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



Data

Derivative

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



Data

Derivative

cos(x)




Data

Derivative

cos(x)


-sin(x)


the tradeoff of parametric modeling



- need to fit a model to the data



- need to fit a model to the data

+ (might be) easier to manipulate model



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

Magn

itude

freq (kHz) freq (kHz)

Magn

itude



two signals = 1500 Hz and 5500 Hz

FFT, array


Magn

itude

freq (kHz) freq (kHz)

Magn

itude




FFT, array


Magn

itude

freq (kHz)

LPC polynomialfreq (kHz)

Magn

itude


what model should we fit to?


what model should we fit to?

a filter with feedback


feedback filters are system models


feedback filtering

a


feedback filtering

want to estimate a

a


feedback filtering

what can we represent with this equation?


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


feedback filter equation in frequency

…


feedback filter equation in frequency

…

Y (z) =E(z)

1�Pp

k=1 akz�k

z = ej!


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)


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)


examples

Y (z) =1Qp

k=1(1� rkz�1)E(z)


another interpretation, vocal tract

sourcefilter

Y (z) =1

1�Pp

k=1 akz�k

E(z)


another interpretation, prediction

…


17


18


summary of interpretations



Spectral Estimation == Auto Regressive



Spectral Estimation == Auto RegressiveForecasting == Linear Prediction



Spectral Estimation == Auto RegressiveForecasting == Linear Prediction

Vocal Tract Model == Source/Filter


common applications


common applications

Speech Vocoders


common applications

Speech VocodersSpectral Analysis


common applications

Speech VocodersSpectral AnalysisPitch Estimation


common applications

Speech VocodersSpectral AnalysisPitch Estimation Voice Changers


common applications

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


common applications

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


common applications


Compression (i.e., mpeg4, CELP)


common applications


Compression (i.e., mpeg4, CELP)

My research– medical sensing from a microphone


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 [email protected]@ec_larson

electrical engineering

computerscience


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applications and derivation of linear predictive coding

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