lecture 15 new

8/2/2019 Lecture 15 New

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eturn to Main

jectives

sic Theory:

Simple Case

General Case

ovariance

Autocorrelation

rror

ectral Matching:

pectrum

Noise-Weightingreemphasis

Typical Front End

-Line Resources:

Signal Modeling

Linear Prediction

MAD SpeechL

E

C

T

U

R

E

15

:

LI

N

E

A

R

PREDICTION

0 Objectives:

0 Introduce the theory of linear prediction

0 Develop autocorrelation and covariance techniques for solution

0 Understand similarities with regression

0 Explain the relationship to windowing and maximum entropy

0 Add a new technique to our signal modeling block diagram

There is a classic textbook on this subject:

J.D. Markel and A.H. Gray, Linear Prediction of Speech , Springer-Verlag, New York,New York, USA, ISBN: 0-13-007444-6, 1976.

This lecture also includes material from two other textbooks:

J. Deller, et. al., Discrete-Time Processing of Speech Signals , MacMillan Publishing Co.,ISBN: 0-7803-5386-2, 2000.

and,

L.R. Rabiner and B.W. Juang, Fundamentals of Speech Recognition , Prentice-Hall, UppSaddle River, New Jersey, USA, ISBN: 0-13-015157-2, 1993.


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turn to Main

oduction:

1: Organizatio

n ( html ,

pdf )

ech Signals:

2: Productio

n ( html ,

pdf )

3: Digital

Models

( html , pdf )

4: Perceptio

n ( html ,

pdf )

5: Maskin

g ( html ,

pdf )

6: Phonetics andPhonology ( html ,pdf )

7: Syntax andSemantics ( html ,pdf )

nal Processing:

8: Samplin

g ( html ,

pdf )

9: Resamplin

g ( html ,

pdf )

10: AcousticTransducers( html , pdf )

11: Temporal Analysis ( html , pdf )

12: Frequency Domain Analysis ( html , pdf )

13: Cepstral Analysis ( html , pdf )

14: Exam No. 1

( html , pdf )

15: Linear Prediction ( html , pdf )

16: LP-Based Representations ( html , pdf )

Parameterization:

17: Differentiation ( html , pdf )

18: Principal Components ( html , pdf )

ECE 8463: FUNDAMENTALS OF SPEECH

RECOGNITIONProfessor Joseph Picone

Department of Electrical and Computer Engineering

Mississippi State University

email: [email protected] phone/fax:601-325-3149; office: 413 Simrall

URL: http://www.isip.msstate.edu/resources/courses/ece_8463

Modern speech understanding systems merge interdisciplinary technologies from Signal Processing, PatternRecognition, Natural Language, and Linguistics into a unified statistical framework. These systems, which

have applications in a wide range of signal processing problems, represent a revolution in Digital Signal

Processing (DSP). Once a field dominated by vector-oriented processors and linear algebra-based mathematics,the current generation of DSP-based systems rely on sophisticated statistical models implemented using a

complex software paradigm. Such systems are now capable of understanding continuous speech input forvocabularies of hundreds of thousands of words in operational environments.

In this course, we will explore the core components of modern statistically-based speech recognition

systems. We will view speech recognition problem in terms of three tasks: signal modeling, network searching, and language understanding. We will conclude our discussion with an overview of state-of-the-art

systems, and a review of available resources to support further research and technology development.
http://www.isip.msstate.edu/publications/courses/ece_8463/http://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_01/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_01/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_01/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_01/lecture_01.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_01/lecture_01.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_01/lecture_01.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_02/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_02/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_02/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_02/lecture_02.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_02/lecture_02.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_03/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_03/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_03/lecture_03.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_03/lecture_03.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_04/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_04/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_04/lecture_04.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_04/lecture_04.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_05/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_05/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_05/lecture_05.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_05/lecture_05.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_06/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_06/lecture_06.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_06/lecture_06.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_07/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_07/lecture_07.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_07/lecture_07.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_08/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_08/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_08/lecture_08.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_08/lecture_08.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_08/lecture_08.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_09/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_09/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_09/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_09/lecture_09.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_09/lecture_09.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_10/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_10/lecture_10.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_11/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_11/lecture_11.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_12/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_12/lecture_12.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_13/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_13/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_13/lecture_13.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_13/lecture_13.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_14/index.htmlhttp://www.isip.msstate.edu/publications/c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3/lectures/current/lecture_13/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_13/lecture_13.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_14/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_14/lecture_14.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_15/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_15/lecture_15.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_16/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_16/lecture_16.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_17/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_17/lecture_17.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_18/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_18/lecture_18.pdfhttp://www.isip.msstate.edu/resources/courses/ece_8463


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files containing a compilationall the notes are available.

wever, these files are large

will require a substantialount of time to download. A

file of the html version of thees is available here . These

e generated using wget:

wget -np -k -mhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current

df file containing the entire setecture notes is available here .se were generated using Adobe

obat.

estions or comments about the

erial presented here can bected to [email protected] .
http://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_all/notes.html.tar.gzhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_all/notes.pdf.tar.gzmailto:[email protected]://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_all/notes.html.tar.gzhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_all/notes.pdf.tar.gzmailto:[email protected]


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19: Linear DiscriminantAnalysis ( html , pdf )
http://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_19/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_19/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_19/lecture_19.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_19/lecture_19.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_19/lecture_19.pdfhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_19/index.htmlhttp://www.isip.msstate.edu/publications/courses/ece_8463/lectures/current/lecture_19/lecture_19.pdf


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LECTURE 15: LINEAR PREDICTION

0 Objectives:

0 Introduce the theory of linear prediction

0 Develop autocorrelation and covariance techniques for solution

0 Understand similarities with regression

0 Explain the relationship to windowing and maximum entropy

0 Add a new technique to our signal modeling block diagram

ere is a classic textbook on this subject:

J.D. Markel and A.H. Gray, Linear Prediction of Speech , Springer-Verlag, New York, New York, USA, ISBN:0-13-007444-6, 1976.

is lecture also includes material from two other textbooks:

J. Deller, et. al., Discrete-Time Processing of Speech Signals , MacMillan Publishing Co., ISBN: 0-7803-5386-2,2000.

d,

L.R. Rabiner and B.W. Juang, Fundamentals of Speech Recognition , Prentice-Hall, Upper Saddle River,New Jersey, USA, ISBN: 0-13-015157-2, 1993.


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LINEAR PREDICTION - A SIMPLE DERIVATION


7/21

LINEAR PREDICTION - GENERAL CASE


8/21

THE COVARIANCE METHOD


9/21

THE AUTOCORRELATION METHOD


10/21

LINEAR PREDICTION ERROR


11/21

SPECTRAL MATCHING INTERPRETATION


12/21

NOISE FLOORING

VIA THE AUTOCORRELATION FUNCTION


13/21

SIGNAL CONDITIONING COMPENSATES FOR

MICROPHONE AND CHANNEL CHARACTERISTICS


14/21

A TYPICAL SPEECH RECOGNITION FRONT END


15/21

ndex of ublications/journals/ieee_proceedings/1993/signal_modeling

Name Last modified SizeDescription

Parent Directory01-Jan-1999 12:07 -

paper_v2.pdf22-Jun-1999 16:14 452k

ache/1.3.9 Server at www.isip.msstate.edu Port 80
http://www.isip.msstate.edu/publications/journals/ieee_proceedings/1993/signal_modeling/?M=Ahttp://www.isip.msstate.edu/publications/journals/ieee_proceedings/1993/http://www.isip.msstate.edu/publications/journals/ieee_proceedings/1993/signal_modeling/paper_v2.pdfhttp://www.isip.msstate.edu/publications/journals/ieee_proceedings/1993/signal_modeling/?M=Ahttp://www.isip.msstate.edu/publications/journals/ieee_proceedings/1993/http://www.isip.msstate.edu/publications/journals/ieee_proceedings/1993/signal_modeling/paper_v2.pdf


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xt: Motivation from lossless tubes Up: Speech Analysis Previous: Z transforms

inear Prediction analysis

near prediction analysis of speech is historically one of the most important speech analysis techniques. The basis issource-filter model where the filter is constrained to be an all-pole linear filter. This amounts to performing a linear

ediction of the next sample as a weighted sum of past samples:

is linear filter has the transfer function:

good introductory article is [ 8], and this subject is also covered well in [ 1, 2, 3].

0 Motivation from lossless tubes0 Parameter estimation0 The autocorrelation method0 The covariance method0 Pre-emphasis0 The LP spectrum0 Gain computation0 The lattice filter implementation0 The Itakura distance measure0 The LP cepstrum0 Log area ratios0 The roots of the predictor polynomial0 Line spectral pairs

peech Vision Robotics group / Tony Robinson
http://svr-www.eng.cam.ac.uk/~ajr/SA95/node39.htmlhttp://svr-www.eng.cam.ac.uk/~ajr/SA95/SpeechAnalysis.htmlhttp://svr-www.eng.cam.ac.uk/~ajr/SA95/node37.htmlhttp://svr-www.eng.cam.ac.uk/~ajr/SA95/node93.html#Makhoul75http://svr-www.eng.cam.ac.uk/~ajr/SA95/node93.html#RabinerSchafer78http://svr-www.eng.cam.ac.uk/~ajr/SA95/node93.html#FallsideWoods85http://svr-www.eng.cam.ac.uk/~ajr/SA95/node93.html#FallsideWoods85http://svr-www.eng.cam.ac.uk/~ajr/SA95/node93.html#DellerProakisHansen93http://svr-www.eng.cam.ac.uk/~ajr/SA95/node93.html#DellerProakisHansen93http://svr-www.eng.cam.ac.uk/~ajr/SA95/node39.html#SECTION00071000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node40.html#SECTION00072000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node41.html#SECTION00073000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node42.html#SECTION00074000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node43.html#SECTION00075000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node44.html#SECTION00076000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node45.html#SECTION00077000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node46.html#SECTION00078000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node47.html#SECTION00079000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node48.html#SECTION000710000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node49.html#SECTION000711000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node50.html#SECTION000712000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node51.html#SECTION000713000000000000000http://svr-www.eng.cam.ac.uk/http://svr-www.eng.cam.ac.uk/~ajrhttp://svr-www.eng.cam.ac.uk/~ajr/SA95/node39.htmlhttp://svr-www.eng.cam.ac.uk/~ajr/SA95/SpeechAnalysis.htmlhttp://svr-www.eng.cam.ac.uk/~ajr/SA95/node37.htmlhttp://svr-www.eng.cam.ac.uk/~ajr/SA95/node93.html#Makhoul75http://svr-www.eng.cam.ac.uk/~ajr/SA95/node93.html#RabinerSchafer78http://svr-www.eng.cam.ac.uk/~ajr/SA95/node93.html#FallsideWoods85http://svr-www.eng.cam.ac.uk/~ajr/SA95/node93.html#DellerProakisHansen93http://svr-www.eng.cam.ac.uk/~ajr/SA95/node39.html#SECTION00071000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node40.html#SECTION00072000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node41.html#SECTION00073000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node42.html#SECTION00074000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node43.html#SECTION00075000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node44.html#SECTION00076000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node45.html#SECTION00077000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node46.html#SECTION00078000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node47.html#SECTION00079000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node48.html#SECTION000710000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node49.html#SECTION000711000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node50.html#SECTION000712000000000000000http://svr-www.eng.cam.ac.uk/~ajr/SA95/node51.html#SECTION000713000000000000000http://svr-www.eng.cam.ac.uk/http://svr-www.eng.cam.ac.uk/~ajr


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linear prediction of speech

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ntroduction

This tool allows users to explore linear prediction of speech and other signals. It also reinforces theconcepts of windowing, preemphasis and frame size selection in speech analysis. Users can selectregions for analysis and see the results as lpc-smoothed spectra and poles. The residual signal and itsspectrum is also displayed. This tool is not a substitute for learning about linear prediction. Tounderstand what the various panels mean, you should read one of the texts listed below. The demorequires the MATLAB signal processing toolbox.

he tool
http://svr-www.eng.cam.ac.uk/~ajrhttp://svr-www.eng.cam.ac.uk/~ajrhttp://svr-www.eng.cam.ac.uk/~ajrhttp://svr-www.eng.cam.ac.uk/~ajrhttp://svr-www.eng.cam.ac.uk/~ajrhttp://svr-www.eng.cam.ac.uk/~ajrhttp://svr-www.eng.cam.ac.uk/~ajrhttp://svr-www.eng.cam.ac.uk/~ajrhttp://svr-www.eng.cam.ac.uk/~ajrhttp://svr-www.eng.cam.ac.uk/~ajrhttp://svr-www.eng.cam.ac.uk/~ajrhttp://svr-www.eng.cam.ac.uk/~ajrhttp://www.dcs.shef.ac.uk/~martin/MAD/docs/download.htmhttp://www.dcs.shef.ac.uk/~martin/MAD/docs/mad.htmhttp://www.dcs.shef.ac.uk/~martin/MAD/docs/mad.htmhttp://www.dcs.shef.ac.uk/~martin/MAD/docs/download.htmhttp://www.dcs.shef.ac.uk/~martin/MAD/docs/mad.htm


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Type 'lpcspect' to launch the demo. The file menu is used to load an existing signal file or to create a new one

using the createsig tool. Supported formats currently include .wav, .snd and .au sound files. The signal

will appear in panel (1), and associated linear prediction signals for the region between the cursors will bedisplayed in the other panels. Use the cursors to select any segment. On cursor release, the segmentappears in panel (2) along with linear prediction residual (error signal). Panel (3) shows the DFTspectrum of this segment, overlaid with the LPC-smoothed spectrum and the DFT of the residual (7). Thepoles corresponding to the linear predictor are shown in panel (4).

The LPC order can be changed using menu (8). The signal can be preemphasised by checking therelevant box in cluster (6). Cursors can be linked (so that a constant segment length is maintained). Thewaveform segment chosen will be played on release if the associated checkbox is checked.

Clicking on any signal waveform (incuding the residual) causes it to be played. Holding the mousebutton down in the z-plane panel (4) will cause the frequency at the selected z-plane angle to be
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displayed in the top left corner of the panel.

The chosen waveform segment can be Hamming-windowed (5). Unchecked, a rectangular window isapplied.


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hings to investigate

1. Choose a vowel segment of speech. Examine what happens to the residual signal (and its meansquare error) as you increase the number of poles. What happens to the LPC-smoothedspectrum? How many poles provide a comfortable fit to a vowel segment.

2. Now repeat this analysis for unvoiced sounds such as fricatives. How does the error compare?3. Again, perform this analysis for a nasal sound.4. Can you predict where the poles will appear for a given analysis order, and how they will

change when you modify the order?5. Explore the effect of preemphasis on the LPC spectrum and the number of poles required

to obtain a given residual error.6. Listen to the waveform segment and the residual signal in sequence. Can you detect a change

in timbre? How does this change manifest itself as the LPC order increases?7. What is the effect of changing LPC order on the spectrum of the residual signal?8. Choose a vowel sound and a relatively low LPC order (10, say). Read off the pole locations

(frequencies) by holding the mouse down in panel (4). Now use the polezero tool to recreate

just these pole locations and listen to the resulting sound.

9. Use the create option on the file menu to create a harmonic series with, say, 5 components.Do you expect to be able to fit it well with a 10th order model? Try it.

10. Now add some noise (using create ) to your harmonic series. Do the pole locations change? (Readabout the peak-hugging properties of LPC).

urther reading

0 A good introduction to LPC is provided by Makhoul, J. (19??)0 This tool was written partly as an example of the interface issues in speech and

hearing demonstrations, and is described further in Cooke et al (1999) The interactiveauditory demonstrations project, Eurospeech'99, Budapest, September.

redits etc

Produced by : Martin Cooke, April 1999.

Permissions : This demonstration may be used and modified freely by anyone. It may be distributed

in unmodified form.
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F to Word
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