The Cepstrum and Homomorphic Speech Processing
Description: The Cepstrum and Homomorphic Speech Processing Seong-gyu Lee Speech and Audio Processing Lab. 2022. 06. 30. Part 1 신입생 세미나 Contents 2 3 8.1 Introduction Frequency of Frequency axis Introduction 4 Introduction 5 Terms Introduction 6 7 8.2
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slide1. The Cepstrum and Homomorphic Speech Processing Seong-gyu Lee
Speech and Audio Processing Lab. 2022. 06. 30. Part 1 신입생 세미나<br>
slide2. Contents 2<br>
slide3. 3 8.1
Introduction<br>
slide4. Frequency of
Frequency axis Introduction 4<br>
slide5. Introduction 5<br>
slide6. Terms Introduction 6<br>
slide7. 7 8.2
Homomorphic Systems for Convolution<br>
slide8. Homomorphic Systems for Convolution 8<br>
slide9. Homomorphic Systems for Convolution 9<br>
slide10. Homomorphic Systems for Convolution 10<br>
slide11. Homomorphic Systems for Convolution 11<br>
slide12. Homomorphic Systems for Convolution 12<br>
slide13. Homomorphic Systems for Convolution 13<br>
slide14. Homomorphic Systems for Convolution 14<br>
slide15. Representation by DTFTs 15 Representation of the canonic form for homomorphic deconvolution in terms of DTFT
Representation of the characteristic system for homomorphic deconvolution in terms of DTFT operators<br>
slide16. Representation by DTFTs 16 Characteristic system using DTFT
Inverse characteristic system using DTFT<br>
slide17. Representation by DTFTs 17<br>
slide18. Representation by DTFTs 18<br>
slide19. Representation by DTFTs 19<br>
slide20. Representation by DTFTs 20<br>
slide21. 21<br>
slide22. 22<br>
slide23. Properties of the Complex Cepstrum 23<br>
slide24. Properties of the Complex Cepstrum 24<br>
slide25. Properties of the Complex Cepstrum 25<br>
slide26. Properties of the Complex Cepstrum 26<br>
slide27. Properties of the Complex Cepstrum 27<br>
slide28. Some Examples of Complex Cepstrum Analysis 28<br>
slide29. Some Examples of Complex Cepstrum Analysis 29<br>
slide30. Some Examples of Complex Cepstrum Analysis 30<br>
slide31. Minimum- and maximum-phase signals 31<br>
slide32. Minimum- and maximum-phase signals 32<br>
slide33. 33 8.3
Homomorphic Analysis of the Speech Model<br>
slide34. Homomorphic Analysis of the Speech Model 34 How can convolution be separated?<br>
slide35. Homomorphic Analysis of the Speech Model 35<br>
slide36. Homomorphic Analysis of the Model for Voiced Speech 36<br>
slide37. Homomorphic Analysis of the Model for Voiced Speech 37 Log magnitude of DTFTs
Output of speech model system and corresponding DTFT<br>
slide38. Homomorphic Analysis of the Model for Voiced Speech 38<br>
slide39. Homomorphic Analysis of the Model for Voiced Speech 39<br>
slide40. Homomorphic Analysis of the Model for Voiced Speech 40<br>
slide41. Homomorphic Analysis of the Model for Unvoiced Speech 41 Real function without phase.
It is impossible to determine minimum phase or maximum phase.<br>
slide42. Homomorphic Analysis of the Model for Unvoiced Speech 42<br>
slide43. Homomorphic Analysis of the Model for Unvoiced Speech 43 Homomorphic analysis of unvoiced speech<br>
slide44. Homomorphic Analysis of the Model for Unvoiced Speech 44 It is possible to observe pitch.<br>
slide45. 45 8.4
Computing the Short-Time Cepstrum and Complex Cepstrum of Speech<br>
slide46. Computing the Short-Time Cepstrum and Complex Cepstrum of Speech Short-time versions of the cepstrum and complex cepstrum
In practice, Analysis is based on short segments of a natural speech signal.
Since the speech signal change continuously with time, it is important to track those changes.
The property that speech signal change continuously leads to short-time versions of the cepstrum and the complex cepstrum. 46<br>
slide47. Computation Based on the Discrete Fourier Transform 47<br>
slide48. 48 Computation Based on the Discrete Fourier Transform<br>
slide49. 49 Computation Based on the Discrete Fourier Transform<br>
slide50. 50 Computation Based on the Discrete Fourier Transform<br>
slide51. 51 Computation Based on the Discrete Fourier Transform<br>
slide52. Computation Based on the z-Transform 52<br>
slide53. Computation Based on the z-Transform 53<br>
slide54. Computation Based on the z-Transform 54 It can be omitted<br>
slide55. Computation Based on the z-Transform 55<br>
slide56. Recursive Computation for Minimum- and Maximum-Phase Signals 56<br>
slide57. Recursive Computation for Minimum- and Maximum-Phase Signals 57<br>
slide58. 58 Thank you for listening.
Q & A<br>
Speech and Audio Processing Lab. 2022. 06. 30. Part 1 신입생 세미나<br>
slide2. Contents 2<br>
slide3. 3 8.1
Introduction<br>
slide4. Frequency of
Frequency axis Introduction 4<br>
slide5. Introduction 5<br>
slide6. Terms Introduction 6<br>
slide7. 7 8.2
Homomorphic Systems for Convolution<br>
slide8. Homomorphic Systems for Convolution 8<br>
slide9. Homomorphic Systems for Convolution 9<br>
slide10. Homomorphic Systems for Convolution 10<br>
slide11. Homomorphic Systems for Convolution 11<br>
slide12. Homomorphic Systems for Convolution 12<br>
slide13. Homomorphic Systems for Convolution 13<br>
slide14. Homomorphic Systems for Convolution 14<br>
slide15. Representation by DTFTs 15 Representation of the canonic form for homomorphic deconvolution in terms of DTFT
Representation of the characteristic system for homomorphic deconvolution in terms of DTFT operators<br>
slide16. Representation by DTFTs 16 Characteristic system using DTFT
Inverse characteristic system using DTFT<br>
slide17. Representation by DTFTs 17<br>
slide18. Representation by DTFTs 18<br>
slide19. Representation by DTFTs 19<br>
slide20. Representation by DTFTs 20<br>
slide21. 21<br>
slide22. 22<br>
slide23. Properties of the Complex Cepstrum 23<br>
slide24. Properties of the Complex Cepstrum 24<br>
slide25. Properties of the Complex Cepstrum 25<br>
slide26. Properties of the Complex Cepstrum 26<br>
slide27. Properties of the Complex Cepstrum 27<br>
slide28. Some Examples of Complex Cepstrum Analysis 28<br>
slide29. Some Examples of Complex Cepstrum Analysis 29<br>
slide30. Some Examples of Complex Cepstrum Analysis 30<br>
slide31. Minimum- and maximum-phase signals 31<br>
slide32. Minimum- and maximum-phase signals 32<br>
slide33. 33 8.3
Homomorphic Analysis of the Speech Model<br>
slide34. Homomorphic Analysis of the Speech Model 34 How can convolution be separated?<br>
slide35. Homomorphic Analysis of the Speech Model 35<br>
slide36. Homomorphic Analysis of the Model for Voiced Speech 36<br>
slide37. Homomorphic Analysis of the Model for Voiced Speech 37 Log magnitude of DTFTs
Output of speech model system and corresponding DTFT<br>
slide38. Homomorphic Analysis of the Model for Voiced Speech 38<br>
slide39. Homomorphic Analysis of the Model for Voiced Speech 39<br>
slide40. Homomorphic Analysis of the Model for Voiced Speech 40<br>
slide41. Homomorphic Analysis of the Model for Unvoiced Speech 41 Real function without phase.
It is impossible to determine minimum phase or maximum phase.<br>
slide42. Homomorphic Analysis of the Model for Unvoiced Speech 42<br>
slide43. Homomorphic Analysis of the Model for Unvoiced Speech 43 Homomorphic analysis of unvoiced speech<br>
slide44. Homomorphic Analysis of the Model for Unvoiced Speech 44 It is possible to observe pitch.<br>
slide45. 45 8.4
Computing the Short-Time Cepstrum and Complex Cepstrum of Speech<br>
slide46. Computing the Short-Time Cepstrum and Complex Cepstrum of Speech Short-time versions of the cepstrum and complex cepstrum
In practice, Analysis is based on short segments of a natural speech signal.
Since the speech signal change continuously with time, it is important to track those changes.
The property that speech signal change continuously leads to short-time versions of the cepstrum and the complex cepstrum. 46<br>
slide47. Computation Based on the Discrete Fourier Transform 47<br>
slide48. 48 Computation Based on the Discrete Fourier Transform<br>
slide49. 49 Computation Based on the Discrete Fourier Transform<br>
slide50. 50 Computation Based on the Discrete Fourier Transform<br>
slide51. 51 Computation Based on the Discrete Fourier Transform<br>
slide52. Computation Based on the z-Transform 52<br>
slide53. Computation Based on the z-Transform 53<br>
slide54. Computation Based on the z-Transform 54 It can be omitted<br>
slide55. Computation Based on the z-Transform 55<br>
slide56. Recursive Computation for Minimum- and Maximum-Phase Signals 56<br>
slide57. Recursive Computation for Minimum- and Maximum-Phase Signals 57<br>
slide58. 58 Thank you for listening.
Q & A<br>