From the air to the iPod

Sound and Digital Audio

• Minute disturbances in the air, caused by a vibrating object

• Air molecules bunch together, then spread out

• Changes in density (air pressure, or sound pressure)

• Causes a chain reaction; sound pressure wave propagates

What is Sound?

Sound Wave Propagation

Compression / Rarefaction

High

Low

Normal

Sou

nd

Pre

ssu

re

Time

Time domain plot of a waveform

Periodic Waveforms

1 Cycle

Period:

Frequency:

How long does one cycle last?

How many cycles per second?Expressed in Hertz (Hz)Ex: 440 Hz (the A above middle C)

• Period = 1 / Frequency (for A440: 0.0023 sec.)

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plit

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Frequency and Pitch

• Frequency is an acoustic fact.Pitch is a human perception.

• Our sense of pitch has a logarithmic relation to frequency — it’s based on ratios.

• Our ear is like a microphone. It changes the physical wave (acoustic energy) into an electrical signal.

• Range of human hearing

•20Hz to 20,000 Hz (20 kHz), approximately(for young folks; old folks can’t hear as high)

The Harmonic Series

Arithmetic series of frequencies gives ever-shrinking intervals.

Frequencies in Hz:

Double frequency: octave higher

(flat)

Analog Representations of Sound

Magnified phonograph grooves, viewed from above:

When viewed from the side, channel 1 goes up and down, and channel 2 goes side to side.

Analog versus Digital

AnalogContinuous signal that mimics shape of acoustic sound pressure wave

DigitalStream of discrete numbers that represent instantaneous amplitudes of analog signal, measured at equally spaced points in time.

Analog to Digital Recording Chain

ADC

Continuously varying electrical energy is an analog of the sound pressure wave.

Microphone converts acoustic to electrical energy. It’s a transducer.

ADC (Analog to Digital Converter) converts analog to digital electrical signal.Digital signal transmits binary numbers.

DAC (Digital to Analog Converter) converts digital signal in computer to analog for your headphones.

Analog to Digital Conversion

Instantaneous amplitudes of continuous analog signal, measured at equally spaced points in time.

A series of “snapshots”

[a.k.a. “sample word length,” “bit depth”]Precision of numbers used for measurement: the more bits, the higher the resolution.

Example: 16 bit

Analog to Digital Overview

Sampling RateHow often analog signal is measured

Sampling Resolution

[samples per second, Hz]Example: 44,100 Hz

Sampling Rate

Nyquist Theorem:

Sampling rate must be at least twice as high as the highest frequency you want to represent.

Determines the highest frequency that you can represent with a digital signal.

Capturing just the crest and trough of a sine wave will represent the wave exactly.

Aliasing

What happens if sampling rate not high enough?

A high frequency signal

sampled at too low a rate

looks like …

… a lower frequency signal.

That’s called aliasing.

Common Sampling Rates

Sampling Rate Uses

44.1 kHz (44100) CD, DAT

48 kHz (48000) DAT, DV, DVD-Video

96 kHz (96000) DVD-Audio

22.05 kHz (22050) Old samplers

Most software can handle all these rates.

Which rates can represent the range of frequencies audible by (fresh) ears?

3-bit Quantization

A 3-bit binary (base 2) number has 23 = 8 values.

0

1

2

3

4

5

6

7

A rough approximation

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Time — measure amp. at each tick of sample clock

4-bit Quantization

A 4-bit binary number has 24 = 16 values.

0

2

4

6

8

10

12

14

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A better approximation

Time — measure amp. at each tick of sample clock

16-bit Sample Word Length

A 16-bit integer can represent 216, or 65,536, values (amplitude points).

We typically use signed 16-bit integers, and center the 65,536 values around 0.

32,767

-32,768

0

Quantization Noise

Round-off error: difference between actual signal and quantization to integer values…

Random errors: sounds like low-amplitude noise

Common Sampling Resolutions

Word length Uses

8-bit integer Low-res web audio

16-bit integer CD, DAT, DV, sound files

24-bit integer DVD-Video, DVD-Audio

32-bit floating point Software (usually only for internal representation)

The Digital Audio Stream

It’s just a series of sample numbers, to be interpreted as instantaneous amplitudes: one for every tick of the sample clock.

Previous example:

11 13 15 13 10 9 6 1 4 9 15 11 13 9

This is what appears in a sound file, along with a header that indicates the sampling rate, bit depth and other things.

Audio File Size

CD characteristics…

- Sampling rate:

44,100 samples per second (44.1 kHz)

How big is a 5-minute CD-quality sound file?

- Sample word length:

16 bits (i.e., 2 bytes) per sample

- Number of channels:

2 (stereo)

Audio File Size

5 minutes * 60 seconds per minute

= 300 seconds

How big is a 5-minute CD-quality sound file?

44,100 samples * 2 bytes per sample * 2 channels

= 176,400 bytes per second

300 seconds * 176,400 bytes per second

= 52,920,000 bytes = c. 50.5 megabytes (MB)

MPEG CompressionMPEG 1-Layer 3 (.mp3)

“Motion Picture Experts Group”Different levels for different purposes

E.g. MPEG 2 used for DVDsTakes out parts of the sound signal that

humans can’t hearHow does the size change?

Lossy compression

MPEG Compression

What is an iPod?

It’s a computer!Look at the von Neumann architecture

I/O2-4GB microdrive, click wheel, LCD panel, USB

connection, FireWire connection, audio outputMemory

32MB RAM, 32MB ROMCPU

Special digital to analog converter chipsWell-designed UI Stores music in various digital formats

AAC (16 to 320 Kbps), MP3 (32 to 320 Kbps), MP3 VBR, Audible, AIFF, Apple Lossless and WAV

iPod Specifications

CPU: ARM7TDMI Playtime: up to 8 hours Scroll wheel: solid state touch Buttons: mechanical CPU Speed: dual 80 Mhz

embedded Data Path: 32 bit ROM: 32 MB Onboard RAM: 32 MB Screen: 1.67" LCD w/ LED

backlight

Maximum Resolution: 1-bit 138x110 Hard Disk: 1" 4 GB 4200 RPM – holds 1000 songs. USB: via Dock Connector FireWire: via Dock Connector Audio Out: stereo 16 bit mini Weight: 0.225 lbs. Dimensions: 3.6" H x 2.0" W x 0.5" D OS: iPod OS 1.1 Introduced: January 2004

Let’s Look Inside!