EG-348_371_09

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Multimedia Communications (371) Speech and Image Communications (348)

John Mason

Engineering

Swansea University

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Features in speech

X1

.

.

.

.Xi

.

.

.

.

.

Acquisition

(frame: 20/30 ms & sampling F: 8khz)

Feature extraction

time

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Features in speech

X1

.

.

.

.Xi

.

.

.

.

.

Acquisition

(frame: 20/30 ms & sampling F: 8khz)

Feature extraction

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Speech production

Air fromthe lungs

Vocal fold Vocal tract Speech

0

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LPC Short and Long

Spectral envelop reflects morphological characteristics of the vocal tract

H1(z) H2(z)noise synthesisedSpeech

Air fromthe lungs

Vocal fold Vocal tract Speech

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Features: building of statistical model

T1

T2

T1

T2

T1

T2

T1

T2

T1

T2

T1

T2

T1

T2

T1

T2

T1

T2

T1

T2 T1

T2

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VT Shape & Some Vowels - Ladefoged ‘62

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Speech Processing - Applications

Why? Communications Synthesis Recognition

Speech & Speaker

How? Frame-based Systems approach

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Some Books

Flanagan -’Speech Analysis, Synthesis and Perception’, Springer-Verlag, - a classic!

Furui - several books on recognition Parsons - `Voice and Speech Processing’ - McGraw Hill,

one of the first text books on computer speech processing O’Shaughnessy - ‘Speech Comms - human and machine’

Addison-Wesley Rabiner & Juang - ‘Fundamentals of Speech Recognition’

Prentice Hall, 1993 Ramachandran & Mamone (eds) ‘Modern Methods of

Speech Processing’ Kluer Academic, 1995

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Speech Communications

Person-to-Person

Person-to-Machinespeech/speaker recognition

Machine-to-Personspeech synthesis

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(Electronic) Speech Communications

perhaps separated by long distance(or in time)

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Telephony & Broadcasting

Acoustic Air Path Acoustic Air Path

Electronic Link

l Transmission Path

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Speech Comms: Telephony

Electronic Link

Channel Transmission Path

MicrophoneADCAnalysisCodingTransmitter

ReceiverDecoding(re-)SynthesisDACLoudspeaker

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Speech Bit Rates

Message

Creation

Language

Coding

Human

Acoustic

generation

Transmission

Message

Realisation

Language

decoding

Human

Hearing

Extraction

Acoustic Space

tens hundreds thousands Tens ofthousands

Approx. bit rate in bps

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Criteria in Speech Comms.

Quality versus Bit-rate

Qua

lity

Excellent

Good

Fair

Poor

4 8 16 32 64 kbps

GSM

ADPCM

CELP

4 Quality Measures:intelligibility loudnessnaturalness ease-of-listening

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Low Bit Rate Speech CodingCompandent http://www.compandent.com/

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Speech Processing

The three main application areas are: Speech Comms. (the ‘electronic link’) Automatic Speech/Speaker recognition Speech Synthesis

Much of the underlying analysis is common, eg linear predictive coding

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What does speech look like?

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What does speech look like?

0 1000 2000 3000 4000 5000 6000 7000

Dynamic Range - for flexibilityand robustness

Time-varying - to convey information

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Frame-based Analysis

0 1000 2000 3000 4000 5000 6000 7000

To capture time variations:• 20-30 ms frames - ‘centi-second’ labeling

• spectral analysisFFTFilter-bankLinear Predictive Coding

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Speech Analysis/Coding

Two general cases: Waveform coders Source (voice) coders (vo-coders)

Source coders eg linear predictive coding (LPC): Model the source ie the vocal tract (VT) Linear, time varying model of VT, plus excitation

H(z)

Excitation:voiced

unvoiced

speechen sn

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Systems Approach

VocalTract

Excitation Speech

Voiced

Unvoiced

Model

Time VaryingParameters

Speechf0

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LPC Analysis/Synthesis

Synthesis: Input: Excitation output: Speech

Analysis: Input: Speech output: Excitation

H(z)hn

S(z)E(z)en sn

1/H(z) E(z)S(z)sn en

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‘Perfect’ Analysis/Synthesis

H(z)S(z)E(z)

en sn

1/H(z) E(z)S(z)sn en

Input sn and output sn are identical (within arithmetic limits)

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Analysis

Coding .Synthesis

De-coding

Source Coding

SnSn

LPC-based Systems (eg CELP)

1

H z( )sn en

Analysis Re-Synthesis

)(ˆ zHne sn

Practical Analysis/Synthesis

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Practical Analysis/Synthesis

1/H(z) E(z)S(z)sn en

H(z)S(z)E(z)

en sn

Transmission ReceivingSending

Parameters for Transmission :• Input / Excitation en

• Source model H(z)Thus Analysis must derive these parameters, and

Synthesis must use them to re-generate speech

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Principle of linear prediction: The next value (or sample) in a series, ie at time n, is predicted

or estimated by a weighted sum of previous values, ie those at time n-1, n-2, ...

Thus for a predictor of order p, we have:

s a s a s a sn n n n

1 1 2 2 3 3 ........ a sn p p

Linear Predictive Coding - LPC

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Linear Prediction

Transforming to the z-domain gives:( ) ( ) ( ) ...... ( )

( ) { ( ) ( ) ...... ( )}

( ) ( ) { ( ) ( ) ...... ( )}

( ) ( )

( ) ( .... )

S z a z S z a z S z a z S z

S z a z S z a z S z a z S z

E z S z a z S z a z S z a z S z

A z S z

where A z a z a z a z

pp

pp

pp

pp

11

22

11

22

11

22

11

22

0

1

......s a s a s a s

a s

n n n p n p

i n ii

p

1 1 2 2

1

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)('1)(

)(zA

zS

zE

LPC Error Terms

Error is simply difference between predicted and actual values:

A’(z)

+ensn

e s s s a s

E z S z S z

S z a z S z a z S z a z S z

A z S z

where A z a z a z a z

n n n n i n ii

p

pp

pp

( ) ( ) ( )

( ) { ( ) ( ) ...... ( )}

( ) ( )

( ) ( .... )

1

11

22

11

221

ˆ-

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Synthesis

H(z)sn

Parameters updated at frame rate

en

A’(z)

+ snen

+

NB ‘hat’ of approximation omitted for simplicity

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The Analysis and Synthesis must match what is needed for the Synthesis?

Answer: en - the excitation and H(z) - the system

Thus the Analysis must derive these terms (from sn ):

The speech signal, sn is analysed to give en and H(z) ie A’(z) parameters for transmission.

Analysis for Synthesis

H(z)sn

en

Synthesis

1/H(z) E(z)S(z)

sn en

Analysis

A’(z)

+

-

ensn

Analysis

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Derivation of LPC Coefficients - A(z)

e s s s a sn n n n i n ii

p

1

Recall:

where ai are the p prediction coefficients.The principlebehind LPC is to find a set of p coefficients, a1, a2, a3, ...ap, which in some sense minimizes the error signal en, over a frame of speech, N. This leads to a set p coefficients for each frame.

1

0

2

1

1

0

22

N

n

p

iinin

N

nnnn sasssE

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Derivation of A(z) – (2)

Minimisation of En is achieved by setting the p partial derivatives to zero:

02

i

n

a

E

for i = 1, 2, .… p

01

p

kjkkj rar where:

1nknjnjk ssr

From which:

In matrix form:

0 aRr rRa 1or

The matrix [R] is Toepliz symmetric, offering numerically efficient inversion techniques - Durbin’s recursion algorithm being one of the most popular.

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Derivation of A(z) – (3)

When N very large r is the autocorrelation coefficients of s S comes from e convolved with h (excitation & vocal tract) we are interested here in separating e and h the predictor order, p, is small to reflect the short-term periodicities

(formants) with higher predictor orders we will get the longer-term periodicities

(pitch) 2 practical problems with evaluating a:

matrix singularities in R-1

unstable resultant H(z)

in practice both are solved by windowing - shaping frame - Hamming

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Speech Signal Characteristics

Duration Dynamic Range Periodicities:

vocal tract pitch

Frame-based Analysis frame size: quasi-stationary

capture transitiontypically 20 - 30ms

frame rate: task dependent: more means moreband-width/computation - up to 100 frames/second

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Harmonic Structures and Periodicities

Harmonic Structures & Periodicities give potential for data reduction

LPC is one way of gaining this compression

Speech has two obvious separate structures

vocal tract resonances

pitch

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Harmonic Structures and Periodicities

0

nenE

sase

sse

sas

in

p

iinn

nnn

in

p

iin

)( 2

1

1

ˆ

ˆ

nssn

p

Vocal tract

voicedorunvoiced

H(z)speechen sn

Tp

Short term prediction

Short Term

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Harmonic Structures and Periodicities

0

nenE

sase

sse

sas

in

P

iinn

nnn

in

P

iin

)( 2

1

1

ˆ

ˆ

nssn

P

Vocal tract

voiced

unvoicedHst(z)

speechepn sn

Tp

Long term prediction

Hlt(z)

Pitchen

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Hst(z)snHlt(z)en ep

n

Two Structures: short-term (formants) & long-term - pitch (excitation)

Harmonic Structures and Periodicities

eg 20ms frame160 samples @ 8Khz

ai eg p=3 ai eg p=10

Gain

k

NB Representations of these parameters are transmitted

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Waveform & Source Coders (Vocoders)Source Coders (Vocoders) 2 periodicities/redundancies in source

short-term (formants) long-term - pitch

Excitation en

Practical Coding Systems

Hst(z)snHlt(z)en epn

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‘Perfect’ Analysis/Synthesis (1)

H(z)S(z)E(z)

en sn

1/H(z) E(z)S(z)sn en

Input sn and output sn are identical (within arithmetic limits)

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‘Perfect’ Analysis/Synthesis (2)

H(z)S(z)E(z)

en sn

1/H(z) E(z)S(z)sn en

1/(1–A’(z))S(z)E(z)

en sn

1 – A’(z) E(z)S(z)sn en

1 – A’(z)sn en 1/(1–A’(z))en sn

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‘Perfect’ Analysis/Synthesis (3)

1 – A’(z)sn en 1/(1–A’(z))en sn

sn en

Z-1

Z-1

Z-1

a1

ai

ap

sn

sn

sn-1

sn-i

sn-p

+-

Note – minus sign:in Matlab combined with ai What determines p?

Original Speech Residual

p

iininnnn sassse

1

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‘Perfect’ Analysis/Synthesis (4)

1 – A’(z)sn en 1/(1–A’(z))en sn

en

Z-1

Z-1

Z-1

a1

ai

ap

sn

snen

Z-1

Z-1

Z-1

a1

ai

ap

sn-1

sn-i

sn-p

sn

sn-1

sn-i

sn-p

sn

Original Speech Residual Re-Synth.

+NoteNo minus

+-

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Practical System

TransmittedData Frame

H(z)S(z)E(z)

en

1/H(z) E(z)S(z)sn en

Input sn and output sn are “similar”

sn

What does the Transmitted Data Frame Contain?

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Analysis-by-Synthesis: LPAS

Integrated encoder & decoder at the encoder

Basicdecoder

Adaptiveencoder

sn

-

+

LPAS Encoder

Weighted error

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Log Spectral Estimates

Comparisons between frames are very important in many situations log spectral estimates are the most common (though in Comms. An

approximation is used to reduce computation)

))(log(

))(log(

1

)()(1

12/

0

2

0

2

zH

orsDFTSwhere

SSN

dwwSwSB

D

jwez

nk

N

kkk

B

In Comms, compuation is expensive and parameter vector approximations to D are used

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Some Standards

GSM European Cellular RPE-LTP13kb/s

FS1016 Secure Voice CELP 4.8

IS54 NA Cellular VSELP 7.95

IS96 “ QCELP 1-8

JDC-FR Japanese Cellular VSELP 6.7

JDC-HR “ PSI-CELP 3.67

G.728 (terrestrial) LD-CELP 16

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Low Bit Rate Speech CodingCompandent http://www.compandent.com/

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Criteria in Speech Comms.

Quality versus Bit-rate

Qua

lity

Excellent

Good

Fair

Poor

4 8 16 32 64 kbps

GSM

ADPCM

CELP

4 Quality Measures:intelligibility loudnessnaturalness ease-of-listening

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CELP eg

enHst(z)

snHlt(z)

CBIndex Gain

Long-term coefficients(pitch)

Short-term coefficients(formants)

Excitation is represented by address ie CB Index en

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CELP – LPAS (Encoder)

enHst(z) snHlt(z)

CBIndex

Gain

Long-term coefficients(pitch)

Short-term coefficients(formants)

Excitation is represented by address ie CB Index en

sn

snen

Basicdecoder

Adaptiveencoder

sn-

+Weighted error

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Conversion of LPC Parameters

• A(z) = 1 + a1 z - 1 + a2 z

- 2 + …… ap z - p and a i are to be Tx’d

• Line Spectral Frequencies (LSF) present a clever way of representing the LPC coefficients, the ai’s of A(z)

• The ai’s are floating point numbers and their accuracy is important

• Factorising A(z) tends to give complex roots in the z-domain

• LSF’s map these complex roots on to the unit circle

LSF’s Lead to efficient coding Ensure a minimum phase filter Bit errors are spectrum localised minimising loss of speech quality

z-plane jy

x

x

ws

LSF = ws . /2

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Line Spectral Frequencies

• Consider

P(z) = A(z) + z—(n+1) A(z—1 )

and

Q(z) = A(z) - z—(n+1) A(z—1 )

then P(z) and Q(z) lead to what is known as LSF’s

• Clearly if P(z) and Q(z) are known then A(z) can be found:A(z) = {P(z) + Q(z)} / 2

• Roots of P(z) and Q(z) lie on the unit circle in z-domain The locations give:

the LSF’s P(z) and Q(z), and whence A(z)

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LSF Evaluation

Consider one pair of complex roots, A1(z) :

A1(z) = 1 + a1 z -1 + a2 z

-2

P1(z) = 1 + a1 z -1 + a2 z

-2 + z -3 (1 + a1 z

1 + a2 z2 )

= (z2 + (a1 + a2 - 1) z + 1 )( z + 1 ) z –3

Q1(z) = 1 + a1 z -1 + a2 z

-2 - z -3 (1 + a1 z

1 + a2 z2 )

= (z2 + (a1 - a2 + 1) z + 1 )( z - 1 ) z -3

 The roots at 0 and 1 are discarded

It follows that the LSF’s, 1 & 2 , are given by:

  

cos (1) = - (a1 + a2 - 1)/2

and cos (2) = - (a1 - a2 + 1)/2

Show:a1 = -(cos (1) + cos (2) ) and

a2 = (cos (2) - cos (1) +1 )

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LSF Test Example

A1(z) = 1 + a1 z -1 + a2 z

- 2

= (z2 + a1 z + a2 )z

- 2

= (z2 + 2 cos() wn z + wn

2 ) z - 2

where wn is radius and is angle from . So: radius = a2 & = -

Note: in P & Q all w n2 terms (of the multiple 2nd orders) are unity

EG 1: a2 = 1 then cos (1) = - (a1 + a2 - 1)/2 = - (a1)/2

roots already on circle and do not move (unstable system – not practical)

EG 2: a1 = 0 then cos (1) = - (a1 + a2 -1)/2 = - (a2 - 1)/2

cos (2) = - (a1 - a2 + 1)/2 = - (-a2 + 1)/2

so LSF’s are symmetric about /4

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LSF Review & Example (1)

LSF’s/LSP’s are defined as:

P(z) = A(z) + z-(n+1) A(z-1 )

and Q(z) = A(z) - z-(n+1) A(z-1 )

thus A(z) = {P(z) + Q(z)} / 2

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For a second order A(z)= 1 + a1 z-1 + a2 z-2

P (z) = 1 + a1 z-1 + a2 z-2 + (1 + a1 z1 + a2 z2)z-3

= (z2 + (a1 + a2 - 1)z + 1)(z + 1)z–3

Q (z) = 1 + a1 z-1 + a2 z-2 - (a1 z1 + a2 z2)z-3

= (z2 + (a1 - a2 + 1)z + 1)(z - 1 )z–3

cf: (s2 + ( 2cos()wn ) s + wn2)

LSF Review & Example (2)

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For a second order A(z)= 1 + a1 z-1 + a2 z-2 :

P (z) = (z2 + (a1 + a2 - 1)z + 1)(z + 1)z–3

Q (z) = (z2 + (a1 - a2 + 1)z + 1)(z - 1 )z–3

cf: (s2 + ( 2cos()wn )s + wn2)

Thus: (a1 + a2 - 1) = 2cos(1) = - 2cos(1)

&(a1 - a2 + 1) = - 2cos(2 )

So, given: i) LPC coeffs., a1 and a2 , then LSFs 1 & 2 can be found

ii) LSFs, 1 & 2 , then the LPC coeffs. a1 and a2 be found

00.20.40.60.8

1

-0.5 0 0.5 1

1

2 P(z)

Q(z)

P(z)Q(z)

2

1

LSF Review & Example (3)

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For a second order and with P(z) corresponding to the first root, Q(z) to the second root, and so P (z) = 1 + a1 z-1 + a2 z-2 + (1 + a1 z1 + a2 z2)z-3 = (z2 + (a1 + a2 - 1)z + 1)(z + 1)z–3 for the second pair of qi, 1.37 and 1.77

= (z2 - 2cos(1.37) z + 1 )(z + 1) z–3= (z3 +(1 - 2cos(1.37) z2 + (1 - 2cos(1.37))z + 1)z–3

 LikewiseQ (z) = 1 + a1 z-1 + a2 z-2 - (a1 z1 + a2 z2)z-3

= (z2 + (a1 - a2 + 1)z + 1)(z - 1 )z–3 = (z2 - 2cos(1.77) z + 1 )(z - 1) z–3= (z3 +(-1 - 2cos(1.77) z2 + (1 + 2cos(1.77))z - 1)z–3

 Then

A(z) = {P(z) + Q(z)} / 2) = (z3 + (cos(1.37) + cos(1.77))z2 + (1 - cos(1.37) + cos(1.77))z)z–3

LSF Review & Example (4)

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LSF Examples LPC coeffs. LSF’s

a1 a2 1 2

0 0.5 1.31812 1.82348

-1.8 0.9 0.31756 0.554811

+1.8 0.9 π-0.554811 π-0. 31756

2.2274 2.3743

-1 0 1

-1 0 1-1 0 1

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LSF Examples

LPC coeffs. LSF’s

a1 a2 1 2

0 0.5 1.31812 1.82348

-1.8 0.9 0.31756 0.554811

+1.8 0.9 π-0.554811

π-0. 31756

2.2274 2.3743

A(z)= 1 + a1 z-1 + a2 z-2

P (z) = 1 + a1 z-1 + a2 z-2 + (1 + a1 z1 + a2 z2)z-3

= (z2 + (a1 + a2 - 1)z + 1)(z + 1)z–3

= (z2 + (-1.8 + 0.9 - 1)z + 1)(z + 1)z–3

= (z2 - 1.9 z + 1) (z + 1)z–3

cf: (z2 + ( 2cos()wn ) z + wn2)

thus cos() = - 1.9/2 or = 2.824 and 1 = π -

= 0.318

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Bit allocation Voiced Unvoiced

V/U decision 1 1

Excitation 11 11

Sync 1 1

Φ1 = 0.3176 5 5

Φ2 = 0.5548 5 5

Φ3 = 1.4454 5 5

Φ4 = 1.6961 5 5

Φ 5 4 0

Φ 6 4 0

Φ 7 4 0

Φ 8 4 0

Φ 9 3 0

Φ 10 2 0

Error check 0 21

Total / frame 54 54

Example Bit Allocation

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Codebooks & VQ

p

N = 2L

i (0 … N-1)

Identical book

Data reduction: (p x B) to Ltime

p

time

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Principle representative data sets data vector is replaced / represented

by “nearest” vector, chosen from a “codebook” - a closed set of vectors

Examples LPC parameter sets Excitation as in CELP

Codebook Compression

M

N = 2 k

i

index, i

A(z)

enH(z)

sn

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P

Codebook Compression - CELP

H(z)sny ms eny ms

en are time domain samples (integers)

R samples per second (eg 8000 Hz)

Frame rate governs vector size

P = 2 j

Bit rate = j/y bits/ms

Codebook of time-domain samples

start point

y ms

NB en also includes gain

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A[z] at time t

time

Codebook Compression of H(z)

M

N = 2 k

i

index, i

Vector with M elements, every x ms

Codebook with N = 2 k vectors

Bit rate = k/x bits per ms (not a function of M)

In practice A[z] is converted to LSF’s.

x ms

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Codebook Generation

1) Initialise:form a single centroid of all training data, N=1

2) RepeatSplit centroids: N -> 2N Repeat

Cluster data to nearest centroiduntil convergence

until N large enough

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VQ Performance on Unseen Data

Ramachandran & Mamone (eds) ‘Modern Methods of Speech Processing’ Kluer Academic, 1995

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Ramachandran & Mamone (eds) ‘Modern Methods of Speech Processing’ Kluer Academic, 1995

VQ Performance on Unseen Data

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710 1 2 3 4 5-40

-20

0

20

40

Ma

gn

itu

de

(d

B)

Frequency (KHz) ( 0-to-Fs/2)

0 3.2 6.4 9.6 12.8 16 19.2 22.4 25.6-1

-0.5

0

0.5

1

Wav

efo

rm

Time (ms)

LPC & FFT SpectraLPC Roots -0.6651 ± 0.6695i -0.0560 ± 0.9709i 0.7228 ± 0.6225i 0.8714 ± 0.3694i 0.5758 -0.4200

2 of Q(z) 1 of P(z)

2.3743 2.2274

1.6540 1.5997

0.8261 0.6954

0.6106 0.3937

LSFs

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0 1 2 3 4 5-40

-20

0

20

40

Ma

gn

itu

de

(d

B)

Frequency (KHz) ( 0-to-Fs/2)

LPC Spectra & LSF’sLPC Roots -0.6651 ± 0.6695i -0.0560 ± 0.9709i 0.7228 ± 0.6225i 0.8714 ± 0.3694i 0.5758 -0.4200

2 of Q(z) 1 of P(z)

2.3743 2.2274

1.6540 1.5997

0.8261 0.6954

0.6106 0.3937

LSFs

-1

-0.5

0

0.5

1

-1 0 1

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730 1 2 3 4 5-40

-20

0

20

40

Frequency (KHz) ( 0-to-Fs/2)

0 3.2 6.4 9.6 12.8 16 19.2 22.4 25.6-1

-0.5

0

0.5

1

Time (ms)

A(z): 1.5537 -0.8276Roots: 0.7769 ± 0.4733i

H(0) = K (1- (1.5537 - 0.8276))

H(ws/2) = K

(1- (-1.5537 - 0.8276))

H(0) K/0.274 = = 21.8dBH(ws /2) K/ 3.38

LPC & FFT Spectra - 2nd Order

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GSM

Groupe Special Mobile - EU First digital cellular system in world See Hodge 1990 Based on TDMA & FDMA at 900MHz, and RPE-LPC

(ie it is an ‘LPAS’ system) Now at 1800 MHz Carriers at 200kHz Supporting 8 TDMA time slots each Time slots: 577s - 156.26 bit slots 8 time slots form 1 GSM frame of 4.62 ms Modulation: Gaussian minimum shift key 26 bit training in every time slot Round-trip delay ~ 80ms EU: GSM US: D-AMPS

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Other Related Topics

Spectral Lifting: H(z) = (1-az-1)

Codebook Training

Spectral Differences between 2 frames

Cepstra

Modeling Speech Space - HMM’s

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Pre-Emphasis Example

-8000

0

8000

-8000

0

8000

1

- 1

1

- 130ms

(a)

(b)

Figure Q1

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Pre-Emphasis Example

a

z-plane jy

1+a = 2

ws/2

G(ws/2) = 1 + aG(0) = 1 - a

For G(ws/2 ) > G(0) then a must be > 0

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1+a = 2

ws/2

0 1 2 3 4 5-30

-20

-10

0

10

20

30

40

50

Mag

nit

ud

e (d

B)

Frequency (KHz) ( 0-to-Fs/2)

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

Real Part

Imag

inar

y P

art

Z-plane to Magnitude Spectrum

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LPC Short and Long

Spectral envelop reflects morphological characteristics of the vocal tract

H1(z) H2(z)noise synthesisedSpeech

Air fromthe lungs

Vocal fold Vocal tract Speech

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ST & LT Prediction

1 – A’(z)sn en

Residual

1 – A’(z) e`n

Z-1

Z-1

Z-1

a1

ai

ai

sn

sn

sn-1

sn-i

sn-p

+-Z-1

Z-1

Z-1

a1

ai

ap

+-

Z-1

ap

LTP

STP

Speech