digital audiodigital audio

In digital audio, the purpose of binary numbers is to express the values of samples that represent analog sound.

(contrasted to MIDI binary use)

frequency (time based)

characteristics of soundcharacteristics of sound

ANALOG DIGITAL

sample rate (time based)

=

measured inhertz - cycles per second

measured inhertz - samples per second

amplitude (level)

frequency (time)

characteristics of soundcharacteristics of sound

ANALOG DIGITAL

quantization (level)

sample rate (time)=

=

measured in decibel

measured in bits

characteristics of soundcharacteristics of sound

analog-to-digital conversion : two steps

(1) sampling

(2) quantization

sampling theorem

“A continuous audio signal can be replaced by a discrete sequence of samples without loss of any information and the original continuous audio signal can be reconstructed from the samples.”

When a digital recorder takes a sample, it takes a snapshot of the audio waveform and turns it into bits that can be stored and manipulated.

010001111101100000110010011000001010010010100011111011000001100100110000010100100101000111110110000011001001100000101001001010001111101100000110010011000001010010010100011111011000001100100110000010100100101000111110110000011001001100000101001001010001111101100000110010011000001010010010100011111011000001100100110000010100100101000111110110000011001001100000101001001010001111101100000110010011000001010010010100011111011000001100100110000010100100101000111110110000011001001100000101001001 0100011111011000001100100110000010100100101000111110110000011001001100000101001001

sample rate

The frequency of the 'snapshots' of the audio stream in a single second

Just as in measuring frequency, hertz is used to define the number of samples taken per second

flip cards

QuickTime™ and aGIF decompressor

are needed to see this picture.

flip cards

http://www.youtube.com/watch?v=xSrDnIVgVv0

flip cards

http://www.youtube.com/watch?v=Ql4Kkb-89D0

sample rate:

the number of samples (measurements) taken of an analog signal in 1 second

sample rate:

The sample rate determines the frequency range (bandwidth) of a system.

sample rate:

The sample rate determines the frequency range (bandwidth) of a system.

the number of samples (measurements) taken of an analog signal signal in 1 second

The faster the sample rate, the better the accuracy of getting a true picture of higher frequencies.

Some common sample rates are:

22,050 aka 22.05 kHz - 22,050 samples per second. A sample every 1/22,050 of a sec.

24,000 aka 24 kHz - 24,000 samples per second. A sample every 1/24,000 of a sec.

30,000 aka 30 kHz - 30,000 samples per second. A sample every 1/30,000 of a sec.

44,100 aka 44.1 kHz - 44,100 samples per second. A sample every 1/44,000 of a sec.

48,000 aka 48 kHz - 48,000 samples per second. A sample every 1/48,000 of a sec.

The higher the sample rate, the better the quality of the sample. A sample taken at 44.1 kHz will contain twice the information as a sample taken at 22,050 kHz.

High sample rates are better at capturing high frequency waveforms, but if you are sampling lower frequency sounds, such as kick drum, bass, etc.,...not as critical.

you might consider sampling at the lower rate to save hard drive space.

high freq. signal

see p. 113-122

NYQUIST THEORY

Named after a Bell engineer who worked on the speed of telegraphs in the 1920s

There must be two samples per period. In other words, the sampling frequency must be at least twice the highest signal frequency recorded in order to be effective.

Sample rates with Nyquist yield 22,050 kHz = 11,025 kHz (Nyquist)24,000 kHz = 12,000 kHz 30,000 kHz = 15,000 kHz 44,100 kHz = 22,050 kHz 

It is therefore important to take into consideration the highest frequency of the audio material to be recorded.

If a frequency of A-14,080 Hz is to be recorded, a sample rate of 44.1 kHz would be the logical choice to use.

14,080 Hz falls within the range of the Nyquist of 44.1 kHz which is 22.05 kHz.

The choice of sample rate determines the audio bandwidth of the recorder used.

CD is 44.1 kHz

Considering that the human hearing range at best ranges from 20 Hz to 20 kHz, a 44.1 kHz sample rate theoretically should satisfy most audio needs.

If a 25 kHz waveform is sampled at 44.1 kHz (which has a Nyquist value of 22.05 kHz), the Nyquist rule is broken.

This is also known as aliasing or foldover.

44 kHz - 25 kHz , results in a 19 kHz waveform which is heard as distortion.

see p. 125

In audio: Alias is mirrored the same distance below the Nyquist frequency as the original was above it, at the original amplitude (foldover)

- 2k - 4k

QuickTime™ and aGIF decompressorare needed to see this picture.

aliasing

Once aliasing is introduced into the digital stream, it can’t be removed.

It must be stopped before entering the digital stream.

QUANTIZATION QUANTIZATION

The technique of measuring an audio event to form a numerical value.

In digital audio, the values = voltages

the more bits, the more voltages that can be represented.

voltages represent amplitude

time (infinite) is quantized

hour 60 minutes...minutes 60 seconds...etc.

sample rate = frequency

quantization = amplitudegain staging (p. 133)

quantization error The difference between the actual analog value

at the sample time and the selected quantization interval value

The amplitude of the audio signal is broken down into a series of discrete steps.

Each step is then given a binary word that digitally encodes the level of the signal.

The length of the digital word determines the quality of the representation.

4 bits

16 voltages

00010000

0010010010000011011011000111etc

The larger the word, the better the quality (16 bit word compared to an 8 bit word).

The larger the bit word, the greater the headroom of the audio system  (6 dB for every bit).

The more steps with which to describe the signal, the smoother the result will be.

SAMPLE BITS

The more bits used to describe something, the better the clarity and fidelity

An 8 bit sample contains 256 steps of information while a 16 bit sample contains up to 65,536 steps.

The bit resolution of a system defines the dynamic range of the system.

6dB is gained for every bit

signal to noise ratio (analog)

signal to error ratio (digital)

8 bits equals 256 states = 48 dB

16 bits equals 65,536 states = 96 dB

To find the dynamic range of a system, multiply the bit rate X 6.

In a 16 bit system, there are 65,536 different numbers, each number representing a different analog signal voltage

Value rounded up or down to closest represented value

Ex: voltage of 1.2v = 00100110

1.3 v= 00100111

1.4v = 00101000

quantization error

Quantization error is the difference between actual analog value and the assigned quantization value

There is always error. 1/2 of LSb

LSb least significant bit

on or off

8 bit reverb decay at end...hear it turn on off

•sample rate = frequency response

•bit depth = amplitude

recap

sample rate

bit depth 0001

00100100

Sample rate and storage

44.1 kHz sample rate with a 16 bit recorder 5 megs per minute...per track

3 minute mono audio file 16/44.1= 15 megs3 minute stereo audio file 16/44.1= 30 megs3 minute 5 mono tracks 16/44.1= 75 megs3 minute 5 stereo tracks 16/44.1=

150 megs

At a sample rate of 22,050 Hz, the formula would be half that of 44.1 kHz...around 2.5 megs a minute or 5 megs a minute in stereo.

Uncompressed video with a sound track takes up 28 MB per second.

16-Bit Audio Files:

* 5 MB per minute per track @ 44.1 kHz sample rate * 5.5 MB per minute per track @ 48 kHz sample rate * 11 MB per minute per track @ 96 kHz sample rate

* 8 MB per minute per track @ 48 kHz sample rate * 16 MB per minute per track @ 96 kHz sample rate

24-Bit Audio Files:

* 7.5 MB per minute per track @ 44.1 kHz sample rate * 8 MB per minute per track @ 48 kHz sample rate * 16 MB per minute per track @ 96 kHz sample rate