applications and derivation of linear predictive coding
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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)
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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
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feedback filtering
a
Friday, August 30, 13
feedback filtering
want to estimate a
a
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feedback filtering
what can we represent with this equation?
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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!
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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)
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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)
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another interpretation, prediction
…
Friday, August 30, 13
another interpretation, prediction
…
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17
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18
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18
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18
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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
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common applications
Friday, August 30, 13
common applications
Speech Vocoders
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common applications
Speech VocodersSpectral Analysis
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common applications
Speech VocodersSpectral AnalysisPitch Estimation
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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 [email protected]@ec_larson
electrical engineering
computerscience
Friday, August 30, 13