applications and derivation of linear predictive coding

linear predictive coding (LPC)an application driven approach

adapted from guest lecture for mobile application development for sensing and control, EE596

Friday, August 30, 13

non-parametric parametricUse Data or Transform Fit Data to a Model

Data

Derivative

Friday, August 30, 13

non-parametric parametricUse Data or Transform Fit Data to a Model

Data

Derivative

Friday, August 30, 13

non-parametric parametricUse Data or Transform Fit Data to a Model

Data

Derivative

derivative[n] = y[n]-y[n-1]

Friday, August 30, 13

non-parametric parametricUse Data or Transform Fit Data to a Model

Data

Derivative

derivative[n] = y[n]-y[n-1]

Friday, August 30, 13

non-parametric parametricUse Data or Transform Fit Data to a Model

Data

Derivative

derivative[n] = y[n]-y[n-1]

Friday, August 30, 13

non-parametric parametricUse Data or Transform Fit Data to a Model

Data

Derivative

cos(x)

derivative[n] = y[n]-y[n-1]

Friday, August 30, 13

non-parametric parametricUse Data or Transform Fit Data to a Model

Data

Derivative

cos(x)

derivative[n] = y[n]-y[n-1]

-sin(x)

Friday, August 30, 13

the tradeoff of parametric modeling

Friday, August 30, 13

the tradeoff of parametric modeling

- need to fit a model to the data

Friday, August 30, 13

the tradeoff of parametric modeling

- need to fit a model to the data

+ (might be) easier to manipulate model

Friday, August 30, 13

non-parametric parametricUse Data or Transform Fit Data to a Model

two signals = 1500 Hz and 5500 Hz two signals = 1500 Hz and 5500 Hz

Magn

itude

freq (kHz) freq (kHz)

Magn

itude

Friday, August 30, 13

non-parametric parametricUse Data or Transform Fit Data to a Model

two signals = 1500 Hz and 5500 Hz

FFT, array

two signals = 1500 Hz and 5500 Hz

Magn

itude

freq (kHz) freq (kHz)

Magn

itude

Friday, August 30, 13

non-parametric parametricUse Data or Transform Fit Data to a Model

two signals = 1500 Hz and 5500 Hz

FFT, array

two signals = 1500 Hz and 5500 Hz

Magn

itude

freq (kHz)

LPC polynomialfreq (kHz)

Magn

itude

Friday, August 30, 13

what model should we fit to?

Friday, August 30, 13

what model should we fit to?

a filter with feedback

Friday, August 30, 13

what model should we fit to?

a filter with feedback

Friday, August 30, 13

what model should we fit to?

a filter with feedback

Friday, August 30, 13

feedback filters are system models

Friday, August 30, 13

feedback filters are system models

Friday, August 30, 13

feedback filters are system models

Friday, August 30, 13

feedback filtering

a

Friday, August 30, 13

feedback filtering

want to estimate a

a

Friday, August 30, 13

feedback filtering

what can we represent with this equation?

Friday, August 30, 13

ak

k k k

feedback filtering

what can we represent with this equation?

3210-1-2-3

1 3 5 7 9 11 13

3210-1-2-3

1 3 5 7 9 11 13

3210-1-2-3

1 3 5 7 9 11 13

piano marimba violin

Friday, August 30, 13

feedback filter equation in frequency

…

Friday, August 30, 13

feedback filter equation in frequency

…

Y (z) =E(z)

1�Pp

k=1 akz�k

z = ej!

Friday, August 30, 13

is this a good model for frequency analysis?

Y (z) =1

1�Pp

k=1 akz�k

E(z)

Y (z) =1Qp

k=1(1� rkz�1)E(z)

Friday, August 30, 13

is this a good model for frequency analysis?

resonant frequency = complex angle of rootresonance bandwidth = related to magnitude of root

Y (z) =1

1�Pp

k=1 akz�k

E(z)

Y (z) =1Qp

k=1(1� rkz�1)E(z)

Friday, August 30, 13

examples

Y (z) =1Qp

k=1(1� rkz�1)E(z)

Friday, August 30, 13

another interpretation, vocal tract

sourcefilter

Y (z) =1

1�Pp

k=1 akz�k

E(z)

Friday, August 30, 13

another interpretation, vocal tract

sourcefilter

Y (z) =1

1�Pp

k=1 akz�k

E(z)

Friday, August 30, 13

another interpretation, vocal tract

sourcefilter

Y (z) =1

1�Pp

k=1 akz�k

E(z)

Friday, August 30, 13

another interpretation, prediction

…

Friday, August 30, 13

another interpretation, prediction

…

Friday, August 30, 13

17

Friday, August 30, 13

18

Friday, August 30, 13

18

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18

Friday, August 30, 13

summary of interpretations

Friday, August 30, 13

summary of interpretations

Spectral Estimation == Auto Regressive

Friday, August 30, 13

summary of interpretations

Spectral Estimation == Auto RegressiveForecasting == Linear Prediction

Friday, August 30, 13

summary of interpretations

Spectral Estimation == Auto RegressiveForecasting == Linear Prediction

Vocal Tract Model == Source/Filter

Friday, August 30, 13

common applications

Friday, August 30, 13

common applications

Speech Vocoders

Friday, August 30, 13

common applications

Speech VocodersSpectral Analysis

Friday, August 30, 13

common applications

Speech VocodersSpectral AnalysisPitch Estimation

Friday, August 30, 13

common applications

Speech VocodersSpectral AnalysisPitch Estimation Voice Changers

Friday, August 30, 13

common applications

Speech VocodersSpectral AnalysisPitch Estimation Voice Changers

Friday, August 30, 13

common applications

Speech VocodersSpectral AnalysisPitch Estimation Voice Changers Analysis/Synthesis of Instrument Sounds

Friday, August 30, 13

common applications

Speech VocodersSpectral AnalysisPitch Estimation Voice Changers Analysis/Synthesis of Instrument Sounds Voice Box

Friday, August 30, 13

common applications

Speech VocodersSpectral AnalysisPitch Estimation Voice Changers Analysis/Synthesis of Instrument Sounds Voice Box

Compression (i.e., mpeg4, CELP)

Friday, August 30, 13

common applications

Speech VocodersSpectral AnalysisPitch Estimation Voice Changers Analysis/Synthesis of Instrument Sounds Voice Box

Compression (i.e., mpeg4, CELP)

My research– medical sensing from a microphone

Friday, August 30, 13

questions?Topics Related to LPC and Further Reading:

LPC10, Ultra Low Bit Rate Voice CodingCode Excited Linear PredictionLevinson-Durbin RecursionBurg’s MethodLP Cepstral CoefficientsThe Talking OrchestraSpiroSmart, the mobile phone spirometer

eclarson.com eclarson@uw.edu@ec_larson

electrical engineering

computerscience

Friday, August 30, 13