1. Frequency Domain Coding of Speech 主講人：虞台文

2. Content Introduction The Short-Time Fourier Transform The Short-Time Discrete Fourier Transform Wide-Band Analysis/Synthesis Sub-Band Coding

3. Frequency Domain Coding of Speech Introduction

4. Speech Coders Waveform Coders – Attempt to reproducing the original waveform according to some fidelity criteria – Performance: successful at producing good quality, robust speech. Vocoders – Correlated with speech production model. – Performance: more fragile and more model dependent. – Lower bit rate

5. Frequency-Domain Coders Sub-band coder (SCB). Adaptive Transform Coding (ATC). Multi-band Excited Vocoder (MBEV). Noise Shaping in Speech Coders.

6. Classification of Speech Coders

7. Frequency Domain Coding of Speech The Short-Time Fourier Transform

8. Definition of STFT Interpretations: Filter Bank Interpretation Block Transform Interpretation

9. Filter Bank Interpretation  is fixed at  0. f ( m ) Analysis Filter

10. Filter Bank Interpretation...... h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) x(n)x(n)

11. Modulation   00

12. Filter Bank Interpretation   00 Lowpass Filter Modulation

13. Filter Bank Interpretation...... h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) x(n)x(n) Modulated Subband signals

14. Block Transform Interpretation n is fixed at n 0. Windowed Data Analysis Window FT of Windowed Data

15. Block Transform Interpretation n is fixed at n 0. n1n1 n2n2 n3n3...... nrnr

16. Analysis/Synthesis Equations Analysis Synthesis In what condition we will have

17. Analysis/Synthesis Equations Analysis Synthesis Replace r with n+r

18. Analysis/Synthesis Equations Analysis Synthesis Therefore, if

19. Analysis/Synthesis Equations More general, Analysis Synthesis Therefore, if

20. Examples

21. h (0) x ( n )

22. Examples

23. Frequency Domain Coding of Speech The Short-Time Discrete Fourier Transform

24. Definition of STDFT Analysis: Synthesis: In what condition we will have

25. Synthesis 1

26. We need only one period. Therefore, the condition is respecified as:

27. Implementation Consideration n Frequency k 0 Spectrogram

28. Sampling n Frequency k 0 Spectrogram R2R2R3R3R4R4R

29. Sampled STDFT Analysis: Synthesis: In what condition we will have

30. Sampled STDFT Analysis: Synthesis: In what condition we will have

31. Frequency Domain Coding of Speech Wide-Band Analysis/Synthesis

32. Short-Time Synthesis --- Filter Bank Summation STFT h(n)h(n) h(n)h(n) x(n)x(n) Lowpass Filter

33. Short-Time Synthesis --- Filter Bank Summation STFT

34. Short-Time Synthesis --- Filter Bank Summation  |H(e j  )|  |H k (e j  )| kk Lowpass filterBandpass filter

35. Short-Time Synthesis --- Filter Bank Summation hk(n)hk(n) hk(n)hk(n) x(n)x(n) Bandpass Filter h(n)h(n) h(n)h(n) x(n)x(n) Lowpass Filter Lowpass representation of for the signal in a band centered at  k.

36. Short-Time Synthesis --- Filter Bank Summation hk(n)hk(n) hk(n)hk(n) x(n)x(n) Bandpass Filter h(n)h(n) h(n)h(n) x(n)x(n) Lowpass Filter Encoding one bandDecoding one band

37. Short-Time Synthesis --- Filter Bank Summation h1(n)h1(n) h1(n)h1(n) x(n)x(n) h0(n)h0(n) h0(n)h0(n) hN1(n)hN1(n) hN1(n)hN1(n)...... Analysis Synthesis

38. Short-Time Synthesis --- Filter Bank Summation h1(n)h1(n) h1(n)h1(n) x(n)x(n) h0(n)h0(n) h0(n)h0(n) hN1(n)hN1(n) hN1(n)hN1(n)...... Analysis Synthesis

39. Short-Time Synthesis --- Filter Bank Summation h1(n)h1(n) h1(n)h1(n) x(n)x(n) h0(n)h0(n) h0(n)h0(n) hN1(n)hN1(n) hN1(n)hN1(n)...... Analysis Synthesis

40. Equal Spaced Ideal Filters 11 22 33 44 55 22  1 0 N = 6

41. Equal Spaced Ideal Filters h1(n)h1(n) x(n)x(n) h0(n)h0(n) hN1(n)hN1(n)...... What condition should be satisfied so that y(n)=x(n)?

42. Equal Spaced Ideal Filters Equal spaced sampling of H ( e j  ) Inverse discrete FT of H ( e j  ) Time-Aliased version of h ( n )

43. Equal Spaced Ideal Filters Consider FIR, i.e., h(n) is of duration of L samples. 0 L1L1 n h(n)h(n) In case that N  L,

44. Equal Spaced Ideal Filters

45. h1(n)h1(n) h1(n)h1(n) x(n)x(n) h0(n)h0(n) h0(n)h0(n) hN1(n)hN1(n) hN1(n)hN1(n)...... 0 L1L1 n h(n)h(n) x(n) can always be Reconstructed if N  L,

46. Equal Spaced Ideal Filters h1(n)h1(n) h1(n)h1(n) x(n)x(n) h0(n)h0(n) h0(n)h0(n) hN1(n)hN1(n) hN1(n)hN1(n)...... 0 L1L1 n h(n)h(n) x(n) can always be Reconstructed if N  L, Does x(n) can still be reconstructed if N<L? If affirmative, what condition should be satisfied?

47. Equal Spaced Ideal Filters h1(n)h1(n) h1(n)h1(n) x(n)x(n) h0(n)h0(n) h0(n)h0(n) hN1(n)hN1(n) hN1(n)hN1(n)...... p(n)p(n)

48. p(n)p(n) Signal can be reconstructed If it equals to  ( n  m ).

49. Typical Sequences of h (n) Ideal lowpass filter with cutoff at  /N. 0 NN 2N2N N2N2N3N3N4N4N p(n)p(n) N 0 NN 2N2N N2N2N3N3N4N4N h(n)h(n) 1/N

50. Typical Sequences of h (n) 0 NN 2N2N N2N2N3N3N4N4N p(n)p(n) N 0 NN 2N2N N2N2N3N3N4N4N h(n)h(n) h(0) LL 2L2L L2L2L3L3L4L4L N  LN  L

51. Typical Sequences of h (n) 0 NN 2N2N N2N2N3N3N4N4N p(n)p(n) N 0 NN 2N2N N2N2N3N3N4N4N h(n)h(n) h(0) 1/N A causal FIR lowpass filter

52. Typical Sequences of h (n) 0 NN 2N2N N2N2N3N3N4N4N p(n)p(n) N 0 NN 2N2N N2N2N3N3N4N4N h(n)h(n) h(0) 1/N A causal IIR lowpass filter

53. Filter Back Implementation for a Single Channel hk(n)hk(n) x(n)x(n) h(n)h(n) x(n)x(n) Analysis Synthesis

54. hk(n)hk(n) x(n)x(n) h(n)h(n) x(n)x(n) Filter Back Implementation for a Single Channel R:1 1:R Analysis Synthesis Decimator Interpolator

55. hk(n)hk(n) x(n)x(n) h(n)h(n) x(n)x(n) Filter Back Implementation for a Single Channel R:1 1:R Analysis Synthesis Decimator Interpolator Depends on the bandwidth of h(n). R=?

56. Frequency Domain Coding of Speech Sub-Band Coding

57. Analysis Synthesis Filter Bank Implementation (Direct Implementation)...... h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) x(n)x(n)...... R:1 1:R............ f(n)f(n) f(n)f(n) f(n)f(n) f(n)f(n) f(n)f(n) f(n)f(n) f(n)f(n) f(n)f(n) x(n)x(n) Complex Channels R=2  B Bandwidth B/2

58. Filter Bank Implementation (Practical Implementation) 0 B kk 0 B  k 0 B/2  B/2 0 B/2  B/2 0 BB 0 B 0 BB B

59. Filter Bank Implementation (Practical Implementation)............ h(n)h(n) h(n)h(n) h(n)h(n) h(n)h(n) x(n)x(n)......

60. ...... h(n)h(n) h(n)h(n) x(n)x(n)...... h(n)h(n) h(n)h(n)

61. ...... h(n)h(n) h(n)h(n) x(n)x(n)...... h(n)h(n) h(n)h(n) D:1 Why?

62. Filter Bank Implementation (Practical Implementation)...... h(n)h(n) h(n)h(n) x(n)x(n)...... h(n)h(n) h(n)h(n) D:1

63. ...... h(n)h(n) h(n)h(n) x(n)x(n)...... h(n)h(n) h(n)h(n) Filter Bank Implementation (Practical Implementation)

64. x(n)x(n)...... h(n)h(n) h(n)h(n)...... h(n)h(n) h(n)h(n) D:1 2D:1

65. Filter Bank Implementation (Practical Implementation) ADPCM CODEC...... h(n)h(n) h(n)h(n)...... h(n)h(n) h(n)h(n) 2D:1 f(n)f(n) f(n)f(n)...... f(n)f(n) f(n)f(n)...... Filter Bank Analysis Filter Bank Analysis Sub-Band Coder Modification Sub-Band Coder Modification Filter Bank Synthesis Filter Bank Synthesis