Frequency Domain Coding of Speech

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 • Filter Bank Interpretation • Block Transform Interpretation Interpretations:

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

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

11.   0 Filter Bank Interpretation Modulation

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

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

14. Block Transform Interpretation n is fixed at n0. Analysis Window FT of Windowed Data Windowed Data

15. n1 n2 n3 nr Block Transform Interpretation n is fixed at n0. . . .

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

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

18. Therefore, if Analysis Analysis/Synthesis Equations Synthesis

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

20. Examples

21. Examples h(0)x(n)

22. Examples

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

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

25. Synthesis 1

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

27. Frequency k n 0 Spectrogram Implementation Consideration

28. Frequency k n 0 Spectrogram Sampling R 2R 3R 4R

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

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

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

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

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

34. |H(ej)| |Hk(ej)|   k Short-Time Synthesis --- Filter Bank Summation Lowpass filter Bandpass filter

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

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

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

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

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

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

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

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

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

44. Equal Spaced Ideal Filters

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

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

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

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

49. p(n) N 2N N 0 N 2N 3N 4N h(n) 1/N 2N N 0 N 2N 3N 4N Typical Sequences of h(n) Ideal lowpass filter with cutoff at /N.

50. p(n) N 2N N 0 N 2N 3N 4N h(n) h(0) 2N N 0 N 2N 3N 4N 2L L L 2L 3L 4L Typical Sequences of h(n) N L