# ANALOG-TO-DIGITAL CONVERSION

## Review of the Nature of Digital Data

• A digital bit has a concrete value that can be accurately stored reproduced.
• Only 2 values means long binary numbers, but easier handling and less error-prone.  This is fine for computers, because they are stoopid, but fast.
• Encoded sound is just one form of digital data, which overlaps with information technology.
• Terms in digital audio also have similar meanings in digital images and video.

## Analog-to-Digital Conversion

• The process of taking a continuous analog signal and encoding it into discrete values.
• Sometimes called ADC or A/D
• Reverse process is digital-to-analog conversion (DAC or D/A)
• Most common method uses PCM (pulse code modulation), but there are other ways to do it.
• Foundation in Harry Nyquist's theorem (Bell Labs, 1928!)
• Claude Shannon proved algebra could be done with electronics, making computing and information theory a reality (Bell Labs, 1949)

# Digital Sound Quality

## Meaningful Measurements?

"CD Quality"

"Audiophile Quality"

Since we care about how it sounds, better go back to the Acoustic World...

What are the most basic components of a sound, again?

# Frequency Response

## Sampling Rate = How Frequently to Measure?

• Nyquist Theorem:  Sample twice as often as the highest frequency:
• To capture 4 kHz, sample 8 kHz (8000 times per second).
• 8 kHz = 16 kHz sample rate
• 20 kHz = 40 kHz sample rate

## Common Sampling Rates

• 44.1 kHz = CD
• 48 kHz = Video
• 88.2, 96, 192, 384 kHZ!
• Sample rate conversion is not a trivial process, and should be avoided unless necessary.

# Amplitude

## Bit Resolution = How Precisely to Measure?

• Measuring amplitude means measuring dynamic range.
• Bits combine to form 'words' (16-bit word, 24-bit word, etc.)
• 1 Bit = 6 dB of dynamic range (meaning it lowers the noise floor by 6 dB)
• More bits = more possible amplitude values = less quantization error
WORD LENGTH DYNAMIC RANGE AMPLITUDE VALUES
2 Bits 12 dB
(6dB/bit x 2 bits)
4
8 Bits 48 dB 256
16 Bits–CD 96 dB 65,536
24 Bits 144 dB 16,777,216

(\( 2 ^2 \))

(\( 2 ^8 \))

(\( 2 ^{16} \))

(\( 2 ^{24} \))

1 Bit (2 values)

2 Bit (4 values)

8 Bit (256 values)

It is difficult to appreciate the accuracy achieved by a 16-bit measurement. An analogy might help: If sheets of typing paper were stacked to a height of 22 feet, a single sheet of paper would represent one quantization level in a 16-bit system.

Longer word lengths are even more impressive. In a 20-bit system, the stack would reach 352 feet. In a 24-bit system, the stack would tower 5632 feet in height-- Over a mile high. The quantizer could measure that mile to an accuracy equaling the thickness of one piece of paper. If a single page were removed, the least significant bit would change from 1 to 0.

Looked at in another way, if the distance between New York and Los Angeles were measured with 24-bit accuracy, the measurement would be accurate to within 9 inches. A high-quality digital audio system thus requires components with similar tolerances-not a trivial feat.

–from Fundamentals of Digital Audio by John Watkinson

By Brian

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