The document discusses linear predictive coding (LPC), which is a technique used for spectral estimation, forecasting, modeling vocal tracts, and other signal processing applications. LPC models a signal using an all-pole filter with feedback and estimates filter coefficients to represent a signal's spectrum or predict future values. Common applications of LPC include speech vocoders, spectral analysis, pitch estimation, voice changing, and musical instrument analysis and synthesis.

1. linear predictive coding (LPC)
an application driven approach
adapted from guest lecture for mobile application development for sensing and control, EE596
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2. non-parametric parametric
Use Data or Transform Fit Data to a Model
Data
Derivative
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3. non-parametric parametric
Use Data or Transform Fit Data to a Model
Data
Derivative
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4. non-parametric parametric
Use Data or Transform Fit Data to a Model
Data
Derivative
derivative[n] = y[n]-y[n-1]
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5. non-parametric parametric
Use Data or Transform Fit Data to a Model
Data
Derivative
derivative[n] = y[n]-y[n-1]
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6. non-parametric parametric
Use Data or Transform Fit Data to a Model
Data
Derivative
derivative[n] = y[n]-y[n-1]
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7. non-parametric parametric
Use Data or Transform Fit Data to a Model
Data
Derivative
cos(x)
derivative[n] = y[n]-y[n-1]
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8. non-parametric parametric
Use 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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9. the tradeoff of parametric modeling
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10. the tradeoff of parametric modeling
- need to fit a model to the data
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11. the tradeoff of parametric modeling
- need to fit a model to the data
+ (might be) easier to manipulate model
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12. non-parametric parametric
Use Data or Transform Fit Data to a Model
two signals = 1500 Hz and 5500 Hz two signals = 1500 Hz and 5500 Hz
Magnitude
freq (kHz) freq (kHz)
Magnitude
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13. non-parametric parametric
Use Data or Transform Fit Data to a Model
two signals = 1500 Hz and 5500 Hz
FFT, array
two signals = 1500 Hz and 5500 Hz
Magnitude
freq (kHz) freq (kHz)
Magnitude
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14. non-parametric parametric
Use Data or Transform Fit Data to a Model
two signals = 1500 Hz and 5500 Hz
FFT, array
two signals = 1500 Hz and 5500 Hz
Magnitude
freq (kHz)
LPC polynomial
freq (kHz)
Magnitude
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15. what model should we fit to?
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16. what model should we fit to?
a filter with feedback
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17. what model should we fit to?
a filter with feedback
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18. what model should we fit to?
a filter with feedback
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19. feedback filters are system models
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20. feedback filters are system models
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21. feedback filters are system models
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22. feedback filtering
a
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23. feedback filtering
want to estimate a
a
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24. feedback filtering
what can we represent with this equation?
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25. ak
k k k
feedback filtering
what can we represent with this equation?
3
2
1
0
-1
-2
-3
1 3 5 7 9 11 13
3
2
1
0
-1
-2
-3
1 3 5 7 9 11 13
3
2
1
0
-1
-2
-3
1 3 5 7 9 11 13
piano marimba violin
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26. feedback filter equation in frequency
…
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27. feedback filter equation in frequency
…
Y (z) =
E(z)
1
Pp
k=1 akz k
z = ej!
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28. is this a good model for frequency analysis?
Y (z) =
1
1
Pp
k=1 akz k
E(z)
Y (z) =
1
Qp
k=1(1 rkz 1)
E(z)
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29. is this a good model for frequency analysis?
resonant frequency = complex angle of root
resonance bandwidth = related to magnitude of root
Y (z) =
1
1
Pp
k=1 akz k
E(z)
Y (z) =
1
Qp
k=1(1 rkz 1)
E(z)
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30. examples
Y (z) =
1
Qp
k=1(1 rkz 1)
E(z)
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31. another interpretation, vocal tract
sourcefilter
Y (z) =
1
1
Pp
k=1 akz k
E(z)
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32. another interpretation, vocal tract
sourcefilter
Y (z) =
1
1
Pp
k=1 akz k
E(z)
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33. another interpretation, vocal tract
sourcefilter
Y (z) =
1
1
Pp
k=1 akz k
E(z)
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34. another interpretation, prediction
…
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35. another interpretation, prediction
…
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36. 17
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37. 18
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38. 18
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39. 18
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40. summary of interpretations
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41. summary of interpretations
Spectral Estimation == Auto Regressive
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42. summary of interpretations
Spectral Estimation == Auto Regressive
Forecasting == Linear Prediction
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43. summary of interpretations
Spectral Estimation == Auto Regressive
Forecasting == Linear Prediction
Vocal Tract Model == Source/Filter
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44. common applications
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45. common applications
Speech Vocoders
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46. common applications
Speech Vocoders
Spectral Analysis
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47. common applications
Speech Vocoders
Spectral Analysis
Pitch Estimation
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48. common applications
Speech Vocoders
Spectral Analysis
Pitch Estimation
Voice Changers
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49. common applications
Speech Vocoders
Spectral Analysis
Pitch Estimation
Voice Changers
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50. common applications
Speech Vocoders
Spectral Analysis
Pitch Estimation
Voice Changers
Analysis/Synthesis of Instrument Sounds
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51. common applications
Speech Vocoders
Spectral Analysis
Pitch Estimation
Voice Changers
Analysis/Synthesis of Instrument Sounds
Voice Box
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52. common applications
Speech Vocoders
Spectral Analysis
Pitch Estimation
Voice Changers
Analysis/Synthesis of Instrument Sounds
Voice Box
Compression (i.e., mpeg4, CELP)
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53. common applications
Speech Vocoders
Spectral Analysis
Pitch Estimation
Voice Changers
Analysis/Synthesis of Instrument Sounds
Voice Box
Compression (i.e., mpeg4, CELP)
My research– medical sensing from a microphone
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54. questions?
Topics Related to LPC and Further Reading:
LPC10, Ultra Low Bit Rate Voice Coding
Code Excited Linear Prediction
Levinson-Durbin Recursion
Burg’s Method
LP Cepstral Coefficients
The Talking Orchestra
SpiroSmart, the mobile phone spirometer
eclarson.com
eclarson@uw.edu
@ec_larson
electrical
engineering
computer
science
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