Speech Processing

References

L.R. Rabiner and R.W. Schafer. Digital Processing of Speech Signals. Prentice-Hall, 1978.

Lawrence Rabiner and Biing-Hwang Juang. Fundamentals of Speech Recognition. Prentice-Hall, 1993.

James H. McClellan, et al. Computer-Based Exercises for Signal Processing Using MATLAB 5. Prentice-Hall, 1998.

The sound of spoken words is divided-up into phonemes. European languages have about forty phonemes. Phonemes are divided into two groups: voiced sounds and unvoiced sounds. Voiced sounds are “vowel-like” sounds where the sound comes from the throat. Unvoiced phonemes are “consonant-like” phonemes where the sound comes from compressed air blown through the mouth. While unvoiced phonemes are “consonant-like,” not all consonants are unvoiced. Phonemes like “s” are unvoiced, but phonemes like “z” are voiced.

Speech production may be modeled by the following diagram:

PulseTrain

Glottis

RandomNoise

VocalTract

LipRadiation

Voiced

Unvoiced

(See Figure 10.5 in Computer-Based Exercises for Signal Processing.)

The glottis (in the throat) produces “quasi-periodic” signals (like singing a long note). These signals are modeled as the output of the glottis block. These signals are then passed into a vocal tract block. The vocal tract models the mouth, nose and teeth. Finally the lip radiation block models the lips.

Unvoiced sounds have no glottal pulse component and can be modeled with the vocal tract and lip radiation blocks. To obtain any kind of sound, the input to the vocal tract and lip radiation blocks cannot be simply a unit step but rather a random process.

PulseTrain

Glottis

RandomNoise

VocalTract

LipRadiation

Voiced

Unvoiced

Let us give function values to these signals and processes:

e[n]

G(z)

V(z) R(z)uG[n] uL[n] pL[n]

e[n] is a periodic pulse train.

G(z) is the transfer function of the glottis

uG[n] is the glottis output.

V(z) is the transfer function of the vocal tract.

R(z) is the transfer function of the lips.

uL[n] is the output of the vocal tract.

pL[n] is the output of the lips.

The glottal transfer function G(z) will be represented by an exponential model:

.)1(

)]ln()[(

)(

)()(

21

1

az

zaae

zE

zUzG G

The symbol e represents the base of natural logarithms. The parameter a is some value less than one that corresponds to the natural frequency of the glottis (which varies from speaker to speaker, man to woman, child to adult, etc.).

The frequency response of G(z) for various values of a is shown on the following slide. (Graph printed using glottal.m.)

0 0.25 0.5 0.75 10

5

10

15

20

25

a = 0.90

a = 0.80

a = 0.70

, x

|G(e

j)|

Frequency Response

The vocal tract V(z) can be modeled after a sequence of “lossless tubes”:

uG[n] uL[n]

AkAk+1

Ak-1

Each “tube” has a cross-sectional area Ak.

The vocal tract transfer function V(z) will be represented by following model:

.)(

)1(

)(

)()( 1

2/

zD

zr

zU

zUzV

N

k

Nk

G

L

The parameters rk (which correspond to reflection coefficients along the vocal tract) are found from

kk

kkk AA

AAr

1

1

The denominator D(z) is found from the recursive relationship:

Where Ak (k=1, … N) are parameters corresponding to cross-sectional areas of the vocal tract. (These values are given for a particular phoneme.)

)()()( 111

zDzrzDzD k

kkkk

starting with D0(z) = 1 and ending with D(z) = DN(z).

The numerator G [of V(z)] is found by

N

kkrG

1

).1(

Finally, the lip radiation transfer function is given by

.1)(

)()( 1 z

zU

zPzR

L

L

The previous voice model was implemented in MATLAB in a script file called voice.m.

The vocal tract transfer function V(z) parameters are computed by a MATLAB function called AtoV().

The glottal transfer function G(z) coefficients are assigned to arrays numg and deng.

The vocal tract/lip radiation transfer function V(z)R(z) coefficients are assigned to arrays numv and denv.

PulseTrain

Glottis

RandomNoise

VocalTract

LipRadiation

Voiced

Unvoiced

e[n]

G(z)

V(z) R(z)uG[n] uL[n] pL[n]

numg, deng

AtoV numv, denv

uG[n] = rand();

kk

kkk AA

AAr

1

1

for k=1:N-1 r = [r (A(k+1)-A(k))/(A(k+1)+A(k))];end;

AtoV()

).()()( 111

zDzrzDzD k

kkkk

for k=1:N D = [D 0] + r(k).*[0 fliplr(D)]; G = G*(1+r(k));end;

N

kkrG

1

).1(

Voiced Speech

ug = 0.1*filter(numg,deng,p);pl = filter(numv,denv,ug);

ug = 0.01*randn(1,10000);pl = filter(numv,denv,ug);

Unvoiced Speech

The array p is a pulse train

Given the vocal tract areas Ak for a given vowel, we can synthesize the vowels.

In the following demonstration, we will synthesize the phonemes AA and IY.

The phoneme AA is like a short a (ă)

The phoneme IY is like a long e (ē).

AA voiced (aav.wav)

AA unvoiced(aau.wav)

IY voiced(iyv.wav)

IY unvoiced(iyu.wav)