards, dividing each new quotient
2) 9 1
by two and writing the remainders to the right of 8-bit (1 byte) 28 256
each dividend. Stop when the quotient is 1.
2) 4 0 3. Starting with the bottom 1, read the sequence is 16-bit (2 bytes) 216 65,536
1’s and 0’s upwards to the top.
2) 2 0
24-bit (3 bytes) 224 16,777,216
1
= 10011100(2) 32-bit (4 bytes) 232 4,294,967,296
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2. Audio signal as a series of bits Sampling
• Analog sounds recorded and digitized using
an Analog-to-digital Converter (ADC).
• A sample of the instantaneous amplitude of
the waveform is taken at regular time
intervals (called the sampling rate).
• The sampling rate is responsible for the
frequency response of the digitized sound.
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Nyquist Theorem
• A Swedish researcher.
• The theorem states that the sampling rate
must be greater than twice the highest
frequency (bandwidth) we wish to
reproduce.
• This frequency is often called the Nyquist
frequency.
• Fail to do that will result “aliasing”.
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Aliasing Standard sampling rates
Rate Uses
32K Older equipment
44.1K CD, DAT
48K DAT
96K Digital recording equipment
192K Digital recording equipment
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3. Low sampling rate Vs High sampling rate
Quantization
• Samples taken are then assigned numeric values that
the computer or digital circuit can use or store in a
process called quantization.
• The number of available values is determined by the
number of bits (0's and 1's) used for each sample, also
called bit depth or bit resolution .
• When a sample is quantized, the instantaneous
snapshot of its analog amplitude has to be rounded off
to the nearest available digital value. This rounding-off
process is called approximation.
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Quantization Error Dynamic range
• The smaller the number of bits used per sample, the
greater the distances the analog values need to be • The greater the magnitude of approximation errors,
the greater the level of digital or quantizing noise
rounded off to. The difference between the analog produced. The solution to reducing digital noise is
value and the digital value is called the to use larger sample sizes (greater bit depth).
approximation or quantizing error as shown in the • rule of thumb is an added 6 dB of dynamic range
illustration below: for every additional bit used per sample.
• The original CD standard proposed by Sony was
for a 14-bit sample size, with a dynamic range of
only 84 dB, but was changed to 16 bits before
inception.
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Low and High bits per sample
• The CD/DAT standard 16-bit samples, with
their impressive 65,536 values for quantizing,
provide the theoretical playback system
optimum of a 96 dB dynamic range.
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4. Digital to Analog Converter Modern audio hardware
Converting digital bits to analog sound signals. • Creative latest X-Fi sound card
•24-bit ADC at 96KHz sample rate.
•24-bit DAC at 96KHz to analog 7.1 speaker output.
•24-bit DAC of stereo digital sources at 192kHz to
stereo output
•16-bit to 24-bit recording sampling rates: 8, 11.025,
16, 22.05, 24, 32, 44.1, 48 and 96kHz
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Digital Audio Tape Deck Common audio file formats
• Tascam DA-45HR • .aif or AIFF (audio interchange file format)
• .ra or .ram (Real Audio)
•20 bit A/D, 20 bit D/A. • .wav or Microsoft WAVE
•Recording resolution: SP 16-bit, HR 24-bit. • WMA (Windows Media Audio)
•Recording sample rate: 44.1KHz, 48KHz. • AAC (Advanced Audio Coding)
•Fading out. Giving ways to computer-based
equipment.
• MPEG (Motion Pictures Expert Group)
– .mp3 (MPEG I-Audio layer 3 compression)
– And watch out for MPEG-4…
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Audio compression basics Psychoacoustics
• Two main categories • Principles of the human perception of sound.
– Lossless, e.g. .zip • MPEG compression algorithm uses model of human
– Lossy, e.g. JPEG hearing to remove data (perceptual coding algorithm).
• Traditional lossless compression methods usually • Frequency range is about 20Hz to 20kHz, most
don’t work well on audio (and image) compression. sensitive to 2 to 4 kHz.
• Thour characteristics: • Dynamic range (quietest to loudest) is about 96db.
– Compression ratio, e.g. 12:1 • Normal voice range is about 500Hz to 2 kHz.
– Bit rate (average no. of bits that 1 sec. of audio will • Low frequencies: vowels (元音), bass.
consume, usually in kbps)
– Speed (compressing, uncompressing) • High frequencies: consonants (子音).
– Quality
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5. Human Hearing Sensitivity Human Frequency Masking
• Experiment: Put a person in a quiet room. Raise • Experiment: Play 1 kHz tone (masking tone) at fixed level (60db). Play
test tone at a different level (e.g. 1.1 kHz), and raise level until just
level of 1 kHz tone until just barely audible. Vary distinguishable.
the frequency and plot: • Vary the frequency of the test tone and plot the threshold when it
becomes audible.
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Frequency Masking Temporal Masking
Repeat for various frequencies of masking tones: • If we hear a loud sound, then it stops, it takes a little while until we can hear
a soft tone nearby.
• Experiment: Play 1 kHz masking tone at 60 dB, plus a test tone at 1.1 kHz at
40 dB. Test tone cannot be heard (it is masked). Stop masking tone, then
stop test tone after a short delay.
• Adjust delay time to the shortest time when test tone can be heard (e.g. 5ms).
• Repeat with different level of the test tone and plot:
Frequency masking on critical band scale:
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Combination Reference
• Total effect of both frequency and temporal • MPEG’s web site
masking: – http://www.mpeg.org
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