2. 1 Speech Enhancement

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6. 5 Wiener Filtering: A linear estimation of clean signal from the noisy signal Using MMSE criterion

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9. 8 Since y and v are zero mean: This is called the time domain Wiener filter

10. 9 We are looking for a frequency-domain Wiener filter, called the non-causal Wiener filter such that: According to the projection theorem, for the error to be minimum, the difference has to be orthogonal to the noisy input

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13. 12 Popular form of Wiener filter

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15. 14 Spectral Subtraction

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20. 19 MAP Speech Enhancement

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24. 23 MMSE Speech Enhancement We try to optimize the function: g(.) is a function on R k and

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27. 26 The computation of Eqn1 is generally difficult. For some specific functions, Eqn1 has been derived. For instance, when g(.) is defined to be: Where is the kth coefficient of the DFT of y t, Eqn1 is equivalent to the popular Wiener filter

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29. 28 Recursive Formula For G:

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41. 40 Automatic Noise Type Selection

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44. 43 Nonstationary State HMM

45. 44 Nonstationary-State HMM

46. 45 Segmentation Algorithm in NS-HMM

47. 46 Segmentation Algorithm in NS-HMM

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50. 49 Now we generalize MMSE formulae for NS-HMM

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