Fundamentals of...Fundamentals of... Fundamentals of Digital Audio.

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Fundamentals of Digital Audio

Transcript of Fundamentals of...Fundamentals of... Fundamentals of Digital Audio.

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Fundamentals of ...

Fundamentalsof

Digital Audio

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Analog vs. Digital

Analog

Digital

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.AMPLIFIER

SOUND PRESSUTRE

WAVE

MICROPHONE SOUND

PRESSUTRE WAVE

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VOLTAGE IN WIRE

ANALOG TO DIGITAL

CONVERTER

COMUTERMEMORY

DIGTAL TO ANALOG

CONVERTERAMPLIFIER

Analog vs. Digital

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Idealized ModelSampling / Reconstruction

f(t) f*(t) quantizerf(nT)

computerg(nT) zero-

orderhold

g(t) smoothingfilter

(low-pass)

g(t)

A/D converterD/A converter

sampler

Model of the sampling and desampling process

Idealized Model...

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Deconstruction of Sampling Deconstruction of Sampling

f(t)

analog

(a)

f(t)

quantized inamplitude

(b)

(c)

quantized intime

f*(t)

f(nT)

(d)

digital

Graphic representation of types of signals:

a) analog signal

b) quantized (continuous time) signal

c) sampled data signal

d) digital signal

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Fidelity

Fidelity

depends on:

• sampling rate

• bit depth

• (encoding scheme)

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Sampling rate

Sampling Rate

Human hearing: 20-20,000 Hz

Sampling Theorem:

Must sample twice as high as highest component

Typical rates:

8 K11 K22 K

44.1 K48 K

dark / dull

bright / clean

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Intensity

10-2

10-4

10-6

10-8

10-10

10-12

2 x 10

2

2 x 10-1

2 x 10-2

2 x 10-3

2 x 10-4

10-5

Watt/m

2

New

ton/m

4

Fletcher & Munson

Fletcher & Munson

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Foldover in time domain

OriginalsignalOriginal

signal

Sampling pulseSampling pulse

ResultantDigitized

Waveform

ResultantDigitized

Waveform

Foldover in time domain

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Positive and negative Frequency

Positive and Negative Frequency

analog

|H(f)|

f-f0

Nyquist frequency

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Digital Spectraquantization in time

0

|H(f)|

digital

sampling rateSR

Nyquist FrequencySR

2

Digital Spectra

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folderover in freq...

foldover sampling rate

foldover frequency =1/2 sampling rate

foldover in frequencydomain

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quantization in amp.

4

3

2

1

0

-1

-2

-3

-4

error

quantization levels

digital

analog

Quantization in Amplitude

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distribution of error

0-1 1

maximum errorof ± 1/2

Distribution of Error

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Computing S/N

“Ideal”

dB = 20 log2N

1

2N-1

0.5or

6 dB / bit

Computing S/N ideal

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Bit DepthExample S/N

bits

248

121624

dB

1224487296

144

voice

CDproaudio

Bit depth Example S/N

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96 dB

24 dB

16 bits

16 bits

4 bits4 bits

Dynamic Range ProblemDynamic range problem

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Low-level Signal Problem

+2+1

0-1-2

intendedresult

Folding Frequency

folded

a

low-level signal problem

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Dither

+2+1

0-1-2

FF

a

f

Dither

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Signal Reconstruction

SR/2 SRf

a

Ideal reconstruction filterhasn’t been found

Signal reconstruction

Reconstruction Filter

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Oversampling Converters

• Multibit oversamplingconvert 44.1 K to

176.4 K (4x)352.8 K (8x)

• 1-bit oversampling1 bit at high rate

sigma-deltaMASH

128 x 1-bit =8 * 16-bits

Oversanpling Converters

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Multibit Oversampling

SR2

SRf

a

3 SR2

f

a

a

t

Multibit Oversampling

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Actual Converters

• Combine oversamplingfirst with 1-bit streamsecond

• Resulting noise lower4x 6dB8x 12dB

• In computers ground isolation of digital noise overwhelms everything else!

Actual Converters