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For Speech Signals

Itay Ben-Lulu & Uri Goldfeld

Instructor : Dr. Yizhar Lavner

Spring 2004

23/9/2004

Abstract

Goal :Estimation of glottal volume velocity (also called glottal pulse) from acoustic speech signal samples.

Three estimation methods are examined:

1. Least Squares Glottal Inverse Filtering from the Acoustic Speech Waveform – by Wong, Markel & Gray, 1979.

2. Pitch Synchronous Iterative Adaptive Inverse Filtering (PSIAIF) – by Alku, 1992.

3. Estimation of the Glottal Flow Derivative Waveform Through Formant Modulation (From: Modeling of the Glottal Flow Derivative Waveform with Application to Speaker Identification)– by Plumpe, Quatieri & Reyndols, 1997.

Applications

- Speech synthesis –knowledge of the glottal frequency is important to produce a synthetic speech that sounds natural.
- There are explicit differences betweenmale and female glottal pulses.
- Different glottal excitations produce differentphonation types: normal, pressed, breathy.
- Glottal pulse has great importance in determining speech types :angry voice, soft voice, happy voice, etc.

Discrete-Time System Model for Speech Production

Voiced/unvoiced switch

Denote:

For voiced speech :the input to is the glottal pulse,

For unvoiced speech :the input to is a random noise

Least Squares Glottal Inverse Filtering from the Acoustic Speech Waveform (Wong, Markel and Gray)

- The vocal-tract model is assumed to be an all-pole model :

where K is an even integer.

- The lip radiation model is given by a differencing filter :

The problem is estimating the vocal-tract transform,

- Assume that an M-th order analysis filter of the form

is to be obtained using covariance method of linear prediction

of the speech signal.

- Then, we can estimate the glottal volume velocity transfer
- function :

where is an all-zero filter:

Analysis Procedure – Block Diagram

Sequential Covariance Analysis

Linear Phase High-Pass Filter

Normalized Error Criterion

LPC

Pitch Detection

Vocal Tract Model Estimation

Searching for Minimal Periods

Polynomial Root Solving

LPC

1. Linear Phase High-Pass Filter –

The speech signal is passed through an high pass filter.

2. Sequential Covariance Analysis –

An N-length analysis window is sequentially moved one sample

at a time throughout . we obtain the total squared error :

when:

3. Normalized Error Criterion – Obtaining by :

where is defined by:

4. Searching for Minimal Values Periods –

Scanning to find the intervals where it gets minimal values.

we denote the first and last samples in each interval by : ,

These intervals are needed for determining the points of glottal

closure and opening : ,

5. Vocal Tract Model Estimation –

The prediction error filter is estimated using LPC at

each closed phase interval, determined by , .

6. Polynomial Root Solving –

Removing real poles (close to zero frequency) and high

bandwidth poles, from the filter .

7. Inverse Filtering + Integration –

The original speech signal is passed through the inverse

filter of , and then through an integrator

.

Finally, we obtain the estimation for the glottal pulse - .

Example of Glottal Pulse Estimation with LS Algorithm for Normal AA Vowel :

Example of Glottal Pulse Estimation with LS Algorithm for Pressed AA Vowel :

- Normalized Error Criterion Calculation -

In long voice signals a problem of over-complexity may appear.

- Closed Period Identification –

In noisy voice signals it may be difficult to determine where the

normalized error criterion, , gets its minimal values (phase 4).

An insufficiently accurate closed period identification causes

poor glottal pulse estimation.

- Minimal Values Periods Criterion –

The numerical criterion for determining the minimal values periods

of may need to be adapted to some voice signals.

PSIAIF - Pitch Synchronous Iterative Adaptive Inverse Filtering (Alku)

- A reliable response to some drawbacks in the first Inverse
- Filtering algorithm.

- This algorithm is based on the speech production model:

Glottal Excitation

Vocal Tract

Lip Radiation

Speech

- Assumptions for this model:
- 1. the model is linear and time-invariant during a short time
- interval.
- 2. the interaction between different processes is negligible.
- 3. the lip radiation effect is modeled with a fixed differentiator.

IAIF Method:

- The main idea: we can estimate the vocal tract accurately
- enough with LPC analysis, if the tilting effect of the glottal
- source is eliminated from the speech spectrum.

- Estimation of the glottal pulse is computed in the IAIF-
- algorithm with an iterative structure that is repeated twice.

PSIAIF Method:

- In order to improve the performance of LPC analysis in the
- estimation of the vocal tract transfer function, the final glottal
- wave estimate is computed pitch synchronously.

Structure of the IAIF Algorithm

LPC analysis of order 1

LPC analysis of order

Inverse Filtering

Inverse Filtering

Integration

LPC analysis of order

LPC analysis of order

Inverse Filtering

Inverse Filtering

Integration

Structure of the PSIAIF Algorithm

High-Pass Filtering

Pitch Synchronism

IAIF-1

IAIF-2

The speech signal to be analyzed is denoted .

The estimated glottal excitation is denoted .

- The speech signal is high-pass filtered.

- The high-pass filtered signal, , is used as an input to the
- first IAIF-analysis. The output is one frame of a pitch
- asynchronously glottal wave estimate, .

The time indices of maximum glottal openings, ,

- are computed for each frame of . This computation requires
- the knowledge of - the average length of pitch period.
- Preliminary knowledge of helps us focusing the search of
- maximum glottal openings on short time periods.

- The final estimate for the glottal excitation is obtained by
- analyzing the high-pass filtered speech signal, , with
- the IAIF-algorithm pitch synchronously.

Example of Glottal Pulse Estimation with PSIAIF Algorithm for Normal AA Vowel :

Example of Glottal Pulse Estimation with PSIAIF Algorithm for Breathy AA Vowel :

Estimation of the Glottal Flow Derivative Waveform Through Formant Modulation (Plumpe)

- This algorithm is similar to Wong’s Least-Squares algorithm,
- with few differences (principles and implementation).

- The vocal-tract model is assumed to be an all-pole model :

where K is an even integer.

- The main goal is to estimate the vocal-tract transfer function,
- using the covariance method of linear prediction.
- When we obtain the vocal-tract model estimation, we can easily
- estimate the glottal flow derivative :

Analysis Procedure – Block Diagram

Speech Waveform Whitening

Linear Phase High-Pass Filter

Peak Picking

LPC

Pitch Detection

Measuring Formant Frequencies

Setting Initial Stationary Region

Formant Tracking

LPC

Vocal Tract Model Estimation

Extending Initial Stationary Region

Polynomial Root Solving

LPC

1. Linear Phase High-Pass Filter –

The speech signal is passed through an high pass filter.

2. Speech Waveform Whitening –

The high-pass filtered speech signal is whitened by inverse

filtering with covariance method solution, using a one pitch-period

frame update and a two pitch-period analysis window. Real zeros

are removed from LPC solution. A rough estimation of the glottal

flow derivative is obtained - .

3. Peak Picking –

The obtained rough estimation, , is scanned to identify the

approximate time of glottal pulses through negative peak picking.

The negative peaks are marked by : .

4. Measuring Formant Frequencies –

At each glottal cycle, a sliding covariance-based linear prediction

analysis with a one-sample shift is used. The size of rectangular

analysis window is , where is linear prediction order.

A vocal-tract estimate is found for each window.

5. Formant Tracking –

At each glottal cycle, the four lowest formants - calculated from the

vocal-tract estimates - are tracked by their frequency using a Viterbi

search. The cost function is the variance of the formant track

including the proposed pole to be added to the end of the track.

We obtain the formant track, .

6. Setting Initial Stationary Region –

Within each glottal cycle, we define a formant change function as:

where is linear prediction order, is glottal cycle length.

The argument is varied to minimize :

The initial stationary formant region is set to be :

This region is denoted by : .

7. Extending Initial Stationary Region –

The initial stationary formant region is extended to

obtain the stationary formant region - .

The extension to right is based on the following procedure :

Identify Initial Stationary Region .

Calculate Average and Standard Deviation over Interval .

Include the Point in the Stationary Region

Is

YES

NO

Extend the Region to Left

Extending to Left : The final mean and standard deviation are kept constant.

8. Vocal Tract Model Estimation –

The prediction error filter is estimated using LPC at

each stationary formant region, determined by , .

9. Polynomial Root Solving –

Removing real poles (close to zero frequency) and high

bandwidth poles, from the filter .

10. Inverse Filtering –

The original speech signal is passed through the inverse

filter of , to obtain the estimation for the glottal pulse

derivative - .

Example of Glottal Pulse Estimation with FM Algorithm for Normal AA Vowel :

Example of Glottal Pulse Estimation with FM Algorithm for Pressed AA Vowel :

- Initial Stationary Region Extension -

In some voice signals, the first formant frequency is not stable

during the closed phase. Hence, an accurate determination of a formant

stationary region is depended on a single numerical parameter.

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