Speech CodingUsing LPC

What is Speech Coding

Speech coding is the procedure of transforming speech signal into more compact form for

Transmission Available Bandwidth

Encryption

Uncompressed Speech signal

Analog speech is a bandpassed signal between 200 and 3400 Hz.

Uncompressed digital speech is a bit stream at 64kB/s.

Transmission technology must transmit the signals from point A to point B:

with minimum degradationusing minimum bandwidth

Speech coding

By coding we mean an efficient representation of the signal

– COMPRESSION

The main approaches: waveform coding transform coding Parametric / hybrid coding

} smart quantizers

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How each of these works:

Waveform coders: try to find an efficient representation of the waveform, directly.

Transform coders: try to find an efficient representation in the frequency domain.

Parametric coders: try to find a small set of parameters that are an efficient representation of the signal.

FFT, etc.

)(Hexc. speech

Comparison of Comparison of speech coders

LPC (Linear Predictive coding)

LPC is a model for signal production: it is based on the assumption that the speech signal is produced by a very specific model.

Speech Production in HumaSpeech Production in Humans

The speech signal is created by: A pressure source (lungs),

exciting ... A Filter (Vocal tract:

pharynx - mouth [soft palate, tongue] - nasal cavity)

For DSP Engineer For DSP Engineer

An excitation source A time varying filter

H(t, )

filter:Excitation speech

The model and its representationThe model and its representation

The LPC model looks at speech as: Excitation:

periodic (voiced) - originating in the larynx

noise (unvoiced) - fricative, produced in the mouth

An all-pole filter representing the vocal tract

H()

all polefilter:.. ..

Block Diagram

Why the name “Linear Predictive Coding”

It is assumed that the new sample is the weighted linear combination of previous samples

p

inGeins

ians

1)()()(

Z-Plane RepresentationZ-Plane Representation

In the z-plane we can write the model as a transfer function:

H zG

a zii

i

p( )

1

1

• Clearly this transfer function has only poles - which is why it represents an all pole filter.

Mathematical analysisMathematical analysis

Reminder: our problem is to find the LPC parameters, for a given speech signal. This is called the Inverse Problem.

How do we find the set of parameters that gives the best match to the signal?

What are these Parameters

The Coefficients of the All Pole Filter Pitch of the speech

How do we find the Coefficients: least squares

Formulation: Given a signal s(n); Defining an error as:

Find the set of that will minize the mean square error:

p

ii insansne

1)()()(

ai

E e nn

2( )

Solution:Solution:

Simply equate the derivative of E to zero:

E

ai p

i

0 1, ...

• Which gives us the Normal Equations:

piinsnsinsknsan

p

k nk ...1,)()()()(

1

• These are no more than p linear equations in p unknowns...

Or in matricial form:

n

n

n

p

nnn

nnn

nnn

nspns

nsns

nsns

a

a

a

pnspnsnspnsnspns

pnsnsnsnsnsns

pnsnsnsnsnsns

)()(

)()2(

)()1(

)()()2()()1()(

)()2()2()2()1()2(

)()1()2()1()1()1(

2

1

A correlation; in other words: take the signal, multiply it by a shifted version, and sum.

Since our signal is long and time varying- we did it on short windows

Two variants: autocorrelation method covariance method

?)()( n

inskns

What is each element of the form-

Solving the Matrix

Found the Coefficients a(i) by Using the

Levinson-Durbin recursion method

Second Parameter

Pitch was found by the finding the correlation of the signal window with itself

Then these parameters were transmitted

Predictor coefficients 18 * 8 = 144

Gain 5

Pitch period 6

Voiced/unvoiced switch

1

Total 156

Overall bit rate50 * 156 = 7800

bits / second

Bit rate for plain LPC vocoder

Predictor coefficients

18 * 8 = 144

Gain 5

DCT coefficients

40 * 4 = 160

Total 309

Overall bit rate

50 * 309 = 15450 bits /

second

Bit rate for voice-excited LPC vocoder with DCT

Conclusion Sound produced through LPC method is

not exactly the real sound but it sounds intelligibly understandable

LPC can be used in Speech recognition systems

LPC was widely used in Military because of low bit rate in transmission

There are many variants over the basic scheme: LPC-10, CELP, MELP, RELP, VSELP, ASELP, LD-CELP...